Emergent classicality in continuous quantum measurements

We develop a classical theoretical description for nonlinear many-body dynamics that incorporates the back-action of a continuous measurement process. The classical approach is compared with the exact quantum solution in an example with an atomic Bose-Einstein condensate in a double-well potential where the atom numbers in both potential wells are monitored by light scattering. In the classical description the back-action of the measurements appears as diffusion of the relative phase of the condensates on each side of the trap. When the measurements are frequent enough to resolve the system dynamics, the system behaves classically. This happens even deep in the quantum regime, and demonstrates how classical physics emerges from quantum mechanics as a result of measurement back-action

Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate

A detailed analysis of the growth of a BEC is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modelling of growth implicitly gives a model of the spatial shape of the condensate vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our method may give substantially different results for condensate numbers and temperatures obtained from phenomentological fits, and indicates the need for more systematic investigation of the growth dynamics of the condensate from a supersaturated vapor.Comment: TeX source; 29 Pages including 26 PostScript figure

Number-Phase Wigner Representation for Efficient Stochastic Simulations

Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many problems using these techniques remain intractable over long integrations times. We present a number-phase Wigner representation that can be unraveled into SDEs. We demonstrate convergence to the correct solution for an anharmonic oscillator with small dampening for significantly longer than other phase space representations. This process requires an effective sampling of a non-classical probability distribution. We describe and demonstrate a method of achieving this sampling using stochastic weights.Comment: 7 pages, 1 figur

Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium

The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88, 070403, 2002) shows dramatic, rapid internal state segregation for two hyperfine levels of rubidium. We simulate an effective one dimensional model of the system for experimental parameters and find reasonable agreement with the data. The Ramsey frequency is found to be insensitive to the decoherence of the superposition, and is only equivalent to the interaction energy shift for a pure superposition. A Quantum Boltzmann equation describing collisions is derived using Quantum Kinetic Theory, taking into account the different scattering lengths of the internal states. As spin-wave experiments are likely to be attempted at lower temperatures we examine the effect of degeneracy on decoherence by considering the recent experiment of Lewandowski et al. where degeneracy is around 10%. We also find that the segregation effect is only possible when transport terms are included in the equations of motion, and that the interactions only directly alter the momentum distributions of the states. The segregation or spin wave effect is thus entirely due to coherent atomic motion as foreseen in the experimental reportComment: 26 pages, 4 figures, to be published in J. Phys.

Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation

The process of cascaded downconversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analysed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearised fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behaviour when quantisation of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.Comment: 24 pages, 15 figure

Trapping and Cooling a mirror to its quantum mechanical ground state

We propose a technique aimed at cooling a harmonically oscillating mirror to its quantum mechanical ground state starting from room temperature. Our method, which involves the two-sided irradiation of the vibrating mirror inside an optical cavity, combines several advantages over the two-mirror arrangements being used currently. For comparable parameters the three-mirror configuration provides a stiffer trap for the oscillating mirror. Furthermore it prevents bistability from limiting the use of higher laser powers for mirror trapping, and also partially does so for mirror cooling. Lastly, it improves the isolation of the mirror from classical noise so that its dynamics are perturbed mostly by the vacuum fluctuations of the optical fields. These improvements are expected to bring the task of achieving ground state occupation for the mirror closer to completion.Comment: 5 pages, 1 figur

Intensity fluctuations in steady state superradiance

Alkaline-earth like atoms with ultra-narrow optical transitions enable superradiance in steady state. The emitted light promises to have an unprecedented stability with a linewidth as narrow as a few millihertz. In order to evaluate the potential usefulness of this light source as an ultrastable oscillator in clock and precision metrology applications it is crucial to understand the noise properties of this device. In this paper we present a detailed analysis of the intensity fluctuations by means of Monte-Carlo simulations and semi-classical approximations. We find that the light exhibits bunching below threshold, is to a good approximation coherent in the superradiant regime, and is chaotic above the second threshold.Comment: 8 pages, 5 figure

Thermalization and temperature distribution in a driven ion chain

We study thermalization and non-equilibrium dynamics in a dissipative quantum many-body system -- a chain of ions with two points of the chain driven by thermal bath under different temperature. Instead of a simple linear temperature gradient as one expects from the classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on the ion coupling rate to the bath, the location of the driven ions, and the dissipation rates of the other ions in the chain. Through simulation of the temperature evolution, we show that these unusual temperature distribution patterns in the ion chain can be quantitatively tested in experiments within a realistic time scale.Comment: 5 pages, 5 figure

Helix or Coil? Fate of a Melting Heteropolymer

We determine the probability that a partially melted heteropolymer at the melting temperature will either melt completely or return to a helix state. This system is equivalent to the splitting probability for a diffusing particle on a finite interval that moves according to the Sinai model. When the initial fraction of melted polymer is f, the melting probability fluctuates between different realizations of monomer sequences on the polymer. For a fixed value of f, the melting probability distribution changes from unimodal to a bimodal as the strength of the disorder is increased.Comment: 4 pages, 5 figure