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arXiv:quant-ph/0305111 · Physical Review A

Quantum limits of stochastic cooling of a bosonic gas

D. Ivanov, S. Wallentowitz, I. A. Walmsley

Published Jun 26, 2003• 12 citations
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Abstract

The quantum limits of stochastic cooling of trapped atoms are studied. The energy subtraction due to the applied feedback is shown to contain an additional noise term due to atom-number fluctuations in the feedback region. This effect is shown to dominate the cooling efficiency near the condensation point. Furthermore, we show results that indicate that Bose-Einstein condensation could be reached via stochastic cooling.

DOI
10.1103/physreva.67.061401

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The quantum limits of stochastic cooling of trapped atoms are studied. The energy subtraction due to the applied feedback is shown to contain an additional noise term due to atom-number fluctuations in the feedback region. This effect is shown to dominate the cooling efficiency near the condensation point. Furthermore, we show results that indicate that Bose-Einstein condensation could be reached via stochastic cooling.
Ultra-cold atomic gases are an ideal platform for precision measurement devices and analogue quantum simulators, which will prove instrumental in unlocking the secrets of quantum gravity and high-temperature superconductivity. However, current experimental techniques cannot cool atomic gases to simulatenously both the low entropies and high particle numbers necessary for these applications. A promising alternative is feedback cooling: using continuous-measurement feedback control to damp out energy fluctuations and cool a gas. So far, feedback cooling has been primarily studied at zero temperature, with the only finite temperature simulation achieved via a computationally expensive numerical method restricted to bosons. This thesis develops a perturbative model for the feedback cooling of a finite temperature condensed Bose gas using Bogoliubov theory, with the aim of deriving dynamic equations for the system that are both analytically tractable, and allow for fast numerical prototyping of new feedback control schemes. Using the measurement-feedback model of Szigeti \textit{et al.} \cite{szigeti_continuous_2009,szigeti_feedback_2010}, we derive a low temperature perturbative model for feedback cooling of a Bose gas in an arbitrary trapping and control potential. Using this general model, we then derive a model for the dynamics of a Bose gas in a hard box trap being cooled with an energy damping control. We complete preliminary simulations of this model in the no-backaction conditional measurement limit, damping out density fluctuations in a gas of 90%90\%90% condensate fraction and cooling it to 93.5±1%93.5 \pm 1\%93.5±1%. We find that, in this limit, the dynamics of the gas are largely independent of number but significantly depend on the inter-particle interaction. We also find an optimal energy damping control strength in this limit. However, our model is not very efficient for simulation, particularly for a large number of particles and measurement strength. As an alternative, we propose an approximation scheme in which steady-state analytic solutions could be obtained from the model. Finally, we propose two methods to develop a Bogoliubov model for the feedback cooling of fermions, which would be the first finite temperature model for the Fermi gas case.
Continuously measured interacting quantum systems almost invariably heat, causing loss of quantum coherence. Here, we study Bose-Einstein condensates (BECs) subject to repeated weak measurement of the atomic density and describe several protocols for generating a feedback signal designed to remove excitations created by measurement back-action. We use a stochastic Gross-Pitaevskii equation to model the system dynamics and find that a feedback protocol utilizing momentum-dependent gain and filtering can effectively cool both one-dimensional (1D) and two-dimensional systems. The performance of these protocols is quantified in terms of the steady-state energy, entropy, and condensed fraction. These are the first feedback cooling protocols demonstrated in two dimensions, and in one dimension our optimal protocol reduces the equilibrium energy by more than a factor of 100 as compared with a previous cooling protocol developed using the same methodology. We also use this protocol to quench-cool 1D BECs from noncondensed highly excited states and find that they rapidly condense into a far-from-equilibrium state with energy orders of magnitude higher than the equilibrium ground-state energy for that condensate fraction. We explain this in terms of the near integrability of our 1D system, whereby efficiently cooled low-momentum modes are effectively decoupled from the energetic ``reservoir'' of the higher-momentum modes. We observe that the quench-cooled condensed states can have nonzero integer winding numbers described by quantized supercurrents.
Degenerate quantum gases are instrumental in advancing many-body quantum physics and underpin emerging precision sensing technologies. All state-of-the-art experiments use evaporative cooling to achieve the ultracold temperatures needed for quantum degeneracy, yet evaporative cooling is extremely lossy: more than 99.9% of the gas is discarded. Such final particle number limitations constrain imaging resolution, gas lifetime, and applications leveraging macroscopic quantum coherence. Here we show that atomic Bose gases can be cooled to quantum degeneracy using real-time feedback, an entirely new method that does not suffer the same limitations as evaporative cooling. Through novel quantum-field simulations and scaling arguments, we demonstrate that an initial low-condensate-fraction thermal Bose gas can be cooled to a high-purity Bose-Einstein condensate (BEC) by feedback control, with substantially lower atomic loss than evaporative cooling. Advantages of feedback cooling are found to be robust to imperfect detection, finite resolution of the control and measurement, time delay in the control loop, and spontaneous emission. Using feedback cooling to create degenerate sources with high coherence and low entropy enables new capabilities in precision measurement, atomtronics, and few- and many-body quantum physics.
We investigate the possibilities of distinguishing the mean-field and fluctuation effects on the critical temperature of a trapped Bose gas with repulsive interatomic interactions. Since in a direct measurement of the critical temperature as a function of the number of trapped atoms these effects are small compared to the ideal gas results, we propose to observe Bose-Einstein condensation by adiabatically ramping down the trapping frequency. Moreover, analyzing this adiabatic cooling scheme, we show that fluctuation effects can lead to the formation of a Bose-Einstein condensate at frequencies which are much larger than those predicted by the mean-field theory.