Quantum dynamics of bouncing atoms in a stable gravitational cavity

Two-level atoms bouncing in a stable gravitational cavity are considered, where the atomic mirror at the bottom of the bounces is an evanescent wave caused by an internally reflected intense Gaussian-mode laser beam. We consider the broadening mechanisms of the atoms from their initially tightly spaced position distribution, using a phenomenological semi-classical model, which includes spontaneous emission. A fully quantum model, which neglects spontaneous emission, is derived, and the broadening of the atomic wave function in the quantum model is compared with the broadening of the atomic distribution in an analogous classical simulation where spontaneous emission is similarly neglected. We find that the broadening is correctly described by the classical simulations in the horizontal directions, while it significantly underestimates the broadening in the vertical direction.Dedicated to H. Walther on the occasion of his 60th birthday     

Quantum motions of ultracooled atoms in resonant laser field

The analysis has been made of quantum motions of cooled atoms in a resonant light field. The existence of the band structure of energetic levels is predicted of quantum atom motions in a standing light wave field. Cooling and trapping of atoms has been described from the quantum point of view. The possibility of detection r.f. photons on the transitions of ultracooled atoms and molecules in a standing light wave field is proposed.     

Quantum optics in waveguides with resonant atoms: Multi-photon scattering

Quantum scattering of photons inside a one-dimensional waveguide caused by a number of closely located resonant two-level atoms is studied using the theory of integrable quantum systems. The multi-particle wave function of scattered photons is represented as a sum of terms of different degrees of “entanglement.” For two-photon scattering we discuss explicitly differences in photon correlations for the single two-level atom case and the case of several atoms.     

Quantum aspects of chaos for three-level atoms interacting with two harmonic oscillators

We treat a simple generalization of the Jaynes-Cummings model to three-level atoms interacting with two harmonic oscillators. The model allows for classical chaos even in the rotating wave approximation, as was recently shown by Shepelyanski. Under conditions most favorable for classical chaos we find linear level repulsion à la Wigner.     

Quantum chaos

A quantum system which is allowed to interact with its boundary in a self-consistent way is shown to exhibit chaos. We conjecture that in general genuine wave chaos (decaying autocorrelation functions, exponential sensitivity of wavefunctions to initial wavefunction configurations) can be obtained whenever a wavefield is allowed to modify its confining boundaries in a self-consistent way. We suggest to test this conjecture in the acoustic regime.     

Quantum chaos

In this paper we present an overview of important recent results in the study of a very controversial topic, the so-called quantum chaos. The theoretical and numerical results are compared with real laboratory experiments with special emphasis on the problem of ionization of hydrogen atoms in external microwave fields. (c) 1996 American Institute of Physics.     

Semiclassical interaction of moving two-level atoms with a cavity field: from integrability to Hamiltonian chaos

The dynamics of an ensemble of two-level atoms moving through a single-mode lossless cavity is investigated in the semiclassical and rotating-wave approximations. The dynamical system for the expectation values of the atomic and field observables is considered as a perturbation to one of the following integrable versions: (i) a model with atoms moving through a spatially inhomogeneous resonant field, and (ii) a model with atoms interacting with a nonresonant eigenmode which is assumed to be homogeneous on the cavity size. We find the general exact solutions for both the models and show that they contain special solutions describing a coherent effect of population and radiation trapping. Using the Melnikov method, we prove analytically transverse intersections of stable and unstable manifolds of a hyperbolic fixed point under a small modulation of the vacuum Rabi frequency. These intersections are believed to provide the Smale horseshoe mechanism of Hamiltonian chaos. The analytical results are accompanied with direct computation of topographical maps of maximal Lyapunov exponents that give a representative image of regularity and chaos in the atom-field system in different ranges of its control parameters--the frequency detuning, the number, and the velocity of atoms.     

Trapping atoms in a gravitational cavity

This paper is devoted to the study of a new atomic cavity consisting of a single horizontal concave mirror placed in the earth gravitational field. Gravity, by bending the atomic trajectories, plays the role of a second mirror closing the cavity. We first discuss the stability criterion for this cavity, assuming that the mirror has a parabolic shape. We then derive the quantum mechanical modes of such a configuration, with particular emphasis on the paraxial (i.e., close to vertical) motion. Finally, we discuss the possibility of populating those modes from an initial cold atomic cloud dropped above the mirror.Laboratoire associé au CNRS et à l'Université Pierre et Marie Curie     

The Purcell-Dicke effect in the emission from a coated small sphere of resonant atoms placed inside a matrix cavity

I investigate a system where both the Purcell effect and Dicke’s superradiance are present. I compute the frequency eigenmode for an ensemble of identical two-level atoms enclosed in a coated nanosphere that is embedded in a matrix. I show that, in a number of configurations, the rate of superradiant emission from the atomic system can be increased many folds from that of a similar cloud of atoms in free space.     

Quasideterministic generation of entangled atoms in a cavity

We present a scheme to generate a maximally entangled state of two three-level atoms in a cavity. The success or failure of the generation of the desired entangled state can be determined by detecting the polarization of the photon leaking out of the cavity. With the use of an automatic feedback, the success probability of the scheme can be made to approach unity.     

Quantum chaos in nuclear physics

A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.     

Collective cooling and self-organization of atoms in a cavity

We theoretically investigate the correlated dynamics of N coherently driven atoms coupled to a standing-wave cavity mode. For red detuning between the driving field and the cavity as well as the atomic resonance frequencies, we predict a light force induced self-organization of the atoms into one of two possible regular patterns, which maximize the cooperative scattering of light into the cavity field. Kinetic energy is extracted from the atoms by superradiant light scattering to reach a final kinetic energy related to the cavity linewidth. The self-organization starts only above a threshold of the pump strength and atom number. We find a quadratic dependence of the cavity mode intensity on the atom number, which demonstrates the cooperative effect.