E. V. Goldstein

QUANTUM THEORY OF ATOMIC FOUR-WAVE MIXING IN BOSE-EINSTEIN CONDENSATES

We present an exact quantum mechanical analysis of collinear four-wave mixing in a multicomponent Bose-Einstein condensate consisting of sodium atoms in the F=1 ground state. Technically, this is achieved by taking advantage of the conservation laws of the system to represent its Hamiltonian in terms of angular momentum operators. We discuss explicitly the build-up of matter-wave side-modes from noise, as well as the correlations between these modes. We show the appearance of a strong quantum entanglement between hyperfine states. We also demonstrate that for finite atomic numbers, the system exhibits periodic collapses and revivals in the exchange of atoms between different spin states.

Eliminating the mean-field shift in two-component Bose-Einstein condensates

We demonstrate that the nonlinear mean-field shift in a multicomponent Bose-Einstein condensate may be eliminated by controlling the two-body interaction coefficients. This modification can be achieved by engineering the environment of the condensate. We consider the case of a two-component condensate in a quasi-one-dimensional atomic waveguide, achieving modification of the atom-atom interactions by varying the transverse wave functions of the components. Eliminating the density-dependent phase shift represents a promising potential application for multicomponent condensates in atom interferometry and precision measurements.

Influence of the dipole-dipole interaction on velocity-selective coherent population trapping

We analyze the influence of the dipole-dipole interaction between ground and excited state atoms on atomic cooling by velocity-selective coherent population trapping. We consider two three-level atoms in the λ-configuration, interacting with two counterpropagating laser fields as well as with the electromagnetic vacuum modes. The elimination of these modes in the Born-Markov approximation results in spontaneous decay, which is essential in providing the momentum diffusion necessary for cooling, as well as a two-body dipole-dipole interaction between ground-and excited-state atoms. The corresponding two-body master equation is solved numerically by Monte-Carlo wave-function simulations. Our main result is that although a dark state survives the inclusion of dipole-dipole interactions, the presence of this interaction can significantly slow down the cooling process for sufficiently high atomic densities.

Atomic phase conjugation from a Bose condensate

We discuss the possibility of observing atomic phase conjugation from Bose condensates, and using it as a diagnostic tool to access the spatial coherence properties and to measure the lifetime of the condensate. We argue that since phase conjugation results from the scattering of a partial matter wave off the spatial grating produced by two other waves, it offers a natural way to directly measure such properties, and as such provides an attractive alternative to the optical methods proposed in the past.

Mutual coherence of optical and matter waves

We propose a scheme to measure the cross correlations and mutual coherence of optical and matter fields. It relies on the combination of a matter-wave detector operating by photoionization of the atoms and a traditional absorption photodetector. We show that the double-detection signal is sensitive to cross-correlation functions of light and matter waves.

Dressed Bose-Einstein condensates in high-Q cavities

We propose and analyze a way in which effective multicomponent condensates can be created inside high-

Characterization and manipulation of matter-wave coherence

Q

Collapse of atomic motion in a quantized cavity mode

multimode cavities. In contrast to the situation involving several atomic species or levels, the coupling between the various components of the dressed condensates is linear. We predict analytically and confirm numerically the onset of instabilities in the quasiparticle excitation spectrum.

Quasiparticle instabilities in multicomponent atomic condensates

We review an extension of the optical coherence theory to the case of atomic Schrodinger waves, and show that this requires the introduction of several classes of coherence. Optical methods to manipulate the coherence of matter-wave fields are discussed.

Phase conjugation of multicomponent Bose-Einstein condensates

Abstract The state of a quantized single-mode cavity field strongly influences the motion of atomic wave packets trapped into the optical potential that it provides, to the point where the atomic motion can be effectively “frozen” for long periods of time. This effect, which should not be confused with cooling, is reminiscent of the collapse and revivals phenomena familiar from the Jaynes-Cummings model.