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Feedback control of atomic Fermi gases

Goh, Matthew

Published Jan 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.25911/5e5f75e3d05c3

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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%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.
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.
The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-Tc_cc​ superconductivity or the behaviour of neutron stars. Ultracold atomic systems can now be used to simulate model Hamiltonians of condensed matter or nuclear physics, in very well-controlled environnement. In this thesis, we have developed a general method to probe the thermodynamics of homogeneous quantum systems using trapped atomic gases. These measurements are directly compared to the predictions of theories of the quantum many-body problem. We have applied this technique to the spin-1/21/21/2 Fermi gas and the Bose with short-range interactions. Using fermionic 6^66Li, we explored a part of the wide parameter space by changing the interaction strength, the spin-population imbalance or the temperature of the gas. This system exhibits remarkably rich physics, such as normal/superfluid phase transitions (that can be of thermal or quantum character) or a Fermi liquid-type behaviour of the normal phase. We have also used this method to probe a Bose gas of 7^77Li atoms close to a Feshbach resonance. We have measured the Equation of State of the Bose gas as a function of interactions at very low temperature. For the first time, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground-state energy of the system, first predicted in 1957. We compared the experimental results to Quantum Monte-Carlo calculations. We have extended this study using out-of-equilibrium measurements of the Bose gas in the strongly interacting regime, which gives a first hint on the properties of the hypothetical unitary Bose gas.
Quantum optics and ultracold gases are established fields, but they almost do not overlap: the quantum nature of light is typically neglected in works on ultracold atoms. In our work the quantumness of both light and ultracold matter plays a key role. First, we show that light is a quantum nondemolition (QND) probe of many-body phases: they can be distinguished by correlations and full distribution functions (we consider bosons, fermions, and dipolar molecules). Light is not only sensitive to densities, but also to the matter-field interference. Second, we prove that the measurement backaction constitutes a novel source of competitions in many-body systems, especially, for non-QND cases. This leads to a plethora of new phenomena: oscillations of multipartite entangled modes, protection and break-up of fermion pairs, antiferromagnetic orders, long-range pair tunnelling and entanglement beyond Hubbard models. We prove that feedback control induces phase transitions and tunes their universality class. Third, the quantization of trapping potential (quantum optical lattices) leads to novel phases, including both density orders (supersolids, density waves) and bond orders of matter fields (superfluid and supersolid dimers, trimers). Results beyond ultracold atoms include: We extend the paradigm of feedback control from the state control to control of phase transitions. We present the measurement backaction as a novel source of competitions in many-body physics. We merge quantum Zeno dynamics and non-Hermitian physics and show a novel type of Zeno phenomena with Raman transitions beyond Zeno dynamics. We propose quantum simulators based on collective light-matter interaction. Our models can be applied to arrays of other systems (qubits). In general, quantum measurements and feedback produce new phenomena untypical to both closed unitary systems and open dissipative ones in many-body physics.
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.
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.