We investigate the fundamental viability of cooling ultracold atomic gases with quantum feedback control. Our Letter shows that the trade-off between the resolution and destructiveness of optical imaging techniques imposes constraints on the efficacy of feedback cooling, and that rapid rethermalization is necessary for cooling thermal gases. We construct a simple model to determine the limits to feedback cooling set by the visibility of density fluctuations, measurement-induced heating, and three-body atomic recombination. We demonstrate that feedback control can rapidly cool high-temperature thermal clouds in quasi-2D geometries to degenerate temperatures with minimal atom loss compared to traditional evaporation. Our analysis confirms the feasibility of feedback cooling ultracold atomic gases, providing a pathway to new regimes of cooling not achievable with current approaches.
We investigate the fundamental viability of cooling ultracold atomic gases with quantum feedback control. Our Letter shows that the trade-off between the resolution and destructiveness of optical imaging techniques imposes constraints on the efficacy of feedback cooling, and that rapid rethermalization is necessary for cooling thermal gases. We construct a simple model to determine the limits to feedback cooling set by the visibility of density fluctuations, measurement-induced heating, and three-body atomic recombination. We demonstrate that feedback control can rapidly cool high-temperature thermal clouds in quasi-2D geometries to degenerate temperatures with minimal atom loss compared to traditional evaporation. Our analysis confirms the feasibility of feedback cooling ultracold atomic gases, providing a pathway to new regimes of cooling not achievable with current approaches.
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.
Ultracold atomic Fermi gases are the leading platform for analogue quantum simulation, and provide a promising avenue to study the origin of high-temperature superconductivity in cuprates. However, current experimental approaches to cooling Fermi gases use evaporative cooling, which is limited by poor thermalisation properties of fermions and is non-number-conserving. This prevents the creation of useful analogue simulators of many collective phenomena. This thesis is the first theoretical investigation into the use of continuous-measurement feedback control as an alternative means of cooling an atomic Fermi gas. Since tractable simulation of Fermi gas dynamics requires simplifications to the full quantum field theory, we derive and simulate a fermionic equivalent to the Gross-Pitaevskii equation, generalising a model of feedback-controlled BECs by Haine et al. to multimode ultracold atomic Fermi gases. We demonstrate that in the absence of measurement effects, a suitable control can drive an interacting Fermi gas arbitrarily close to its ground state. However, although control schemes based upon damping spatial density fluctuations work well for single-spatial-mode BECs, we show that they perform poorly for Fermi gases with a large number of atoms due to counter-oscillation of multiple spatial modes, which must exist due to Pauli exclusion. We generalise a feedback-measurement model of BECs by Szigeti et al. to a multimode atomic Fermi gas, and perform stochastic simulations of measured, feedback-controlled fermions in the single-atom and many-atom mean-field limits. The effects of measurement backaction are an important consideration, since in a realistic experiment knowledge of the system state used for feedback must be obtained from measurement, leading to competition between measurement-induced heating and feedback cooling. We show that weaker and less precise measurements cool the system to a lower equilibrium excitation energy, but are unable to place practical lower bounds on measurement strength due to the lack of a system-filter separation. When measurement-induced heating is accounted for, we find that the equilibrium energy per particle scales superlinearly, suggesting that existing control schemes which work well for bosons would not be effective for fermions. In light of this, we propose several avenues of future investigation to overcome this limitation, leaving open the possibility of feedback control of atomic Fermi gases as a pathway to analogue quantum simulation.
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% condensate fraction and cooling it to 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.
Abstract. Recent experiments with ultracold neutral plasmas show an intrinsic heating effect based on the development of spatial correlations, which has been termed “correlation heating”. We investigate whether this effect can be reversed, so that imposing strong spatial correlations could in fact lead to cooling. We find that cooling is indeed possible. It requires, however, a very precise preparation of the initial state. Quantum mechanical zero-point motion sets a lower limit for cooling. PACS numbers: 32.80.Pj,52.27.Gr Submitted to: J. Phys. B: At. Mol. Opt. Phys. Letter to the Editor 2 Over the last two decades, techniques of cooling and trapping of ions and neutral atoms have made tremendous progress, making the regime of ultralow temperatures (T ≪ 1 K) accessible to experiment. Using sophisticated cooling schemes, temperatures far below 1µK have been realized, allowing, among many other applications, Bose-Einstein condensation of dilute atomic gases. Nevertheless, known cooling mechanisms either have a lower limit beyond which cooling is not possible (such as in “standard” laser cooling) or suffer from other drawbacks (such as loss of particles in evaporative
Feedback cooling plays a critical role in stabilizing quantum systems and achieving low temperatures, where a key question is to determine the fundamental thermodynamic limits on cooling performance. We establish a fundamental bound on quantum feedback cooling in Gaussian systems, by deriving a generalized second law of thermodynamics involving the kinetic temperatures of the system and a measure of quantum information flow obtained by continuous measurement. In contrast to previously known bounds, the obtained bound can be saturated by experimentally feasible situations using the quantum Kalman filter with a large feedback gain, where the cooling efficiency approaches its maximum. Our theoretical result is numerically demonstrated using parameters from an experiment of levitated nanoparticles. Our theory provides a general framework for understanding the thermodynamic constraints on quantum feedback cooling.