Dynamical tunnelling of ultracold atoms

The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling(1,2) between two regions of classically stable motion. An archetype of such nonclassical motion is tunnelling through an energy barrier. In the 1980s, a new process, 'dynamical' tunnelling(1-3), was predicted, involving no potential energy barrier; however, a constant of the motion (other than energy) still forbids classically the quantum-allowed motion. This process should occur, for example, in periodically driven, nonlinear hamiltonian systems with one degree of freedom(4-6). Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted(4) dynamical tunnelling between these stable regions. Here we observe dynamical tunnelling of ultracold atoms from a Bose-Einstein condensate in an amplitude-modulated optical standing wave. Atoms coherently tunnel back and forth between their initial state of oscillatory motion (corresponding to an island of regular motion) and the state oscillating 180 degrees out of phase with the initial state.

Atom counting in ultracold gases using photoionization and ion detection

We analyze photoionization and ion detection as a means of accurately counting ultracold atoms. We show that it is possible to count clouds containing many thousands of atoms with accuracies better than N-1/2 with current technology. This allows the direct probing of sub-Poissonian number statistics of atomic samples. The scheme can also be used for efficient single-atom detection with high spatiotemporal resolution. All aspects of a realistic detection scheme are considered, and we discuss experimental situations in which such a scheme could be implemented.

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Signature of mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behavior of a simple homogeneous Bose gas, finding a very slight increase of the loss rate compared to that obtained by using the standard method.

Two-wire waveguide and interferometer for cold atoms

A versatile miniature de Broglie waveguide is formed by two parallel current-carrying wires in the presence of a uniform bias field. We derive a variety of analytical expressions to describe the guide and present a quantum theory to show that it offers a remarkable range of possibilities for atom manipulation on the submicron scale. These include controlled and coherent splitting of the wave function as well as cooling, trapping, and guiding. In particular, we discuss a novel microscopic atom interferometer with the potential to be exceedingly sensitive.

A comparison of bichromatic beam splitters for atoms

We analyse and compare various aspects of the performance of atomic beam splitters fur two- and three-level atoms, both of which use bichromatic optical fields. We calculate the extent to which spontaneous emission degrades the sharpness of the splitting, and how it might degrade the visibility of an idealised atom interferometer which includes either beam splitting mechanism. (C) 1998 Elsevier Science B.V.

Interference pattern with a dark center from two atoms driven by a coherent laser field

In a recent paper Meyer and Yeoman [Phys. Rev. Lett. 79, 2650 (1997)] have shown that the resonance fluorescence from two atoms placed in a cavity and driven by an incoherent field can produce an interference pattern with a dark center. We study the fluorescence from two coherently driven atoms in free space and show that this system can also produce an interference pattern with a dark center. This happens when the atoms are in nonequivalent positions in the driving: field, i.e., the atoms experience different intensities and phases of the driving field. We discuss the role of the interatomic interactions in this process and find that the interference pattern with a dark center results from the participation of the antisymmetric state in the dynamics of the driven two-atom system.

Interference pattern with a dark center in resonance fluorescence from two atoms driven by a squeezed vacuum field

We study the resonance fluorescence from two interacting atoms driven by a squeezed vacuum field and show that this system produces an interference pattern with a dark center. We discuss the role of the interatomic interactions in this process and find that the interference pattern results from an unequal population of the symmetric and antisymmetric states of the two-atom system. We also identify intrinsically nonclassical effects versus classical squeezed field effects, (C) 1998 Elsevier Science B.V. All rights reserved.

Three-dimensional quantum solitons with parametric coupling

We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values.

Atoms in squeezed light fields

Squeezed light is of interest as an example of a non-classical state of the electromagnetic field and because of its applications both in technology and in fundamental quantum physics. This review concentrates on one aspect of squeezed light, namely its application in atomic spectroscopy. The general properties, detection and application of squeezed light are first reviewed. The basic features of the main theoretical methods (master equations, quantum Langevin equations, coupled systems) used to treat squeezed light spectroscopy are then outlined. The physics of squeezed light interactions with atomic systems is dealt with first for the simpler case of two-level atoms and then for the more complex situation of multi-level atoms and multi-atom systems. Finally the specific applications of squeezed light spectroscopy are reviewed.

Chaotic dynamics of cold atoms in far-off-resonant donut beams

We describe the classical two-dimensional nonlinear dynamics of cold atoms in far-off-resonant donut beams. We show that chaotic dynamics exists there for charge greater than unity, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in the (x,y) plant for charge 2 are simulated. We show that the atoms will accumulate on several ring regions when the system enters a regime of global chaos. [S1063-651X(99)03903-3].

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.

Atoms in an amplitude-modulated standing wave - dynamics and pathways to quantum chaos

Cold rubidium atoms are subjected to an amplitude-modulated far-detuned standing wave of light to form a quantum-driven pendulum. Here we discuss the dynamics of these atoms. Phase space resonances and chaotic transients of the system exhibit dynamics which can be useful in many atom optics applications as they can be utilized as means for phase space state preparation. We explain the occurrence of distinct peaks in the atomic momentum distribution, analyse them in detail and give evidence for the importance of the system for quantum chaos and decoherence studies.

Pure two-atom squeezed state in spontaneous emission from two non-identical atoms

We calculate the stationary state of the system of two non-identical two-level atoms driven by a finite-bandwidth two-mode squeezed vacuum. It is well known that two identical two-level atoms driven by a broadband squeezed vacuum may decay to a pure state, called the pure two-atom squeezed state, and that the presence of the antisymmetric state can change its purity. Here, we show that for small interatomic separations the stationary state of two non-identical atoms is not sensitive to the presence of the antisymmetric state and is the pure two-atom squeezed state. This effect is a consequence of the fact that in the system of two non-identical atoms the antisymmetric state is no longer the trapping state. We also calculate the squeezing properties of the emitted field and find that the squeezing spectrum of the output field may exhibit larger squeezing than that in the input squeezed vacuum. Moreover, we show that squeezing in the total field attains the optimum value which can ever be achieved in the field emitted by two atoms.