Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2206.05069

Feedback cooling Bose gases to quantum degeneracy

Matthew L. Goh, Zain Mehdi, Taylor, Richard L., Thomas, Ryan J., Ashton S. Bradley, Michael Hush, J. J. Hope, Stuart S. Szigeti

Published Jun 10, 2022• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2206.05069

Related papers

A perturbative model for the feedback cooling of finite temperature Bose gases

Matthew J. Blacker

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 $93.5 \pm 1\%$. 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.

•Jan 1, 2020•0 citations

Fundamental Limits of Feedback Cooling Ultracold Atomic Gases

Zain Mehdi, Simon A. Haine, J. J. Hope +1 more

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.

arXiv:2306.09846•Physical Review Letters•Aug 13, 2024•3 citations

An ultracold Bose-Einstein condensate in steady state

Chun-Chia Chen, Rodrigo González Escudero, Jiří Minář +3 more

Quantum degenerate atomic gases are prominent platforms for quantum simulation and high precision sensing. A key challenge for these applications is intrinsic atom loss, which limits quantum gas lifetimes to typically tens of seconds. Here we create a Bose-Einstein condensate of $^{84}\mathrm{Sr}$ atoms that is sustained in steady state for minutes. We achieve this by guiding a continuous stream of Sr gas through a sequence of spatially separated laser cooling stages, until it reaches the condensate's location, which we protect against harmful laser cooling photons. This steady-state quantum degenerate gas paves the way to design and study novel driven-dissipative, non-equilibrium quantum systems, and overcomes a key bottleneck in the realization of a continuous-wave atom laser.

•Dec 14, 2020•1 citation

Feedback control of atomic Fermi gases

Goh, Matthew

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.

•Jan 1, 2019•0 citations

Experiments with Ultracold Quantum-degenerate Fermionic Lithium Atoms

Wolfgang Ketterle

Experimental methods of laser and evaporative cooling, used in the production of atomic Bose-Einstein condensates have recently been extended to realize quantum degeneracy in trapped Fermi gases. Fermi gases are a new rich system to explore the implications of Pauli exclusion on scattering properties of the system, and ultimately fermionic superfluidity. We have produced a new macroscopic quantum system, in which a degenerate Li-6 Fermi gas coexists with a large and stable Na-23 BEC. This was accomplished using inter-species sympathetic cooling of fermionic 6Li in a thermal bath of bosonic Na-23. We have achieved high numbers of both fermions (less than 10(exp 5) and bosons (less than 10(exp 6), and Li-6 quantum degeneracy corresponding to one half of the Fermi temperature. This is the first time that a Fermi sea was produced with a condensate as a "refrigerator".

•Jan 1, 2003•0 citations

Creation of a Bose-condensed gas of ⁸⁷Rb by laser cooling

Jiazhong Hu, Alban Urvoy, Zachary Vendeiro +3 more

Protocols for attaining quantum degeneracy in atomic gases almost exclusively rely on evaporative cooling, a time-consuming final step associated with substantial atom loss. We demonstrate direct laser cooling of a gas of rubidium-87 (⁸⁷Rb) atoms to quantum degeneracy. The method is fast and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of compression to increase the density, followed by Raman sideband cooling to decrease the temperature. From a starting number of 2000 atoms, 1400 atoms reach quantum degeneracy in 300 milliseconds, as confirmed by a bimodal velocity distribution. The method should be broadly applicable to many bosonic and fermionic species and to systems where evaporative cooling is not possible.

•Nov 1, 2017•14 citations
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.
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.
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.
Quantum degenerate atomic gases are prominent platforms for quantum simulation and high precision sensing. A key challenge for these applications is intrinsic atom loss, which limits quantum gas lifetimes to typically tens of seconds. Here we create a Bose-Einstein condensate of 84Sr^{84}\mathrm{Sr}84Sr atoms that is sustained in steady state for minutes. We achieve this by guiding a continuous stream of Sr gas through a sequence of spatially separated laser cooling stages, until it reaches the condensate's location, which we protect against harmful laser cooling photons. This steady-state quantum degenerate gas paves the way to design and study novel driven-dissipative, non-equilibrium quantum systems, and overcomes a key bottleneck in the realization of a continuous-wave atom laser.
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.
Experimental methods of laser and evaporative cooling, used in the production of atomic Bose-Einstein condensates have recently been extended to realize quantum degeneracy in trapped Fermi gases. Fermi gases are a new rich system to explore the implications of Pauli exclusion on scattering properties of the system, and ultimately fermionic superfluidity. We have produced a new macroscopic quantum system, in which a degenerate Li-6 Fermi gas coexists with a large and stable Na-23 BEC. This was accomplished using inter-species sympathetic cooling of fermionic 6Li in a thermal bath of bosonic Na-23. We have achieved high numbers of both fermions (less than 10(exp 5) and bosons (less than 10(exp 6), and Li-6 quantum degeneracy corresponding to one half of the Fermi temperature. This is the first time that a Fermi sea was produced with a condensate as a "refrigerator".
Protocols for attaining quantum degeneracy in atomic gases almost exclusively rely on evaporative cooling, a time-consuming final step associated with substantial atom loss. We demonstrate direct laser cooling of a gas of rubidium-87 (⁸⁷Rb) atoms to quantum degeneracy. The method is fast and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of compression to increase the density, followed by Raman sideband cooling to decrease the temperature. From a starting number of 2000 atoms, 1400 atoms reach quantum degeneracy in 300 milliseconds, as confirmed by a bimodal velocity distribution. The method should be broadly applicable to many bosonic and fermionic species and to systems where evaporative cooling is not possible.