7,421 research outputs found
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
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
Isolating intrinsic noise sources in a stochastic genetic switch
The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be unrepressed, leaving three possible promotor states. This model is analysed in its bistable regime in which the deterministic limit exhibits two stable fixed points and an unstable saddle, and the case of small noise is considered. On small time scales, the stochastic process fluctuates near one of the stable fixed points, and on large time scales, a metastable transition can occur, where fluctuations drive the system past the unstable saddle to the other stable fixed point. To explore how different intrinsic noise sources affect these transitions, fluctuations in protein production and degradation are eliminated, leaving fluctuations in the promotor state as the only source of noise in the system. Perturbation methods are then used to compute the stability landscape and the distribution of transition times, or first exit time density. To understand how protein noise affects the system, small magnitude fluctuations are added back into the process, and the stability landscape is compared to that of the process without protein noise. It is found that significant differences in the random process emerge in the presence of protein noise
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.
Optimal Stochastic Enhancement of Photoionization
The effect of noise on the nonlinear photoionization of an atom due to a
femtosecond pulse is investigated in the framework of the stochastic
Schr\"odinger equation. A modest amount of white noise results in an
enhancement of the net ionization yield by several orders of magnitude, giving
rise to a form of quantum stochastic resonance. We demonstrate that this effect
is preserved if the white noise is replaced by broadband chaotic light.Comment: 4 pages, 4 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
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
Non-destructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms
We describe a scheme for probing a gas of ultracold atoms trapped in an
optical lattice and moving in the presence of an external potential. The probe
is non-destructive and uses the existing lattice fields as the measurement
device. Two counter-propagating cavity fields simultaneously set up a
conservative lattice potential and a weak quantum probe of the atomic motion.
Balanced heterodyne detection of the probe field at the cavity output along
with integration in time and across the atomic cloud yield information about
the atomic dynamics in a single run. The scheme is applied to a measurement of
the Bloch oscillation frequency for atoms moving in the presence of the local
gravitational potential. Signal-to-noise ratios are estimated to be as high as
.Comment: 8 pages, 6 figures, submitted to Phys. Rev.
Quadripartite continuous-variable entanglement via quadruply concurrent downconversion
We investigate an intra-cavity coupled down-conversion scheme to generate
quadripartite entanglement using concurrently resonant nonlinearities. We
verify that quadripartite entanglement is present in this system by calculating
the output fluctuation spectra and then considering violations of optimized
inequalities of the van Loock-Furusawa type. The entanglement characteristics
both above and below the oscillation threshold are considered. We also present
analytic solutions for the quadrature operators and the van Loock-Furusawa
correlations in the undepleted pump approximation.Comment: 9 pages, 5 figure
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