Narrow Results

We describe the action of the symplectic group on the homogeneous space of squeezed states (quantum blobs) and extend this action to the semigroup. We then extend the metaplectic representation to the metaplectic (or oscillator) semigroup and study the properties of such an extension using Bargmann-Fock space. The shape geometry of squeezing is analyzed and noncommuting elements from the symplectic semigroup are proposed to be used in simultaneous monitoring of noncommuting quantum variables — which should lead to fractal patterns on the manifold of squeezed states.

Generally, one thinks of a “quantum jump” as the process in which an electron “jumps” between a pair of quantum states, even as the process is treated within perturbation theory. This jump of an electron has remained a key point of conservative (i.e., traditional) quantum mechanics. But, the question of the time dependence of such a transition, e.g. the time for an atom to be ionized by radiation, is somewhat different than this view. A detailed approach in which an incoming wave first polarizes the quantum states and then completes the transition has allowed for a detailed discussion of the smooth transition of the electron from one state to the next. Here, we will discuss the history of the process, and illustrate the approach with the question of “how long does it take for an electron to emit a phonon?” The entire process arises from the proper application of wave mechanics and obviates the need to even consider a discussion of quantum jumps.

The sophistication of recent experimental procedures has made it possible to detect experimentally the so-called Quantum Jumps (QJ), i.e. the stop and restart of the wave function as a real phenomenon. In this work, we connect this experimental evidence to a foundational interpretation of QM, based on an a-temporal vacuum. In that picture, the QJ is a localization process, defined as the time-symmetric action of a self-conjugate projection operator. The compatibility of these discontinuous processes with the Theory of Relativity is demonstrated using the Bohm representation of quantum mechanics.

We review two topics of quantum optics that shed new light on the effect of state reduction by a quantum measurement. One topic is the observation of quantum jumps switching on and off the fluorescence of a trapped atomic ion. The other one is the spontaneous decay of a single atom, described by the method of quantum trajectories. This method is based on the decomposition of the density matrix of an open system into an ensemble of time-dependent pure state vectors. Here we consider single histories of the spontaneously emitting atom. It is shown that in both cases the evolution is affected by a detection with a null result.

We treat the motion of two-level atoms in a strong standing-wave laser field taking into account photon recoil effect caused by induced and spontaneous emission. Spontaneous emission is considered as random jumps to be incorporated in the equations of motion by a Monte Carlo method. We derive nonlinear equations with jumps for real-valued renormalized Bloch-like variables composed of complex-valued Schrödinger probability amplitudes and connected to classical atomic position and momentum variables. Well-known dissipative mechanical effects of cooling, heating and velocity grouping of atoms are found numerically with those equations. Correlations between internal and external degrees of freedom of an atom in the optical lattice, i.e. between center-of-mass motion and Rabi oscillations, are found.

Optomechanical devices in which a flexible SiN membrane is placed inside an optical cavity allow for very high finesse and mechanical quality factor in a single device. They also provide fundamentally new functionality: the cavity detuning can be a quadratic function of membrane position. This enables a measurement of "position squared" (x²) and in principle a QND phonon number readout of the membrane. However, the readout achieved using a single transverse cavity mode is not sensitive enough to observe quantum jumps between phonon Fock states.

Here we demonstrate an x²-sensitivity that is orders of magnitude stronger using two transverse cavity modes that are nearly degenerate. We derive a first-order perturbation theory to describe the interactions between nearly-degenerate cavity modes and achieve good agreement with our measurements using realistic parameters. We also demonstrate theoretically that the x²-coupling should be easily tunable over a wide range.