Sze M. Tan

DYNAMICAL QUANTUM NOISE IN TRAPPED BOSE-EINSTEIN CONDENSATES

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

Bell's inequality for systems with quadrature phase coherence

Abstract We show that a violation of Bells inequalities by quadrature phase measurements is not due to the interference of the two photons in a photon pair state. Rather the violation predicted by Grangier et al. for a parametric down-converter is due to the interference of the photon pair state with the vacuum. We propose new sources which violate the quadrature phase Bells inequalities, including one which employs squeezed light and another which demonstrates the non-local properties of a single photon state.

Violation of Bell's inequalities with parametric down-conversion

Abstract We analyze the experiment demonstrating a violation of Bells inequalities with parametric down-conversion as performed by Alley and Shih, and Ou and Mandel. We obtain analytic results which show a continuous transition between quantum and classical behaviour. In the limit of weak parametric conversion, the results agree with those obtained for an initial correlated photon pair. In the opposite limit of strong parametric conversion, the results coincide with those obtained for classical fields.

RECONSTRUCTION OF THE JOINT STATE OF A TWO-MODE BOSE-EINSTEIN CONDENSATE

We propose a scheme to reconstruct the state of a two-mode Bose-Einstein condensate, with a given total number of atoms, using an atom interferometer that requires beam splitter, phase shift, and nonideal atom counting operations. The density matrix in the number-state basis can be computed directly from the probabilities of different counts for various phase shifts between the original modes, unless the beam splitter is exactly balanced. Simulated noisy data from a two-mode coherent state are produced and the state is reconstructed, for 49atoms. The error can be estimated from the singular values of the transformation matrix between state and probability data. {copyright} {ital 1997} {ital The American Physical Society}

EFFECTS OF MOTION IN CAVITY QED

We consider effects of motion in cavity quantum electrodynamics experiments where single cold atoms can now be observed inside the cavity for many Rabi cycles. We discuss the timescales involved in the problem and the need for good control of the atomic motion, particularly the heating due to exchange of excitation between the atom and the cavity, in order to realize nearly unitary dynamics of the internal atomic states and the cavity mode which is required for several schemes of current interest such as quantum computing. Using a simple model we establish the ultimate effects of the external atomic degrees of freedom on the action of quantum gates. The performance of the gate is characterized by a measure based on the entanglement fidelity and the motional excitation caused by the action of the gate is calculated. We find that schemes which rely on adiabatic passage, and are not therefore critically dependent on laser pulse areas, are very much more robust against interaction with the external degrees of freedom of atoms in the quantum gate.

Analysis of the bichromatic atomic beam splitter

We compare the properties of the bichromatic atomic beam splitter where the light field is treated classically and quantum mechanically. This beam splitter has been proposed as a configuration which produces two cleanly-separated diffracted beams. It is found that for a classical field with a definite temporal phase relationship between the standing waves, an incoming atomic beam is in general split unequally between the two orders, the ratio of the outgoing beams being dependent on the atomic state and on the phase relationship at the time at which the atom enters the field. In previous analyses of this beam splitter, the light fields have been assumed to be in number states leading to a symmetrical splitting of the atomic beam. The relative insensitivity of the bichromatic beam-splitter to the failure of the Raman-Nath approximation predicted by Grimm et al. is confirmed for a rectangular optical profile, but the results for a Gaussian profile suggest that operation in the Raman-Nath regime is still required for clean beam-splitting.

A comparison of bichromatic beam splitters for atoms

We analyse and compare various aspects of the performance of atomic beam splitters for 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.

Amplitude Noise Reduction in Quietly Pumped Lasers

Motivated by the recent experiments of Machida et al.,1 we shall consider two models for a laser with regular pump excitation. Machida et al. have demonstrated that the intensity fluctuations in the output light may be reduced below the shot noise limit if the pump fluctuations are suppressed. There have been a number of theoretical papers which have analysed the effect of reduced pump fluctuations on both lasers and masers.2–7