D. F. Walls

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].

COLLAPSES AND REVIVALS IN THE INTERFERENCE BETWEEN TWO BOSE-EINSTEIN CONDENSATES FORMED IN SMALL ATOMIC SAMPLES

We investigate the quantum interference between two Bose-Einstein condensates formed in small atomic samples composed of a few thousand atoms both by imposing Bose broken gauge symmetry from the outset and also using an explicit model of atomic detection. In the former case we show that the macroscopic wave function collapses and revives in time, and we calculate the characteristic times for current experiments. Collapses and revivals are also predicted in the interference between two Bose-Einstein condensates which are initially in Fock states, a relative phase between the condensates being established via atomic detections corresponding to uncertainty in the number difference between them.

Large Kerr nonlinearity with a single atom

We propose a scheme to generate a large Kerr nonlinearity based on electromagnetically induced transparency in a single atom placed in a high-finesse microcavity. We perform a thorough analysis of the system dynamics using a dressed states approach. This system is shown to create a photon blockade effect equivalent to that for an ideal Kerr nonlinearity as recently proposed by Imamoglu et al 1997 Phys. Rev. Lett. 79 1467.

STATE DETERMINATION IN CONTINUOUS MEASUREMENT

The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. Initial lack of knowledge of the system and external noises are accounted for by considering the evolution of conditioned density matrices under a stochastic master equation. It is shown that after a finite time the state of the system is a pure state and can be inferred from the measurement record alone. The relation to emerging possibilities for the continuous experimental observation of single quanta, as for example in cavity quantum electrodynamics, is discussed.

BOSE-EINSTEIN CONDENSATE IN A DOUBLE-WELL POTENTIAL AS AN OPEN QUANTUM SYSTEM

We study the dynamics of a Bose-Einstein condensate in a double-well potential in the two-mode approximation. The dissipation of energy from the condensate is described by the coupling to a thermal reservoir of non-condensate modes. As a consequence of the coupling the self-locked population imbalance in the macroscopic quantum self-trapping decays away. We show that a coherent state predicted by spontaneous symmetry breaking is not robust and decoheres rapidly into a statistical mixture due to the interactions between condensate and non-condensate atoms. However, via stochastic simulations we find that with a sufficiently fast measurement rate of the relative phase between the two wells the matter wave coherence is established even in the presence of the decoherence.

Generic model of an atom laser

We present a generic model of an atom laser by including a pump and loss term in the Gross-Pitaevskii equation. We show that there exists a threshold for the pump above which the mean matter field assumes a non-vanishing value in steady-state. We study the transient regime of this atom laser and find oscillations around the stationary solution even in the presence of a loss term. These oscillations are damped away when we introduce a position dependent loss term. For this case we present a modified Thomas-Fermi solution that takes into account the pump and loss. Our generic model of an atom laser is analogous to the semi-classical theory of the laser.

Quantum state of a trapped Bose-Einstein condensate

Abstract The quantum state of a single symmetry-broken condensate at zero temperature is calculated using perturbative techniques. For a fixed mean number of atoms, the state is found to closely approximate a number squeezed state. We propose a means of experimentally testing this state, based on the periodic collapses and revivals of its phase.

MACROSCOPIC SUPERPOSITIONS OF BOSE-EINSTEIN CONDENSATES

We consider two dilute gas Bose-Einstein condensates with opposite velocities from which a monochromatic light field detuned far from the resonance of the optical transition is coherently scattered. In the thermodynamic limit, when the relative fluctuations of the atom number difference between the two condensates vanish, the relative phase between the Bose-Einstein condensates may be established in a superposition state by detections of spontaneously scattered photons, even though the condensates have initially well-defined atom numbers. For a finite system, stochastic simulations show that the measurements of the scattered photons lead to a randomly drifting relative phase and drive the condensates into entangled superpositions of number states. This is because according to Bose-Einstein statistics the scattering to an already occupied state is enhanced.

DETECTION OF VORTICITY IN BOSE-EINSTEIN CONDENSED GASES BY MATTER-WAVE INTERFERENCE

A phase-slip in the fringes of an interference pattern is an unmistakable characteristic of vorticity. We show dramatic two-dimensional simulations of interference between expanding condensate clouds with and without vorticity. In this way, vortices may be detected even when the core itself cannot be resolved.

NONDESTRUCTIVE OPTICAL MEASUREMENT OF RELATIVE PHASE BETWEEN TWO BOSE-EINSTEIN CONDENSATES

We study the interaction of light with two Bose condensates as an open quantum system. The two overlapping condensates occupy two different Zeeman sublevels and two driving light beams induce a coherent quantum tunneling between the condensates. We derive the master equation for the system. It is shown that stochastic simulations of the measurements of spontaneously scattered photons establish the relative phase between two Bose condensates, even though the condensates are initially in pure number states. These measurements are non-destructive for the condensates, because only light is scattered, but no atoms are removed from the system. Due to the macroscopic quantum interference the detection rate of photons depends substantially on the relative phase between the condensates. This may provide a way to distinguish, whether the condensates are initially in number states or in coherent states.