Foundations of Quantum Mechanics in the Light of New Technology

PREFACE.

COMMITTEES.

CONTENTS.

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Across a broad front in physics, an important advance in recent years has been the increasing ability to observe and manipulate the dynamical processes of individual quantum Systems. Within this context, an important physical system has been a single atom strongly coupled to the electromagnetic field of a high-Q cavity within the setting of cavity quantum electrodynamics (cavity QED). Another promising possibility is provided by the cooperative interaction of light with an atomic ensemble for writing and reading single quanta. Here, I present a brief overview of recent advances in the Quantum Optics Group at Caltech related to optical interactions with single photons and atoms and to applications in quantum information science.

This paper reviews the single photon sources based on semiconductor quantum dots and their applications to quantum information systems. By optically pumping a system consisting of a semiconductor single quantum dot confined in a monolithic microcavity, it is possible to produce a single photon pulse stream at the Fourier transform limit with a negligible jitter. This single photon source is not only useful for BB84 quantum key distribution (QKD), but also find applications in other quantum information systems such as Ekert91/BBM92 QKD and quantum teleportation gate for linear optics quantum computers.

Entangled photons provided the first evidence of a violation of Bell's inequality which implies a breakdown of the philosophical world-view of local realism. These experiments, having been extended over the years over ever longer distances, also provided the experimental foundation of the emerging field of quantum communication. There, quantum cryptography and quantum teleportation are key topics, which are already fairly advanced, being able to cover significant distances. Originally, it was thought that in a future quantum internet scheme, communication would be provided by photons while the local computers were to be realized with ions, atoms, atomic nuclei, solid state devices and the like. Interestingly, most recently the field of linear optics quantum computation has emerged with interesting possibilities and advantages.

We show the progress of continuous-variable quantum information processing, especially on realization of high-fidelity teleportation and entanglement swapping, and a quantum teleportation network.

We investigate entangled states of two trapped ⁴⁰Ca⁺ ions. By encoding the quantum information in the Zeeman-manifold of the ground state, we observe entangled states lasting for more than 20 seconds.

A system of three particles in an entangled state is used to display a non-Bell type of quantum non-locality. The measured values of particle 1 are changed by changing the state of particle 3 even though the preparation of 3 and the measurement of 1 occur at spatially separated locations and the particles never interact. The third particle, particle 2, has non-orthogonal states which do not change during the process. Therefore the effect cannot be explained in terms of a classical intervention mediated by particle 2.

I derive a measure of entanglement for general pure multipartite states that coincides with the generalized concurrence for a general pure bipartite and three-partite states based on wedge product.

The process of spontaneous parametric down-conversion (SPDC) in nonlinear crystals makes it fairly easy to generate entangled photon states. It has been known for some time that the conversion efficiency can be improved by employing quasi-phase-matching in periodically poled crystals. Using two single-photon detectors, we have analyzed the photon pairs generated by SPDC in a periodically poled lithium niobate crystal pumped by a femtosecond laser. Several parameters could be varied in our setup, allowing us to obtain data in close agreement with both thermal and Poissonian photon-pair distributions.

We demonstrate the generation of entangled photon pairs via biexciton-resonant hyper parametric scattering in CuCl crystal. Quantum state tomography show that the generated photon pairs have a high degree of polarization entanglement. Also we show that the photon pairs violate Clauser-Horne-Shimony-Holt type Bell's inequality.

We have investigated decoherence mechanisms in a Josephson-junction flux qubit. Loss of the coherence due to energy relaxation and dephasing was studied by measurements of the time evolution of qubit states subjected to simple control pulse sequences. As a function of qubit bias parameters, the characteristic time scales of the decoherence as well as the decay envelope functions varied, from which information about the fluctuation spectrum of the environment were deduced.

We report low temperature electron-transport measurements on two single-electron transistors operated simultaneously and coupled capacitively to two isolated double quantum-dots in silicon. The gate voltage dependencies and microwave induced responses are presented. A gate-voltage dependent anti-crossing type response with effective Q-value ~10⁵ and splitting energy 91 neV is observed. The sharp resonance peaks are attributed to population of charge states due to photon absorption from the incident microwave irradiation, and the peak splitting is attributed to the coupling between the isolated double quantum-dots.

We analyzed adiabatic geometric phase in a composite system; charge-coupled superconducting flux qubits. When we change two external magnetic fields along a contour, an finite off-diagonal Berry phase is accumulated between the ground and third excited states. The effect of decoherence on the Berry phase caused by magnetic field fluctuation is also examined numerically with a master equation. It seems that decoherence destroys energy-eigenstate superpositions much significantly than the values of Berry phase.

The information obtained from the operation of a quantum gate on only two complementary sets of input states is sufficient to estimate the quantum process fidelity of the gate. In the case of entangling gates, these conditions can be used to predict the multi qubit entanglement capability from the fidelities of two non-entangling local operations. It is then possible to predict highly non-classical features of the gate such as violations of local realism from the fidelities of two completely classical input-output relations, without generating any actual entanglement.

We analyze optical selection rules of microwave assisted transitions in a superconducting flux qubit circuit (SQC). We show that the parities of the states relevant to the superconducting phases in the SQC are well-defined at a special value Φ₀/2 of the external magnetic flux Φ_e. When Φ_e ≠ Φ₀/2, the symmetry of the potential of the SQC is broken, and a so-called Δ-type cyclic three-level artificial "atom" is formed, where one- and two-photon processes can coexist.

We analyze robustness of decoherence-free (DF) subspace in charge qubits when there are a local structure and non-uniformity that violate collective decoherence measurement condition. We solve master equations of up to four charge qubits and a detector as two serially coupled quantum point contacts (QPC) with an island structure. We show that robustness of DF states is strongly affected by local structure as well as by non-uniformities of qubits.

This paper reviews some recent developments in asymptotic estimation theory for a parametric family {Γ_θ}_θ of quantum channels, putting emphasis on an active interplay between noncommutative statistics and information geometry.

We propose a new qubit consisting of a superconducting ring with an ordinary Josephson junction and a ferromagnetic π-junction. In the system, two degenerate stable states appear in the phase space without an external magnetic field due to a competition between the 0- and π-states. Because of quantum tunneling between the two degenerate states, bonding and antibonding states, which are used as a bit, are formed. For manipulating the states of the qubit, only small external magnetic field around zero is required. This feature leads to a large-scale integration and a construction of the qubit with a smaller size which is robust to decoherence by external noises.

We theoretically investigate generation of the entangled three macroscopic objects, i.e., macroscopic Greenberger-Horne-Zeilinger states, in Josephson systems by using the Cirac-Zoller scheme. We propose a quantum breather in a long Josephson junction as a macroscopic artifical atom and derive the Jaynes-Cummings-type interaction Hamiltonian required in the scheme. Macroscopic Greenberger-Horne-Zeilinger states play a crucial role in fundamental tests of quantum mechanics versus local realism at a macroscopic level.

We prepare a novel double dot device in a hybrid vertical-lateral geometry to study the electronic configurations of the tunnel-coupled and exchange-coupled states. In this device two two-dimensional quantum dots coupled side by side, and current flows vertically. From transport measurements we derive important parameters such as the inter- and intra-dot Coulomb energies, the tunnel coupling energy and the potential detuning between the two dots to influence the electronic configurations in a double dot. Thus we confirm the formation of the Heitler-London two-electron state in the weak tunnel coupling regime, and also find that the tunnel and exchange couplings are tunable with coupling gate voltage and magnetic field.

We report experiments on the transport through interference circuits, in which semiconductor quantum dots are embedded. The interference picks up coherent transport through the dots, which provides information on electronic states including many body effects in them. Here we focus on the role of spin scattering in a quantum dot to the coherent transport through it. We present evidence of quantum decoherence due to the spin-flip scattering in a dot through the Aharonov-Bohm (AB) amplitude when the Kondo effect does not emerge. Around a resonance peak of the dot, the interference effect appears as the Fano effect, which also gives information on the phase shift through the dot. We have observed the combined effect of the Fano effect and the Kondo effect – the Fano-Kondo effect in a side-coupled quantum dot system, which manifests the quantum coherence of the Kondo singlet state and at the same time the phase shift locking to π/2. In an AB ring system, the Fano-Kondo effect has been also observed and the parameter of interference is tuned by the AB flux.

We demonstrate electrically pumped single-photon emission from single quantum dots in a lateral p-i-n junction without metal apertures. In such a structure, strong antibunching effects of exciton and biexciton emission are observed and imply that single-photon emission has been achieved. The devices can be operated with electric pulses with repetition rates of more than 100 MHz. New wafers with emission wavelength around 1.3 μm are investigated for future development.

We have investigated the Aharonov-Bohm(AB)-type quantum oscillations in triangular and square arrays of antidots fabricated from two-dimensional electron systems in GaAs/AlGaAs heterostructure.

We studied theoretically the Kondo effect in a quantum dot coupled to ferromagnetic leads. Spin-dependent charge fluctuations induce a kinetic exchange interaction between a spin inside the quantum dot and the lead magnetizations, resulting in a splitting of a zero bias anomaly. A left-right asymmetry in tunnel barriers significantly affects the nonlinear differential conductance. Our results agree qualitatively well with recent experiments. We also show that the decoherence of the Kondo resonance is significant in this system.

Using the Majorana representation and the Schwinger-Keldysh approach, we evaluate the distribution of current through a single-electron transistor for the large conductance. The strong quantum fluctuations induce the lifetime broadening of charge-state levels out of equilibrium, as well as the renormalization effect. We find that the lifetime broadening suppresses higher cumulants of current fluctuations.

The geometric ideas underlying the Berry phase and the modern viewpoint of Karplus and Luttinger's theory of the anomalous Hall effect are discussed in an elementary way. We briefly review recent Hall and Nernst experiments which support the dominant role of the KL velocity term in ferromagnets.

Nontrivial spin texture on some topological lattice can give rise to the quantal phase in the conduction electron hopping term, and hence affect the transverse transport as gigantic fictitious magnetic field. In Nd₂Mo₂O₇ (NMO) and related R₂Mo₂O₇ (R being a rare-earth ion) compounds, the Ising anisotropy of Nd (or R) moments on the pyrochlore lattice interact ferromagnetically with each other and anitiferomagentically with Mo spins, giving rise to the non-coplanar configuration with spin chirality. The Hall resistivity in NMO changes sign with increasing magnetic field applied along [111] direction, while it monotonously approaches zero with the field applied along [100] or [110] direction. This is in accord with the prediction by the Berry phase theory and is interpreted in terms of field-induced reversal of spin chirality on the pyrochlore lattice, i.e. the transformation from the two-in two-out to three-in one-out configuration of the Nd (and hence Mo) moments.

Geometrical phase for the Bloch states in solids leads to the motion of electrons transverse to the applied electric field. This leads to the intrinsic Hall effect, respresentative examples of which are the anomalous Hall effect in ferromagnets and spin Hall effect in semiconductors. This intrinsic Hall current is essentially dissipationless, but the disorder effect is crucial to understand the realistic situation. We review here the conventional view and recent new perspectives developed for these phenomena.

Semiconductor spintronics is based on the controlled generation of localized spin densities. Finite spin densities in semiconductors have traditionally [1] been generated by external magnetic fields, by circularly polarized light sources, or by spin injection from spin-aligning materials, such as ferromagnets. Recently there has been considerable interest [2] in an alternate strategy in which edge spin densities are generated electrically via the spin Hall effect (SHE) [3,4], i.e., in a planar device by the current of spins oriented perpendicular to the plane that is generated by and flows perpendicular to an electric field. The SHE has traditionally been thought of as a consequence of spin-dependent chirality in impurity scattering that occurs in systems with spin-orbit (SO) coupling [5, 6]. Recently it has been recognized that the SHE also has an intrinsic contribution due to SO coupling in a perfect crystal [7, 8]. In this work, we study SHE induced edge spin accumulation in a two-dimensional hole gas (2DHG) with strong SO interactions. The 2D hole layer is a part of a p-n junction light-emitting diode with a specially designed coplanar geometry which allows an angle-resolved polarization detection at opposite edges of the 2D hole system. In equilibrium the angular momenta of the spin-orbit split heavy-hole states lie in the plane of the 2D layer. When an electric field is applied across the hole channel, a nonzero out-of-plane component of the angular momentum is detected whose sign depends on the sign of the electric field and is opposite for the two edges. Microscopic quantum transport calculations show only a weak effect of disorder, suggesting that the clean limit spin-Hall conductance description (intrinsic spin-Hall effect) might apply to our system.

We theoretically propose that the spin Hall effect occurs in p-type semiconductors even without an aid of impurity scattering. An effect of disorder is also investigated. We also discuss a criterion for nonzero spin Hall effect. With this criterion, we predict that some band insulators have nonzero spin Hall effect.

Spin-transfer refers to the transfer of spin angular momentum between transport quasiparticles and the magnetic condensate of a ferromagnetic metal. It is ususally regarded as a consequence of total spin conservation. We discuss a theory that views spin-transfer from a more microscopic point of view and sees it as an example of a more general class of phenomena that occurs in any magnetic metal or semiconductor, and indeed in any system in which interactions contribute importantly to the quasiparticle self-energy. Our theory of spin transfer in ferromagnets does not rest on an appeal to conservation of total spin, can assess whether or not current-induced magnetization precession and switching in a particular geometry will occur coherently, and can estimate the efficacy of spin-transfer when spin-orbit interactions are present. We illustrate our theory by applying it to a toy-model two-dimensional-electron-gas ferromagnet with Rashba spin-orbit interactions and mention examples of related phenomena in other systems, most of which have not yet been realized experimentally.

Our recent works on spin filters built of semiconductor nanostructures are reviewed. It is shown that in appropriately design ballistic wires spin filtering can occur in the tens' millitesla range of the external field. In the case of high mobility electrons at the GaAs/AlGaAs interface, spin-related effects are revealed by applying an in-plane local magnetic field produced by micromagnets of ferrmagnetic metals. The observed effects are attributed to switching between Zeeman and Stern-Gerlach modes – the former dominating at low electron densities. Due to a large spin-orbit coupling in PbTe, which results in |g*| ≈ 66, the spin-splitting can become larger than 1D quantization energy in rather weak magnetic fields. Evidences for generation of spin polarized current carried by many 1D subbands in PbTe nanoconstrictions are described.

Current-driven domain wall (DW) motion for a well-defined single DW in a micro-fabricated magnetic wire with submicron width was investigated by real-space observation with magnetic force microscopy. Magnetic force microscopy visualizes that a single DW introduced in a wire is displaced back and forth by positive and negative pulsed-current, respectively. Effect of the Joule heating, reduction of the threshold current density by shape control, and magnetic ratchet effect are also presented.

We here demonstrate non-local spin injection into a nano-scale ferromagnetic particle configured in a lateral spin valve structure to switch its magnetization without charge current. The non-local spin injection is found to align the magnetization of the nano-magnetic particle along the magnetization of the spin injector. The magnitude of the spin current for reversal is determined to be about 158 μA, which is reasonable compared with the estimated value of the spin current required for switching free layer in conventional nano-pillar structures.

Motion of a planar domain wall in a nanoscale ferromagnetic wire under electric current is studied based on microscopic description. In the adiabatic case, domain wall is driven by spin torque (spin transfer), and there is an intrinsic pinning arising from hard-axis anisotropy energy. Extrinsic pinning does not affect the threshold current in this case. A resonating oscillation of domain wall occurs under AC current, and this was recently used for a spectroscopy of a single "domain wall particle". Nucleation of domain walls by spin torque is discussed. Fundamental mechanism of spin transfer effect is understood in terms of spin Josephson effect.

The electronic structure of diluted magnetic semiconductors is studied, especially focusing on the hole character. The Haldane-Anderson model is extend to a magnetic impurity, and is analyzed in the Hartree-Fock approximation. Due to the strong hybridization of an impurity d-states with host p-states, it is shown that holes are created in the valence band, at the same time the localized magnetic moments are formed. These holes are weakly bound around the impurity site with the characteristic length of several lattice constants. For the case of the two impurities, it is found that when the separation of two impurities is of the order of the length of holes, the overlap of these holes favors the ferromagnetic interaction. The spatially extended holes play an essential role for the ferromagnetic exchange interaction.

The spatial distribution of spin accumulation and spin current in the non-local geometry is studied taking into account the finite size effect of the contact areas by applying a finite element method in two-dimension. It is shown that, when the contacts are tunneling-like, the sign and the value of spin accumulation signal are consistent with the experimental results, and the one-dimensional analysis is appropriate to analyze the experimental results.

Magneto-optical Faraday rotation angle of ferromagnetic anatase Co-doped TiO₂ films is enhanced and can be controlled by Nb doping. A carrier density of films can be varied by Nb doping in this room-temperature ferromagnetic degenerate semiconductor. A Ti_0.89Nb_0.06Co_0.05O₂ film showed a Faraday rotation angle of 1.5 × 10⁴ deg/cm at 400 nm. An anomalous Hall eflfect, showing that the charge carriers are spin polarized, is observed in this film.

We have investigated superconductivity in thin mesoscopic regular polygons in a perpendicular magnetic field. For that, we have used an analytical gauge transformation for the vector potential which takes into account the superconductor/vacuum boundary condition. As reported previously, this has opened the way to investigate the nucleation of superconductivity in nanosu-perconductors at the normal-superconducting phase boundary in the framework of the linearized Ginzburg-Landau (GL) equations. We report now on the extension of this work to the superconducting phase beyond the phase boundary, by using the full non-linear GL equations. The stability in the superconducting phase of the symmetry induced vortex-antivortex molecules has been examined in detail for squared and equilateral triangle geometries.

We report an experimental observation of coalescence and rearrangement of vortices in mesoscopic superconductors by using the multiple-small-tunnel-junction method. The former corresponds to a second-order multivortex state (MVS) - giant vortex state (GVS) transition and the latter to a first-order MVS-MVS transition with a fixed vorticity. The experimental results are in good agreement with the theoretical simulations based on the nonlinear Ginzburg-Landau theory.

Superconducting states in topologically nontrivial spaces, such as Möbius strip and networks, are discussed. Attention has been paid especially to the effects of finite system size or boundaries on the superconducting phase transition under a magnetic field. We show that topology can affect the superconducting transition temperature and the vortex structure strongly and various types of novel vortex states can be generated, which may be called "topologically (or geometrically) induced vortices".

We argue that an asymmetric dc SQUID composed of a tunnel junction and an atomic point contact when it is threaded by a magnetic flux can produce a ratchet potential for the superconducting phase. Preliminary experiment shows the rocking ratchet effect, i.e., generation of dc voltage by ac current biasing.

A two-dimensional (2D) superconducting square network under spatially modulated magnetic field is studied. The super/normal phase boundaries were measured with field modulation varied. The dependence on the strength of field modulation exhibited the behavior reproducing the calculation we had done before. In addition, I-V characteristics measurements were also conducted.

Aiming at determining the current-phase relation of a superconducting atomic point contact (SAPC), we made an interference experiment using a dc-SQUID consisting of an SAPC and a tunnel junction. In this paper, the experimental method, especially the control of SAPC by the mechanical break junction method is described in detail.

Here we summarize results on our study of the critical depinning current J_c versus the applied magnetic flux Φ, for quasiperiodic (QP) one-dimensional (1D) chains and 2D arrays of pinning centers placed on the nodes of a five-fold Penrose lattice. In 1D QP chains, the peaks in J_c(Φ) are determined by a sequence of harmonics of the long and short segments of the chain. The critical current J_c(Φ) has a remarkable self-similarity. In 2D QP pinning arrays, we predict analytically and numerically the main features of J_c(Φ), and demonstrate that the Penrose lattice of pinning sites provides an enormous enhancement of J_c(Φ), even compared to triangular and random pinning site arrays. This huge increase in J_c(Φ) could be useful for applications.

We investigate the macroscopic quantum tunneling (MQT) in d-wave high-T_c superconductor Josephson junctions. Using the path-integral method, we analytically obtain the MQT rate for the c-axis twist Josephson junctions. In the case of the zero twist angle, the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is largely suppressed compared with the finite twist angle cases. Furthermore, the effect of the zero energy bound states (ZES) on the MQT in the in-plane junctions is theoretically investigated. We obtained the analytical formula of the MQT rate and showed that the presence of the ZES at the insulator/superconductor interface leads to a strong Ohmic quasiparticle dissipation. Therefore, the MQT rate is noticeably inhibited compared with the c-axis junctions in which the ZES are completely absent.

A brief review is given on transport properties of carbon nanotubes mainly from a theoretical point of view. The topics include an effective-mass description of electronic states, the absence of backward scattering except for scatterers with a potential range smaller than the lattice constant, the presence of perfectly conducting channel, and roles of symmetry and channel numbers.

Single-walled carbon nanotubes threaded by a magnetic flux φ are predicted to posses novel magnetic and optical properties, critically depending on the value of φ/φ₀ where φ₀ is the magnetic flux quantum. This is a consequence of the Aharonov-Bohm phase 2πφ/φ₀ influencing the boundary conditions on the Bloch wavefunctions. Here we report results of a series of magneto-optical studies of micelle-suspended single-walled carbon nanotubes in aqueous solutions in high magnetic fields. Their exotic magnetic properties manifest themselves in near-infrared magneto-absorption and magneto-photoluminescence spectra, including static and dynamic magnetic linear dichroism, splittings of exciton peaks, and field-induced band gap shrinkage. We show that these observations are quantitatively consistent with existing theories based on the Aharonov-Bohm effect.

We consider transport through a single-walled carbon nanotube (CNT) in the ballistic regime where weak backscattering at the two contacts gives rise to Fabry-Perot (FP) oscillations in conductance and shot noise. We include the electron-electron interaction and the finite length L of the CNT within the inhomogeneous Tomonaga-Luttinger liquid (TLL) model appropriate for the CNT and treat the non-equilibrium effects due to an applied bias voltage within the Keldysh approach. At low frequencies, the shot noise is S = 2e|I_B|, where e is the elementary charge and I_B is the backscattered current. Interaction effects are apparent via a characteristic power-law and FP-oscillation suppression of I_B at large bias voltage in agreement with our low-frequency shot noise experiments. The extracted TLL parameter g agrees well with theoretical predictions. At frequencies above v_F/gL, with v_F the Fermi velocity, the theoretical impurity noise as a function of bias voltage and frequency shows clear and distinct signatures of the two velocities of collective modes present in the CNT which distinguish spin from charge degrees of freedom (spin-charge separation).

Transport properties were examined in monolayer and sub-monolayer films composed of Au nanoparticles covered with organic thiol ligands. In the monolayer film, the observed linear conductance scaled exponentially with the ligand chain length. On the other hand, in the sub-monolayer film, nonlinear current-voltage characteristics were observed as expected for one-dimensional meandering paths induced by structural defects.

On a H-terminated Si(100)-2×1 surface, a dihydride-chain structure parallel to the step edge is often found by Scanning Tunneling Microscopy. The chain is located near an S_B step edge, but away from it by more than one Si-dimer's distance. We performed first principles calculations to determine the mechanism of the chain formation. As a result, we found that the rebonded step edge of the clean Si surface turns into a combination of a dihydride chain and a non-rebonded step edge after hydrogen termination. We also found that the chain adjacent to the step edge is energetically less stable than that at one Si-dimer distance away from the step.

Current-voltage characteristics were measured of atomic-scale Ag wires on the hydrogenated surface of Si(100) using four-probe fine electrodes fabricated with scanning-probe nanofabrication technique. Carrier transport was observed even at the initial stage of Ag deposition and conductivity increased as a function of supplied Ag atoms. Ballistic and diffusive transport are discussed as possible mechanisms of carrier transport.

By increasing the lifetime of the excited atoms embedded in a solid-state cavity, the field-ionization rate was enhanced approximately three times over that without the cavity effect. The characteristic temperature dependence of the enhanced field-ionization rate suggested the generation process was dissipative quantum tunneling induced by the strong electron-phonon coupling between localized electrons in the excited atoms and the surrounding lattice vibrations of the host in the cavity.

We have developed a first principles software, universal virtual spectroscope for opto-electronics research (UVSOR), which can calculate dielectric functions of materials at atomistic levels on the basis of the density functional pseudopotential method in the frequency range from the static to ultra-violet region. The UVSOR can calculate separately electronic and lattice components of the dielectric function, by using the random phase approximation and the Berry phase polarization theory, respectively. This makes the UVSOR unique "virtual spectroscope" on computer, covering all frequencies interested in materials science; i. e., radio, Tera-Hz, infrared, visible, and ultra-violet frequencies. Since the UVSOR can quantitatively calculate the dielectric constant of materials, it is quite effective for studying new dielectrics such as high-k and low-k materials discussed in nano-scale semiconductor technologies. The UVSOR is free software and can be downloaded from our web site: http://www.fsis.iis.u-tokyo.ac.jp.

We report our recent predictions on the quantum Nernst effect, a novel thermomagnetic effect in the quantum Hall regime. We assume that, when the chemical potential is located between a pair of neighboring Landau levels, edge currents convect around the system. This yields theoretical predictions that the Nernst coefficient is strongly suppressed and the thermal conductance is quantized. The present system is a physical realization of the non-equilibrium steady state.

Phase information of bright and monochromatic field-emission electron beams, which we had been repeatedly developing for the past 30 years, was used to visualize quantum phenomena, which have recently begun to crop up in many microscopic regions. Recent examples include microscopic quantum phenomena we directly observed in superconductors such as quantized vortices that exhibited strange behaviors peculiar to anisotropic layered high-T_c superconductors.

An optical lattice clock was realized for ⁸⁷Sr atoms and its absolute frequency has been measured. Projected uncertainty in the lattice clock is illustrated for the case of ⁸⁷Sr. We discuss application of the clock scheme to other atom species, in search for better lattice clocks as well as for the variation of fine-structure constant.

We are developing multilayer interferometer of Mach-Zehnder type for cold neutrons. To fulfill severe requirements for aligning the four mirrors, we utilize six solid-etalon-plates and a high precision flat base plate. New devices making use of magnetic birefringence have been developed and demonstrated to be useful for fine adjustment of superposition between the two paths labeled with neutron spin.

Scanning Kelvin probe microscopy is demonstrated by using a noncontact atomic force microscope with a 1 MHz quartz length-extensional resonator as a force sensor. A tungsten probe tip glued onto the end of the quartz rod is electrically connected to the electrode of the resonator. To detect Coulomb force, frequency shift signal is used instead of oscillation amplitude of the resonator. A surface potential on a Au(111) single crystal with nanoscale carbon dots is measured. The potential difference is observed between the Au surface and the carbon dots.

The level crossing problem is neatly formulated by the second quantized formulation, which exhibits a hidden local gauge symmetry. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial (and thus no monopole singularity) for arbitrarily large but finite time interval T. The topological proof of the Longuet-Higgins' phase-change rule, for example, thus fails in the practical Born-Oppenheimer approximation where T is identified with the period of the slower system. The crucial difference between the Aharonov-Bohm phase and the geometric phase is explained. It is also noted that the gauge symmetries involved in the adaibatic and non-adiabatic geometric phases are quite different.

We show that the self-trapped condensate can be dynamically stabilized in two and three dimensional free space by periodic oscillation of the scattering length. The oscillating interaction produces an effective potential that prevents the condensate from collapsing. We take into account the effect of dissipation to simulate realistic situations.

Matter-wave solitons in Bose-Einstein condensates of ultracold gaseous atoms with spin degrees of freedom are investigated based on the exact solution method. Combining some theoretical and experimental results, we present the undiscovered spin dependent soliton dynamics such as macroscopic spin precession and spin switching.

We discuss a mechanism of spin decoherence in gravitation within the framework of general relativity. The spin state of a particle moving in a gravitational field is shown to decohere due to the curvature of spacetime. As an example, we analyze a particle going around a static spherically-symmetric object.

Berry's phase of the atom in the state with a positive or negative g factor for partial cycles of a conical rotating magnetic field was determined using a time-domain atom interferometer. The experimental results show that the solid angle for positive g-factor is ϕ(1-cosθ) and that for a negative g-factor is ϕ(1+cosθ) addition to the reversing the sign.

LIST OF PARTICIPANTS.

Author Index.