Collected Papers of Carl Wieman

The following sections are included:

• CONTENTS

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We have observed the 1S-2S transition in atomic hydrogen and deuterium by Doppler-free two-photon spectroscopy, using a frequency-doubled pulsed dye laser at 2430 Å. Simultaneous recording of the absorption spectrum of the Balmer-β line at 4860 Å, using the fundamental dye-laser output, allowed us to precisely compare the energy intervals 1S-2S and 2S,P-4S,P,D and to determine the Lamb shift of the 1S ground state to be 8.3±0.3 GHz (D) and 8.6±0.8 GHz (H).

We have demonstrated a sensitive new method of Doppler-free spectroscopy, monitoring the nonlinear interaction of two monochromatic laser beams in an absorbing gas via changes in light polarization. The signal-to-background ratio can greatly surpass that of saturated absorption. Polarization spectra of the hydrogen Balmer-β line, recorded with a cw dye laser, reveal the Stark splitting of single fine-structure components in a Wood discharge.

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A precision measurement of the 1S Lamb shift of atomic hydrogen and deuterium, using high-resolution laser spectroscopy is reported. The 1S-2S transition was observed by Doppler-free two-photon spectroscopy, using a single-frequency cw dye laser near 4860 Å with a nitrogen-pumped pulsed dye amplifier and a lithium formate frequency doubler. The n = 2–4 Balmer-β line was simultaneously recorded with the fundamental cw dye-laser output in a low-pressure glow discharge, using sensitive laser polarization spectroscopy. From a comparison of the two energy intervals a ground-state Lamb shift of 8151 ± 30 MHz has been determined for hydrogen and 8177 ± 30 MHz for deuterium, in agreement with theory. The same experiments yield a tenfold improved value of the 1S-2S isotope shift 670992.3 ± 6.3 MHz and provide the first experimental confirmation of the rclativistic nuclear recoil contribution to hydrogenic energy levels.

We present a new method for locking the frequency of a laser to a reference-interferometer cavity. For a non-mode-matched input beam, the light reflected off a cavity contains an interference between the wave fronts corresponding to the various cavity modes. A detector placed at the proper position on the interference pattern provides a signal proportional to the imaginary component of the reflected field. As a function of laser frequency, this signal is dispersion shaped and can be used as the error signal for electronic frequency stabilization.

The hyperfine structure of the 7S_1/2 state of ¹³³Cs has been measured with the use of laser spectroscopy on a cesium atomic beam. We find the magnetic dipole coupling constant A = 545.90(09) MHz. From the amplitude of the hyperfine components we find the ratio of the scalar to tensor polarizabilities (| α/ β|) for the 6S → 7S transition to be 9.80(12).

We have measured the Stark shift of the 6S-7S transition in a beam of atomic cesium with the use of laser spectroscopy. We find this shift to be 0.7103(24) Hz (V/cm) ⁻². From this value we determine the static polarizability of the 7S state, α_7S = [6111 (21)] α₀³, and the 7P-7S oscillator strength, f_7P,7S = 1.540(7). Finally, we derive a new empirical value for the 6S-7S Stark-induced electric dipole transition probability.

The forbidden 6S→7S magnetic dipole transition amplitude in cesium has been measured by laser spectroscopy of an atomic beam in crossed electric and weak magnetic fields. The M1 amplitude was determined by observing the change in the transition rate caused by interference with a Stark-induced E1 amplitude. The result for the nuclear-spin-independent amplitude is −42.10(80) × 10⁻⁶ μ_B; the result for the nuclear-spin-dependent amplitude is 7.59(55) × 10⁻⁶ μ_B. These values disagree with earlier measurements but they are in good agreement with theory. The experimental approach is well suited to measuring parity-violating neutral-current interactions.

We report the first measurement of the absolute cross section for photoionization of the 7S state of cesium. The measurement employed a new technique in which the density of the excited-state atoms was determined by the amount of fluorescence. The cross section for photoionization by 540-nm light is 1.14(10) × 10^{− 19}cm². We also propose a second new technique for the absolute measurement of photoionization cross sections which is based on modulated fluorescence.

A new measurement of parity nonconservation in cesium is reported. The experimental technique involves measurement of the 6S → 7S transition rate by use of crossed atomic and laser beams in a region of perpendicular electric and magnetic fields. Our results are ImE _PNC/β = −1.65 ± 0.13 mV/cm and C_2p = −2 ± 2. These results are in agreement with previous measurements in cesium and the predictions of the electroweak standard model. This experimental technique will allow future measurements of significantly higher precision.

We have produced a cesium beam of 10¹⁴ atoms s⁻¹ with more than 98% of the atoms in a single spin state. The beam was polarized by optically pumping it with a single laser diode whose frequency was switched between the 6s (F = 4)−6p_3/2(F = 5) and 6s(F = 3)−6p_3/2 (F = 4) transitions at 100 kHz. To do this, it was necessary to determine the frequency modulation characteristics of the laser. The same laser was used to simultaneously probe the atomic population distribution. We find this to be a remarkably simple and inexpensive way to produce a highly spin polarized beam.

We present a new measurement of parity nonconservation in cesium. In this experiment, a laser excited the 6S → 7S transition in an atomic beam in a region of static electric and magnetic fields. The quantity measured was the component of the transition rate arising from the interference between the parity nonconserving amplitude, 𝒞_PNC, and the Stark amplitude, βE. Our results are Im𝒞_PNC/β = − 1.65±0.13 mV/cm and C_2p= −2 ± 2, where C_2p is the proton-axial-vector–electron-vector neutral-current coupling constant. These results are in agreement with previous less precise measurements in cesium and with the predictions of the electroweak standard model. We give a detailed discussion of the experiment with particular emphasis on the treatment and elimination of systematic errors. This experimental technique will allow future measurements of significantly higher precision.

We have measured the hyperfine mixing of the 6S and 7S states of cesium using a new high-precision experimental technique. By comparing the diagonal and off-diagonal hyperfine interaction for these states, we find that a single-particle description of the states is accurate to better than 2%.

We have observed the resonance line shape for a very weak atomic transition excited when an atomic beam intersects a strong standing-wave laser field. The line shape has a dramatic intensity-dependent distortion which is Doppler free and independent of the excitation rate. We have calculated the line shape predicted by optical Bloch equations that include a spatially varying ac Stark shift, and find good agreement with our experimental results.

We employ crossed-beam laser spectroscopy with a frequency-stabilized laser diode to measure the Stark shift of the 6P_3/2 state relative to the ground state of atomic cesium. The scalar and tensor polarizabilities are determined from the measured Stark shifts in the transitions 6S_1/2 F=4→6P_3/2 F′=5, M_F=5 and 4. Our results are and .

We report measurements of the hyperfine structure of the 6P_3/2 state of atomic ¹³³Cs(I = 7/2). A frequency-stabilized laser diode is used to perform crossed-beam laser spectroscopy of the Cs 6S_1/2(F = 3,4)) 6P_3/2 (F′) transitions. From the measured hyperfine splittings, we determine the coefficients of the magnetic dipole (A) and electric quadrupole (B) contributions to the hyperfine structure. Our results are A = 50.273(3) MHz and B = −0.53(2) MHz.

We have made an improved measurement of the parity-nonconserving electric-dipole transition amplitude between the 6S and 7S states of atomic cesium. We obtain Im(E_PNC)/β= −1.576(34) mV/cm. which is in good agreement with the predictions of the standard model and earlier less precise measurements. This places more stringent constraints on alternatives to the standard model. We also see the first evidence of a nuclear-spin–dependent contribution to atomic parity nonconservation. The nuclear spin dependence observed is in agreement with that predicted to arise from a nuclear anapole moment.

We describe a cesium atomic beam (10¹⁴ atoms s^{− 1}, 6× 10¹⁶ atoms sr⁻¹ s⁻¹) spin polarized using light from two diode lasers. Of the atoms, 95% may be placed into either the 6S_1/2 (F,m_F) = (3,3) or (4,4) state, with less than 2 × 10⁻⁴ of the atoms left in the depleted hyperfine level. The latter fraction rises linearly with atomic beam intensity because of reabsorption of light scattered during the optical pumping process. This and other effects limiting complete hyperfine pumping are discussed.

Parity nonconservation has now been measured in atomic cesium with a fractional uncertainty of 2%. This was done by observing the 6S-7S laser excited transition rate in a “handed” apparatus. When combined with recent precise calculations of the cesium atomic structure, this provides an important test of the Standard Model. Efforts are under way to achieve a more sensitive test by measuring parity nonconservation in a series of radioactive cesium isotopes which have been trapped using laser light.

The following sections are included:

• Introduction

• PNC Neutral Currents in Atoms

• Experimental Approaches

• Design Concepts of Colorado Experiments

• Details of Apparatus
  • Signal and Noise Analysis
  • Atomic Beam
  • Laser Power Buildup
  • Detection
  • Technical Noise
  • Servo Systems
  • Field Reversals and Signal Processing

• Systematic Errors

• Implications

• Future Improvements
  • Near Term
  • Long Term

Time-correlated single-photon counting is used to measure the lifetimes of the 6p ²P_1/2 and 6p ²P_3/2 levels in atomic Cs with accuracies ≈ 0.2–0.3 %. A high-repetition-rate, femtosecond, self-mode-locked Ti:sapphire laser is used to excite Cs produced in a well-collimated atomic beam. The time interval between the excitation pulse and the arrival of a fluorescence photon is measured repetitively until the desired statistics are obtained. The lifetime results are 34.75(7) and 30.41(10) ns for the 6p ²P_1/2 and 6p²P_3/2 levels, respectively. These lifetimes fall between those extracted from ab initio many-body perturbation-theory calculations by Blundell, Johnson, and Sapirstein [Phys. Rev. A 43, 3407 (1991)] and V. A. Dzuba et al. [Phys. Lett. A 142, 373 (1989)] and are in all cases within 0.9% of the calculated values. The measurement errors are dominated by systematic effects, and methods to alleviate these and to approach an accuracy of 0.1% are discussed. The technique is a viable alternative to the fast-beam laser approach for measuring lifetimes with extreme accuracy.

The ratio of scalar to tensor transition polarizabilities (α/β) for the cesium 6S_1/2F=3 to 7S_1/2F′ = 3 transition has been measured using a spin-polarized atomic beam and an interference technique. We use an electric- and magnetic-field configuration where the Stark-induced electric dipole transition amplitudes arising from the scalar and tensor polarizabilities interfere. giving rise to large changes in the 6S-7S transition rate. The measured ratio is α/β=−9.905±0.011. This result represents a tenfold improvement in precision, and agrees well with previous measurements and calculations. The ratio α/β is of critical importance for cesium atomic parity violation experiments. [Sl050-2947(97)08202-4]

The amplitude of the parity-nonconserving transition between the 6S and 7S states of cesium was precisely measured with the use of a spin-polarized atomic beam. This measurement gives Im(E1_pnc)/β = −1.5935(56) millivolts per centimeter and provides an improved test of the standard model at low energy, including a value for the S parameter of −1.3(3)_exp(11)_theory. The nuclear spin–dependent contribution was 0.077(11) millivolts per centimeter; this contribution is a manifestation of parity violation in atomic nuclei and is a measurement of the long-sought anapole moment.

We have measured the dc Stark shift of the 6S→7S transition in atomic cesium using laser spectroscopy. The result of our experiment is 0.7262(8) Hz (V/cm)⁻². This value disagrees with a previous experiment but is within 0.3% of the value predicted by ab initio calculations. This measurement removes the largest outstanding disagreement between experiment and ab initio theory of low-lying states in atomic cesium. [S1050-2947(99)51101-3]

The ratio of the off-diagonal hyperfine amplitude to the tensor transition polarizability (M_hf/β) for the 6S → 7S transition in cesium has been measured. The value of is then obtained using an accurate semiempirical value of M_hf. This is combined with a previous measurement of parity nonconservation in atomic cesium and previous atomic structure calculations to determine the value of the weak charge. The uncertainties in the atomic structure calculations are updated (and reduced) in light of new experimental tests. The result Q_W = −72.06(28)_expt(34)_theor differs from the prediction of the standard model of elementary particle physics by 2.5σ. [S0031-9007(99)08690-1]

Anapole moments are parity-odd, time-reversal-even moments of the E1 projection of the electromagnetic current. Although it was recognized, soon after the discovery of parity violation in the weak interaction, that elementary particles and composite systems such as nuclei must have anapole moments, it proved difficult to isolate this weak radiative correction. The first successful measurement, an extraction of the nuclear anapole moment of ¹³³Cs from the hyperfine dependence of the atomic parity violation, was obtained only recently. An important anapole moment bound in thallium also exists. We discuss these measurements and their significance as tests of the hadronic weak interaction, focusing on the mechanisms that operate within the nucleus to generate the anapole moment. The atomic results place new constraints on weak meson-nucleon couplings, constraints we compare to existing bounds from a variety of and nuclear tests of parity nonconservation.

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We have used counterpropagating radiation from a diode laser to cool and stop a beam of cesium atoms. The laser frequency was chirped to keep it in resonance with the slowing atoms. The same laser was used to probe the resulting velocity distributions. We have cooled more than 10¹⁰ atoms/sec to a temperature of 1 K. This is an extremely simple and inexpensive way to manipulate atomic velocities and has a wide range of possible applications.

We show that the optical Earnshaw theorem does not always apply to atoms and that it is possible to confine atoms by spontaneous light forces produced by static laser beams. A necessary condition for such traps is that the atomic transition rate cannot depend only on the light intensity. We give several general approaches by which this condition can be met and present a number of specific trap designs illustrating these approaches. These traps have depths on the order of a kelvin and volumes of several cubic centimeters.

We have demonstrated a self-locking power-buildup cavity for laser diodes. This device requires only a few simple optical elements and can provide a standing wave containing as much as 1000 times the power emitted by the laser diode. With this device we have obtained an intense standing wave of tunable light that was used to collimate a cesium atomic beam. We have studied the power and frequency dependence of the beam collimation.

We have used the light from diode lasers (λ = 852 nm) to damp the motion of atoms in a cesium vapor. We have been able to contain more than 10⁷ atoms for 0.2 sec and cool them to a temperature of in this viscous photon medium (the so-called optical molasses).

We have used the light from diode lasers to produce a nearly stationary (υ ~ 15 cm/sec) sample of atomic cesium in optical molasses that is entirely in the F = 3 hyperfine state. In this sample we excite the 9.2-GHz6S F = 3, m = 0 to F = 4, m = 0 clock transition. Most of the atoms remain for ~20 msec in the 0.4-cm³ observation region. We observe that transitions take place by monitoring the fluorescence when the atoms are illuminated with light tuned to the 6S F = 4 to 6P_3/2 F = 5 transition. Rabi resonance linewidths of less than 50 Hz are obtained.

We have studied the collisional loss rates for very cold cesium atoms held in a spontaneous-force optical trap. In contrast with previous work, we find that collisions involving excitation by the trapping light fields are the dominant loss mechanism. We also find that hyperfine-changing collisions between atoms in the ground state can be significant under some circumstances.

We describe experiments that show collective behavior in clouds of optically trapped neutral atoms. This collective behavior is demonstrated in a variety of observed spatial distributions with abrupt bistable transitions between them. These distributions include stable rings of atoms around a small core and clumps of atoms rotating about the core. The size of the cloud grows rapidly as more atoms are loaded into it, implying a strong long-range repulsive force between the atoms. We show that a force arising from radiation trapping can explain much of this behavior.

A classical collective behavior is observed in the spatial distributions of a cloud of optically trapped neutral atoms. They include extended uniform-density ellipsoids, rings of atoms around a small central ball, and clumps of atoms orbiting a central core. The distributions depend sensitively on the number of atoms and the alignment of the laser beams. Abrupt bistable transitions between different distributions are seen. This system is studied in detail, and much of this behavior can be explained by the incorporation of long-range interactions between the atoms in the equation of equilibrium. It is shown how attenuation and multiple scattering of the incident photons lead to these interactions.

We have produced a very cold sample of spin-polarized trapped atoms. The technique used dramatically simplifies the production of laser-cooled atoms. In this experiment, 1.8×10⁷ neutral cesium atoms were optically captured directly from a low-pressure vapor in in small glass cell. We then cooled the < 1-mm³ cloud of trapped atoms and loaded it into a low-field magnetic trap in the same cell. The magnetically trapped atoms had an effective temperature as low as 1.1 ± 0.2 µK, which is the lowest kinetic temperature ever observed and far colder than any previous sample of trapped atoms.

Cesium atoms in a vapor cell have been trapped and cooled by using light from laser diodes. The 6S F = 4, m = 0 → 6S F = 3, m = 0 hyperfine clock transition was excited as these atoms then fell 2.5 cm in darkness. We observed a linewidth of 8 Hz with good signal-to-noise ratio. This gave a short-term fractional frequency resolution of , and there is potential for substantial improvement. The apparatus is extremely simple and compact, consisting of a small cesium vapor cell and two diode lasers.

We have demonstrated an oscillating-gradient magnetic trap for confining cesium atoms in the lowest-energy spin state. In this state spin-flip collisions are energetically forbidden and thus the primary density- and temperature-limiting process for magnetic traps is eliminated. The atoms are initially collected in a vapor-cell optical trap, then repetitively tossed into a high-vacuum region, focused in three dimensions, and accumulated in the magnetic trap. An optical pumping scheme inserts each new batch of atoms into the magnetic trap without perturbing the atoms already trapped.

We discuss two experiments which appear feasible because of the progress in laser trapping and cooling of neutral atoms. First, using laser trapping, it should be possible trap a number of radioactive isotopes of cesium and francium. Precise measurements of parity nonconservation could be carried out in these samples. The comparison of the these measurements would be a very sensitive probe for physics beyond the Standard model. In the second experiment we are attempting to achieve Bose-Einstein condensation in a dilute cesium vapor. This involves optically trapping and cooling atoms, and then transporting them into a new type of magnetic trap. This trap avoids the spin-flip-changing collisions which have limited earlier attempts to reach Bose condensation.

We present an experimental study of the number and density of trapped atoms in a vapor-cell Zeeman optical trap. We have investigated how the number (and therefore the capture rate) and density change with the trapping laser's beam diameter, intensity, and detuning and with the magnetic-field gradient of the trap. We have developed a quasi-one-dimensional numerical model that accurately predicts the number of trapped atoms for all conditions. We also have investigated chirping the laser frequency and trapping with broadband light, neither of which increase the number of trapped atoms.

The following sections are included:

• INTRODUCTION

• THE ZEEMAN-SHIFT OPTICAL TRAP

• THE VAPOR CELL TRAP

• THE dc MAGNETIC TRAP

• THE ac MAGNETIC TRAP

• EVAPORATIVE COOLING AND ADIABATIC COMPRESSION: THE FINISH LINE

• CONCLUSION

• REFERENCES

We have measured the elastic collision cross section for spin polarized atomic cesium. Neutral cesium atoms are optically cooled, then loaded into a dc magnetic trap. We infer the scattering rate from the rate at which anisotropies in the initial energy distribution are observed to relax. The cross section for F = 3, m_F = − 3 on F = 3, m_F = − 3 is 1.5(4) × 10⁻¹² cm², and is independent of temperature from 30 to 250 μK, This determination clarifies the technical requirements for attaining Bose-Einstein condensation in a magnetically trapped Cs vapor. We also study heating due to glancing collisions with 300 K background Cs atoms.

We demonstrate direct microwave modulation of diode lasers operated with optical feedback from a diffraction grating. We obtain substantial fractions of the laser power (2–30%) in a single sideband at frequencies as high as 6.8 GHz with 20 mW of microwave power and simple inefficient microwave coupling. Using a single diode laser modulated at 6.6 GHz, we trapped ⁸⁷Rb atoms in a vapor cell. With only 10 mW of microwave power we trapped 85% as many atoms as were obtained by using two lasers in the conventional manner.

• LASER COOLING

• NEUTRAL ATOM TRAPPING

• A BRIEF HISTORY

• SIMPLER SYSTEMS

• APPLICATIONS TO FREQUENCY AND WAVELENGTH STANDARDS

• APPLICATIONS TO BASIC PHYSICS

• ACKNOWLEDGEMENTS

• REFERENCES

We present techniques for the most efficient capture of atoms in a modified vaporcell magneto-optical trap. We explain how changing the size and power of the trapping beams affects the capture rate of the trap. We calculate the requirement of wall coatings designed to minimize the interaction of an alkali vapor with the wall and explain how this affects trapping efficiency. Finally, we present measurements of the performance of a “Dryfilm” coated cell.

We present the results of the first study of the fundamental processes governing collection efficiency of neutral atoms in a vapor cell laser trap. The experimental test of our model of the collection process closely agrees with our predictions based on the measured properties of the laser beams and cell. This study has led to the development of special vapor cell wall coatings. We have demonstrated a collection efficiency of 6% for cesium and predict more than 50% could be achieved under optimum conditions. This work develops the concepts for and demonstrates the feasibility of new experiments using shortlived radioactive isotopes.

Efficient collection of atoms into a vapor-cell laser trap requires a special wall material for the cell that minimizes the interactions between the vapor and the wall. Tests of several different wall coatings and materials are reported, and measurements of adsorption energies, outgassing, and chemical reaction rates between the alkali vapor and the walls are described. It is demonstrated that each of these parameters affects the collection efficiency.

We present detailed instructions for the construction and operation of an inexpensive apparatus for laser cooling and trapping of rubidium atoms. This apparatus allows one to use the light from low power diode lasers to produce a magneto-optical trap in a low pressure vapor cell. We present a design which has reduced the cost to less than $3000 and does not require any machining or glassblowing skills in the construction. It has the additional virtues that the alignment of the trapping laser beams is very easy, and the rubidium pressure is conveniently and rapidly controlled. These features make the trap simple and reliable to operate, and the trapped atoms can be easily seen and studied. With a few milliwatts of laser power we are able to trap 4×10⁷ atoms for 3.5 s in this apparatus. A step-by-step procedure is given for construction of the cell, setup of the optical system, and operation of the trap. A list of parts with prices and vendors is given in the Appendix. © 1995 American Association of Physics Teachers.

We describe a method for cooling magnetically trapped ⁸⁷Rb atoms by irreversibly cycling the atoms between two trapped states. The cooling force is proportional to gravity. The atoms are cooled to 1.5 μK in the vertical dimension. We have extended this cooling method to two dimensions through anharmonic mixing, achieving a factor of 25 increase in the phase space density over an uncooled sample. This cooling method should be an important intermediate step toward achieving a Bose-Einstein condensate of Rb atoms.

We have measured the elastic-scattering cross section of ⁸⁷Rb atoms in the |F = 1, m_F. = − 1〉 ground state at 25 μK. The cross section is almost purely s wave at these temperatures and has a value of (5.4 ± 1.3) × 10⁻¹² cm². We have searched for the predicted Feshbach-type resonances in the elastic cross section [Ticsinga et al., Phys. Rev. A 46, 1167 (1992)] as a function of magnetic field. There are no resonances with a magnetic-field width ≥ 2 G over a magnetic-field range of 15–540 G.

We have used optical forces to guide atoms through hollow-core optical fibers. Laser light is launched into the hollow region of a glass capillary fiber and guided by grazing-incidence reflection from the walls. When the laser is detuned 1–30 GHz red of the Rb D₂ resonance lines, dipole forces attract atoms to the high-intensity region along the axis and guide them through the fiber. We show that atoms may be guided around bends in the fiber and that in initial experiments the atoms experience up to 18 reflections from the potential walls with minimal loss.

We report a two-chambered, differentially pumped system that permits rapid collection of trapped atoms with a vapor cell magneto-optical trap (MOT) and efficient transfer of these atoms to a second MOT in a lower-pressure chamber. During the transfer the atoms are guided down a long, thin tube by a magnetic potential, with 90(15%) transfer efficiency. By multiply loading, we accumulate and hold as many as 30 times the number collected by the vapor cell MOT. By thus separating the collection and holding functions of a MOT, we can collect as many as 1.5(0.6) × 10¹⁰ rubidium atoms and hold them for longer than 100 s, using inexpensive low-power diode lasers.

This Resource Letter provides a guide to the literature on trapping of neutral atoms.

We use evanescent laser light to guide atoms through hollow-core optical fibers. The light detuned to the blue side of rubidium's D₂ resonance lines, is launched into the glass region of a hollow capillary fiber and guided through the fiber by total internal reflection from the glass walls. Atoms interacting with the evanescent component of the field are repelled from the wall and guided through the fiber hollow. A second laser tuned to the red side of resonance is used to initially inject the atoms into the evanescent guide. An optical intensity threshold for guiding is observed as the evanescent-field-induced dipole forces exceed the van der Waals forces

We have produced and characterized an intense, slow, and highly collimated atomic beam extracted from a standard vapor cell magneto-optical trap (MOT). The technique used is dramatically simpler than previous methods for producing very cold atomic beams. We have created a 0.6 mm diameter rubidium atomic beam with a continuous flux of 5 × 10⁹/s and a pulsed flux 10 times greater. Its longitudinal velocity distribution is centered at 14 m/s with a FWHM of 2.7 m/s. Through an efficient recycling process, 70% of the atoms trapped in the MOT are loaded into the atomic beam. [S0031-9007(96)01434-2]

We have efficiently loaded a vapor cell magneto-optical trap from an orthotropic source of ²²¹Fr with a trapping efficiency of 56(10)%. A novel detection scheme allowed us to measure 900 trapped atoms with a signal to noise ratio of ~60 in 1 sec. We have measured the energies and the hyperfine constants of the 7²P_1/2 and 7²P_3/2 states. [S003 1-9007(97)03811-8]

The behavior of atoms in an optical far-off resonance trap is found to depend strongly on the trap polarization. Large loss rates occur unless the polarization is perfectly linear or perfectly circular, in which case exponential lifetimes up to 10 s are observed. Through optimization of trap loading, samples of 4 × 10⁶ atoms are obtained in a circularly polarized trap. Spin polarization of 98(1)% is measured. This trap should prove useful for precision measurements such as β-decay asymmetry and should make rf cooling possible in optical traps.

We present a detailed experimental study of the physics involved in transferring atoms from a magneto-optical trap (MOT) to an optical dipole trap. The loading is a dynamical process determined by a loading rate and a density dependent loss rate. The loading rate depends on cooling and the flux of atoms into the trapping volume, and the loss rate is due to excited slate collisions induced by the MOT light fields. From this study we found ways to optimize the loading of the optical dipole trap. Key ingredients, for maximum loading are found to be a reduction of the hyperfine repump intensity, increased detuning of the MOT light, and a displacement or the optical dipole trap center with respect to the MOT. A factor of 2 increase in the number of loaded atoms is demonstrated by using a hyperfine repump beam with a shadow n it. In this way we load 8 × 10^{6 85}Rb atoms into a 1 mK deep optical dipole trap with a worst of 58 μm, which is 40% of the atoms initially trapped in the MOT.

We investigate two-body loss in an optical dipole trap for ⁸⁷Rb atoms. In the presence of additional near-resonant light, such as from a magneto-optical trap during the trap loading, the two-body loss is strongly enhanced by long-range radiative escape. We suppressed this loss by a factor of 15 by adding a sideband to the optical dipole trap laser. This allows more atoms to be loaded into the optical dipole trap.

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A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 × 10¹² per cubic centimeter and could be preserved for more than 15 seconds. Three primary signatures of Bose–Einstein condensation were seen. (i) On top of a broad thermal velocity distribution, a narrow peak appeared that was centered at zero velocity. (ii) The fraction of the atoms that were in this low-velocity peak increased abruptly as the sample temperature was lowered. (iii) The peak exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.

We observe phononlike excitations of a Bose-Einstein condensate (BEC) in a dilute atomic gas. ⁸⁷Rb atoms are optically trapped and precooled, loaded into a magnetic trap, and then evaporatively cooled through the BEC phase transition to form a condensate. We excite the condensate by applying an inhomogeneous oscillatory force with adjustable frequency and symmetry. We have observed modes with different angular momenta and different energies and have studied how their characteristics depend on interaction energy. We find that the condensate excitations persist longer than their counterparts in uncondensed clouds. [S0031-9007(96)00722-3]

We measure the ground-state occupation and energy of a dilute Bose gas of ⁸⁷Rb atoms as a function of temperature. The ground-state fraction shows good agreement with the predictions for an ideal Bose gas in a 3D harmonic potential. The measured transition temperature is 0.94(5)T_o, where T_o, is the value for a noninteracting gas in the thermodynamic limit. We determine the energy from a model independent analysis of the velocity distribution, after ballistic expansion, of the atom cloud. We observe a distinct change in slope of the energy-temperature curve near the transition, which indicates a sharp feature in the specific heat. [S0031-9007(96)01891-1]

The following article is a written version of the Richtmyer award lecture given to the annual meeting of the American Association of Physics Teachers in January, 1996. I discuss the basic idea of Bose-Einstein condensation in a gas and how it has been produced and examined. To cool the atom to the point of condensation we use laser cooling and trapping, followed by magnetic trapping and evaporative cooling. These techniques are explained, along with the signatures of Bose-Einstein condensation that we observe. I also discuss how very similar laser cooling and trapping techniques have been incorporated into undergraduate laboratory experiments.

A new apparatus featuring a double magneto-optic trap and an Ioffe-type magnetic trap was used to create condensates of 2 × 10⁶ atoms in either of the |F = 2, m = 2〉 spin states of ⁸⁷Rb. Overlapping condensates of the two states were also created using nearly lossless sympathetic cooling of one state via thermal contact with the other evaporatively cooled state. We observed that (i) the scattering length of the |1, −1〉 state is positive, (ii) the rate constant for binary inelastic collisions between the two states is 2.2(9) × 10⁻¹⁴cm³/s, and (iii) there is a repulsive interaction between the two condensates. Similarities and differences between the behaviors of the two spin states are observed. [S0031-9007(96)02208-9]

We extend to finite temperature the study of collective excitations of a Bose-Einstein condensate in a dilute gas of ⁸⁷Rb. Measurements of two modes with different angular momenta show unexpected temperature-dependent frequency shifts, with very different behavior for the two symmetries; in addition there is a sharp feature in the temperature dependence of one mode. The damping of these excitations exhibits dramatic temperature dependence, with condensate modes at temperatures near the transition damping even faster than analogous noncondensate oscillations. [S0031-9007(96)02283-1]

We have used three-body recombination rates as a sensitive probe of the statistical correlations between atoms in Bose-Einstein condensates (BEC) and in ultracold noncondensed dilute atomic gases. We infer that density fluctuations are suppressed in the BEC samples. We measured the three-body recombination rate constants for condensates and cold noncondensates from number loss in the F = 1, m_f = −1 hyperfine state of ⁸⁷Rb. The ratio of these is 7.4(2.6) which agrees with the theoretical factor of 3! and demonstrates that condensate atoms are less bunched than noncondensate atoms. [S0031-9007(97)03611-9]

We investigate the possibility of obtaining Bose-Einstein condensation (BEC) in a steady state by continuously loading atoms into a magnetic trap while keeping the frequency of the radio frequency field fixed. A steady state is obtained when the gain of atoms due to loading is balanced with the three dominant loss mechanisms due to elastic collisions with hot atoms from the background gas, inelastic three-body collisions, and evaporation. We describe our model of this system and present results of calculations of the peak phase-space density ρ₀ in order to investigate the conditions under which one can reach the regime ρ₀ ≥ 2.612 and attain BEC in steady state. [S1050-2947(98)05503-6]

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We describe the first experiments that study in a controlled way the dynamics of distinguishable and interpenetrating bosonic quantum fluids. We work with a two-component system of Bose-Einstein condensates in the |F = 1, m_f = −1〉 and |2, 1〉 spin states of ⁸⁷Rb. The two condensates are created with complete spatial overlap, and in subsequent evolution they undergo complex relative motions that tend to preserve the total density profile. The motions quickly damp out, leaving the condensates in a steady state with a non-negligible (and adjustable) overlap region.

We have measured the relative phase of two Bose-Einstein condensates using a time-domain, separated-oscillatory-field condensate interferometer. A single two-photon coupling pulse prepares the double-condensate system with a well-defined relative phase; at a later time, a second pulse reads out the phase difference accumulated between the two condensates. We find that the accumulated phase difference reproduces from realization to realization of the experiment, even after the individual components have separated spatially and their relative center-of-mass motion has damped. [S0031-9007(98)06973-7]

A two-photon transition is used to convert an arbitrary fraction of the ⁸⁷Rb atoms in a |F = 1, m_f = −1〉 condensate to the |F = 2, m_f = 1〉 state. Transferring the entire population imposes a discontinuous change on the condensate's mean-field repulsion, which leaves a residual ringing in the condensate width. A calculation based on Gross-Pitaevskii theory agrees well with the observed behavior, and from the comparison we obtain the ratio of the intraspecies scattering lengths for the two states, a_|1,−1〉/a_|2,1〉 = 1.062(12). [S0031-9007(98)06574-0]

A magnetic field-dependent Feshbach resonance has been observed in the elastic scattering collision rate between atom in the F = 2, M = −2 state of ⁸⁵Rb. Changing the magnetic field by several Gauss caused the collision rate to vary by a Factor of 10⁴, and the sign of the scattering length could be reversed. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction potential: The van der Waals coefficient C₆, the singlet scattering length a_S, and the triplet scattering length a_T. [S0031-9007(98)07904-6]

The following sections are included:

• Introduction

• History

• Survey of BEC technology, present and future

• Effects of interactions

• Excitations

• Condensates and quantum phase

• Stray heating: a pessimistic note

• Collisions and evaporation: an optimistic note

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of ⁸⁷Rb.

We have created vortices in two-component Bose-Einstein condensates. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using an interference technique, we map the phase of the vortex state to confirm that it possesses angular momentum. We can create vortices in either of the two components and have observed differences in the dynamics and stability.

Bose-Einstein condensation has been achieved in a magnetically trapped sample of ⁸⁵Rb atoms. Longlived condensates of up to 10⁴ atoms have been produced by using a magnetic-field-induced Feshbach resonance to reverse the sign of the scattering length. This system provides new opportunities for the study of condensate physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a wide range, extending from strong repulsive to large attractive interactions. When the interactions were switched from repulsive to attractive, the condensate shrank to below our resolution limit, and after ~5 ms emitted a burst of high-energy atoms.

We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of ⁸⁷Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value of the healing length. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the procession frequency of the vortex core about the condensate axis changes by only a factor of 2.

Inelastic collision rates for ultracold ⁸⁵Rb atoms in the F = 2, m_f = −2 state have been measured as a function of magnetic field. At 250 gauss (G), the two- and three-body loss rates were measured to be K₂= (1.87 ± 0.95 ± 0.19) × 10⁻¹⁴ cm³/s and . respectively. As the magnetic field is decreased from 250 G towards a Feshbach resonance at 155 G. the inelastic rates decrease to a minimum and then increase dramatically, peaking at the Feshbach resonance. Both two- and three-body losses are important, and individual contributions have been compared with theory.

The point of instability of a Bose-Einstein condensate (BEC) due to attractive interactions was studied. Stable ⁸⁵Rb BECs were created and then caused to collapse by slowly changing the atom-atom interaction from repulsive to attractive using a Feshbach resonance. At a critical value, an abrupt transition was observed in which atoms were ejected from the condensate. By measuring the onset of this transition as a function of number and attractive interaction strength, we determined the stability condition to be , slightly lower than the predicted value of 0.574.

We report extensions and corrections to the measurement of the Feshbaeh resonance in ⁸⁵Rb cold atom collisions reported earlier [J. L. Roberts el al., Phys. Rev. Lett. 81, 5109 (1998)]. In addition to a better determination of the position of the resonance peak 154.9(4) Gl and its width [11.0(4) G], improvements in our techniques now allow the measurement of the absolute size of the classic-scattering rate. This provides a measure of the, s-wave scattering length as a function of magnetic field near the Feshbaeh resonance and constrains the Rb-Rb interaction potential.

When atoms in a gas are cooled to extremely low temperatures, they will—under the appropriate conditions—condense into a single quantum-mechanical state known as a Bose–Einstein condensate. In such systems, quantum-mechanical behaviour is evident on a macroscopic scale. Here we explore the dynamics of how a Bose–Einstein condensate collapses and subsequently explodes when the balance of forces governing its size and shape is suddenly altered. A condensate's equilibrium size and shape is strongly affected by the interatomic interactions. Our ability to induce a collapse by switching the interactions from repulsive to attractive by tuning an externally applied magnetic field yields detailed information on the violent collapse process. We observe anisotropic atom bursts that explode from the condensate, atoms leaving the condensate in undetected forms, spikes appearing in the condensate wave function and oscillating remnant condensates that survive the collapse. All these processes have curious dependences on time, on the strength of the interaction and on the number of condensate atoms. Although the system would seem to be simple and well characterized, our measurements reveal many phenomena that challenge theoretical models.

An initially stable ⁸⁵Rb Bose-Einstein condensate (BEC) was subjected to a carefully controlled magnetic field pulse near a Feshbach resonance. This pulse probed the strongly interacting regime for the BEC, with the diluteness parameter (na³) ranging from 0.01 to 0.5. Condensate number loss resulted from the pulse, and for triangular pulses shorter than 1 ms, decreasing the pulse length actually increased the loss, until very short time scales (~10 µs) were reached. The observed time dependence is very different from that expected in traditional inelastic loss processes, suggesting the presence of new microscopic BEC physics.

Recent advances in the precise control of ultracold atomic systems have led to the realisation of Bose–Einstein condensates (BECs) and degenerate Fermi gases. An important challenge is to extend this level of control to more complicated molecular systems. One route for producing ultracold molecules is to form them from the atoms in a BEC. For example, a two-photon stimulated Raman transition in a ⁸⁷Rb BEC has been used to produce ⁸⁷Rb₂ molecules in a single rotational-vibrational state¹, and ultracold molecules have also been formed² through photo-association of a sodium BEC. Although the coherence properties of such systems have not hitherto been probed, the prospect of creating a superposition of atomic and molecular condensates has initiated much theoretical work^3–7. Here we make use of a time-varying magnetic field near a Feshbach resonance^8–12 to produce coherent coupling between atoms and molecules in a ⁸⁵Rb BEC. A mixture of atomic and molecular states is created and probed by sudden changes in the magnetic field, which lead to oscillations in the number of atoms that remain in the condensate. The oscillation frequency, measured over a large range of magnetic fields, is in excellent agreement with the theoretical molecular binding energy, indicating that we have created a quantum superposition of atoms and diatomic molecules–two chemically different species.

Bose-Einstein condensation, or BEC, has a long and rich history dating from the early 1920s. In this article we will trace briefly over this history and some of the developments in physics that made possible our successful pursuit of BEC in a gas. We will then discuss what was involved in this quest. In this discussion we will go beyond the usual technical description to try and address certain questions that we now hear frequently, but are not covered in our past research papers. These are questions along the lines of: How did you get the idea and decide to pursue it? Did you know it was going to work? How long did it take you and why? We will review some our favorites from among the experiments we have carried out with BEC. There will then be a brief encore on why we are optimistic that BEC can be created with nearly any species of magnetically trappable atom. Throughout this article we will try to explain what makes BEC in a dilute gas so interesting, unique, and experimentally challenging.

We precisely measured the binding energy ∊_bind) of a molecular stale near the Feshbach resonance In a ⁸⁵Rb Bose-Einstein condensate (BEC). Rapid magnetic-field pulses induced coherent atom-molecule oscillations in the BEC. We measured the oscillation frequency as a function B tield and fit the data TO a coupled-channel model. Our analysis constrained the Feshbach resonance position [155.041(18) Gl, width 10.71(2; G] and background scattering length [−443[3]a₀] and yielded new values fur the Rb interaction parameters. These results improved our estimate lor the stability condition of an attractive BEC. We also found evidence for a mean-field shift to ∊_bind.

The spontaneous dissociation of ⁸⁵Rb dimers in the highest lying vibrational level has been observed in the vicinity of the Feshbach resonance that was used to produce them. The molecular lifetime shows a strong dependence on magnetic field, varying by 3 orders of magnitude between 155.5 G and 162.2 G. Our measurements are in good agreement with theoretical predictions in which molecular dissociation is driven by inelastic spin relaxation. Molecule lifetimes of tens of milliseconds can be achieved within approximately a 1 G wide region directly above the Feshbach resonance.

We investigate the production efficiency of ultracold molecules in bosonic ⁸⁵Rb and fermionic ⁴⁰K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of both species is solely determined by the phase space density of the atomic cloud, in contrast with a number of theoretical predictions. In the nonadiabatic regime our measurements of the ⁸⁵Rb molecule conversion efficiency follow a Landau-Zener model.

A novel atom-molecule conversion technique has been investigated. Ultracold ⁸⁵Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.

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Detailed instructions for the construction and operation of a diode laser system with optical feedback are presented. This system uses feedback from a diffraction grating to provide a narrow-band continuously tuneable source of light at red or near-IR wavelengths. These instructions include machine drawings for the parts to be constructed, electronic circuit diagrams, and prices and vendors of the items to be purchased. It is also explained how to align the system and how to use it to observe saturated absorption spectra of atomic cesium or rubidium.

We present detailed instructions for the construction and operation of an inexpensive apparatus for laser cooling and trapping of rubidium atoms. This apparatus allows one to use the light from low power diode lasers to produce a magneto-optical trap in a low pressure vapor cell. We present a design which has reduced the cost to less than $3000 and does not require any machining or glassblowing skills in the construction. It has the additional virtues that the alignment of the trapping laser beams is very easy, and the rubidium pressure is conveniently and rapidly controlled. These features make the trap simple and reliable to operate, and the trapped atoms can be easily seen and studied. With a few milliwatts of laser power we are able to trap 4×10⁷ atoms for 3.5 s in this apparatus. A step-by-step procedure is given for construction of the cell, setup of the optical system, and operation of the trap. A list of parts with prices and vendors is given in the Appendix.

This Resource Letter provides a guide to the literature on trapping of neutral atoms.

The reliance of modem society on science and technology has created a serious and growing need for a large high-technology workforce and a technically literate population. Nowhere is this clearer than in the area of optics. Furthermore, providing an effective science education for a large and diverse segment of the population is something no educational system has ever achieved (see Laser Focus World, December 2003, p. 47).

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The following sections are included:

• Electricity and circuits

• From motion to maths

• Acknowledgments

The following sections are included:

• Creating PhET Sims for Engagement and Learning

• Making PhET Sims Accessible

• Teaching and Learning with PhET Sims

• Hearing from the students

• References

The Colorado Learning Attitudes about Science Survey (CLASS) is a new instrument designed to measure various facets of student attitudes and beliefs about learning physics. This instrument extends previous work by probing additional facets of student attitudes and beliefs. It has been written to be suitably worded for students in a variety of different courses. This paper introduces the CLASS and its design and validation studies which include analyzing results from over 2400 students, interviews and factor analyses. Methodology used to determine categories and how to analyze the robustness of categories for probing various facets of student learning are also described. This paper serves as the foundation for the results and conclusions from the analysis of our survey data.^4,5

The following sections are included:

• The Course

• The Lecture

• The Grading

• The Impact of Seat Location

• Acknowledgments

• References

A number of instruments have been designed to probe the variety of attitudes, beliefs, expectations, and epistemological frames taught in our introductory physics courses. Using a newly developed instrument – the Colorado Learning Attitudes about Science Survey (CLASS)[1] – we examine the relationship between students' beliefs about physics and other educational outcomes, such as conceptual learning and student retention. We report results from surveys of over 750 students in a variety of courses, including several courses modified to promote favorable beliefs about physics. We find positive correlations between particular student beliefs and conceptual learning gains, and between student retention and favorable beliefs in select categories. We also note the influence of teaching practices on student beliefs.

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This Peer Review issue focuses on science and engaged learning. As any advertising executive or politician can tell you, engaging people is all about attitudes and beliefs, not abstract tacts. There is a lot we can learn from these professional communicators about how to effectively engage students. Far too often we, as educators, provide students with the content of science-often in the distilled formal representations that we have found to be the most concise and general-but fail to address students' own attitudes and beliefs. (Although heaven forbid that we should totally abandon reason and facts, as is typical in politics and advertising).

The following sections are included:

• Research on traditional instruction

• A better approach

• New educational technology

• The reality of virtual physics

• References

We present a study of student understanding of energy in quantum mechanical tunneling and barrier penetration. This paper will focus on student responses to two questions that were part of a test given in class to two modem physics classes and in individual interviews with 17 students. The test, which we refer to as the Quantum Mechanics Conceptual Survey (QMCS), is being developed to measure student understanding of basic concepts in quantum mechanics. In this paper we explore and clarify the previously reported misconception that reflection fiom a barrier is due to particles having a range of energies rather than wave properties. We also confirm previous studies reporting the student misconception that energy is lost in tunneling, and report a misconception not previously reported, that potential energy diagrams shown in tunneling problems do not represent the potential energy of the particle itself. The present work is part of a much larger study of student understanding of quantum mechanics.

The Colorado Learning Attitudes about Science Survey (CLASS) is a new instrument designed to measure student beliefs about physics and about learning physics. This instrument extends previous work by probing additional aspects of student beliefs and by using wording suitable for students in a wide variety of physics courses. The CLASS has been validated using interviews, reliability studies, and extensive statistical analyses of responses from over 5000 students, in addition, a new methodology for determining useful and statisically robust categories of student beliefs has been developed. This paper serves as the foundation for an extensive study of how student beliefs impact and are impacted by their educational experience. For example, this survey measures the following: that most teaching practices cause substantial drops in student scores; that a student's likelihood of becoming a physics major correlates with their “Personal Interest” score; and that, for a majority of student populations, women's scores in some categories. including “Personal Interest” and “Real World Connections,” are significantly different from men's scores.

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The response of an isolated magnetic bubble domain to pulsed magnetic fields normal to the film plane is measured with high spatial and temporal resolution. Digital signal averaging techniques are used on a succession of identical pulses, permitting changes in bubble radius to be measured to a precision of 2 nanometres, in successive time intervals of 10 nanoseconds. The radial wall velocity, obtained by differentiation, is determined with a precision of 0.2 metres per second. Significant “inertial” effects and velocity non-linearities are seen at quite modest drive fields (a few tenths of kA/m, or, a few 0e) and wall velocities (a few m/s), in response both to an applied bias-field step and to a pulse.

We present a design for a high-vacuum valve which can be built very quickly and easily. It has the additional feature that it is very thin.

We have constructed an efficient high frequency phase modulator using a KDP crystal modulator in a Fabry-Perot interferometer. We present the theoretical analysis for the performance of such a modulator and compare this with experimental results. We have obtained a modulation index of 0.6 at 2.7 GHz with 0.3 W of microwave power. This implies that the use of a Fabry-Perot cavity can reduce the amount of drive power needed to achieve a given modulation index by 3 orders of magnitude or more. Such a device is particularly useful in the ultraviolet region of the spectrum where one must use relatively inefficient modulator crystals.

Using a potassium niobate crystal in a modified self-locking power-buildup cavity, we have frequency doubled the 865-nm output from a GaAlAs laser diode. With 12.4 mW of input power we have obtained a unidirectional output of 0.215 mW at 432 nm. In contrast to previous diode doubling experiments, the output was both single frequency and circular Gaussian. With better optics, substantially higher conversion efficiencies should be possible using this technique.

We present a review of the use of diode lasers in atomic physics with an extensive list of references. We discuss the relevant characteristics of diode lasers and explain how to purchase and use them. We also review the various techniques that have been used to control and narrow the spectral outputs of diode lasers. Finally we present a number of examples illustrating the use of diode lasers in atomic physics experiments.

We present a system which uses optical feedback from a diffraction grating to provide primary control over the frequency tuning of a diode laser, and employs simultaneous optical feedback from a narrowband Fabry–Perot cavity to reduce the linewidth. The frequencies of the optical feedback from the diffraction grating and narrowband cavity are electronically locked using a novel technique. The reduction in the linewidth is measured as a reduction in the frequency noise seen on the side of a Cs-saturated absorption line. The presence of optical feedback from the narrowband cavity reduces the frequency noise by a factor of 3 compared to the frequency noise obtained using the grating feedback alone.

A three dimensional magnetic confinement system is presented which will trap both macroscopic and atomic magnetic dipoles. The dipole is confined by dc and oscillating magnetic fields, and its motion is described by the Mathieu equation. Most aspects of the dynamics of the trapped objects depend only on the ratio of the magnetic moment to the mass of the dipole. Similar motion was observed for masses varying over 21 orders of magnitude (from 1 atom to 0.2 g). The trap is constructed from inexpensive permanent magnets and small coils which are driven by 60 Hz line current. The design of the trap as well as the behavior of the trapped particle are discussed herein.

We describe a sensitive and inexpensive vibrometer based on optical feedback by diffuse scattering to a single-mode diode laser. Fluctuations in the diode laser's operating frequency that are due to scattered light from a vibrating surface are used to detect the amplitude and frequency of surface vibrations. An additional physical vibration of the laser provides an absolute amplitude calibration. The fundamental bandwidth is determined by the laser response time of roughly 10⁻⁹ s. A noise floor of 0.23 nm/Hz^1/2 at 30 kHz with 5 × 10⁻⁵ of the incident light returning is demonstrated. This instrument provides an inexpensive and sensitive method of noncontact measurement in solid materials with low or uneven reflectivity. It can be used as a vibration or velocity sensor.

We demonstrate a robust method of stabilizing a diode laser frequency to an atomic transition. This technique employs the Zeeman shift to generate an antisymmetric signal about a Doppler-broadened atomic resonance, and therefore offers a large recapture range as well as high stability. The frequency of a 780-nm diode laser, stabilized to such a signal in Rb, drifted less than 0.5 MHz peak–peak (1 part in 10⁹) in 38 h. This tunable frequency lock can be constructed inexpensively, requires little laser power, rarely loses lock, and can be extended to other wavelengths by use of different atomic species.