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Thermodynamics of ultracold Bose and Fermi gases

Nir Navon

Published Sep 9, 2011• 2 citations
OpenAlex

Abstract

The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-T$_c$ 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-$1/2$ Fermi gas and the Bose with short-range interactions. Using fermionic $^6$Li, 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 $^7$Li 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.

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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.
Ultracold dilute atomic gases can be considered as model systems to address some pending problem in Many-Body physics that occur in condensed matter systems, nuclear physics, and astrophysics. We have developed a general method to probe with high precision the thermodynamics of locally homogeneous ultracold Bose and Fermi gases. This method allows stringent tests of recent many-body theories. For attractive spin 1/2 fermions with tunable interaction (6Li), we will show that the gas thermodynamic properties can continuously change from those of weakly interacting Cooper pairs described by BardeenCooper-Schrieffer theory to those of strongly bound molecules undergoing Bose-Einstein condensation. First, we focus on the finite-temperature Equation of State (EoS) of the unpolarized unitary gas. Surprisingly, the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid phase transition. A detailed comparison with theories including Monte-Carlo calculations has revealed some surprises and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids are quantitatively measured for the first time. Despite orders of magnitude difference in density and temperature, our equation of state can be used to describe low density neutron matter such as the outer shell of neutron stars.
We will present recent experimental work on the thermodynamics of strongly interacting Fermi gases. We have developed a general method to probe with high precision the Equation of State (EoS) of locally homogeneous ultracold gases. This allows stringent tests of recent many-body theories. First, we focus on the finite-temperature EoS of the unpolarized unitary gas. Precise thermometry is provided by adding to the Fermi gas of 6Li a trace of bosonic 7Li. We show that the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid transition. Second, we address the zero-temperature EoS of the spin-polarized system in the BEC-BCS crossover. Surprisingly, despite strong interactions, the polarized phase behaves as a mixture of two ideal gases: a Fermi gas of majority atoms and a non-interacting gas of dressed quasi-particles, the Fermi polarons. We also obtain the equation of state of the superfluid state as a function of interaction strength, that we compare to Monte Carlo simulations and to the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids.
Complex Hamiltonians from condensed matter, such as the Fermi-Hubbard model, can be experimentally studied using ultracold gases. This thesis describes a new method for determining the equation of state of an ultracold gas, making the comparison with many-body theories straightforward. It is based on the measurement of the local pressure inside a trapped gas from the analysis of its in situ image. We first apply this method to the study of a Fermi gas with resonant interactions, a weakly-interacting 7Li gas acting as a thermometer. Surprisingly, none of the existing many-body theories of the unitary gas accounts for the equation of state deduced from our study over its full range. The virial expansion extracted from the high-temperature data agrees with the resolution of the three-body problem. At low temperature, we observe, contrary to some previous studies, that the normal phase behaves as a Fermi liquid. Finally we obtain the critical temperature for superfluidity from a clear signature on the equation of state. We also measure the pressure of the ground state as a function of spin imbalance and interaction strength -- measure directly relevant to describe the crust of neutron stars. Our data validate Monte-Carlo simulations and quantify the Lee-Huang-Yang corrections to mean-field interactions in low-density fermionic or bosonic superfluids. We show that, in most cases, the partially polarized normal phase can be described as a Fermi liquid of polarons. The polaron effective mass extracted from the equation of state is in agreement with a study of collective modes.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the sss-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
Abstract. We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of an harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature [1]. We compare our equation of state with an equation of state measured by the Tokyo group in [2], that reveals a significant difference in the high-temperature regime. The normal phase, at low temperature, is well described by a Landau Fermi liquid model, and we observe a clear thermodynamic signature of the superfluid transition. In a second part we apply the same procedure to Bose gases. From a single image of a quasi ideal Bose gas we determine the equation of state from the classical to the condensed regime. Finally the method is applied to a Bose gas in a 3D optical lattice in the Mott insulator regime. Our equation of state directly reveals the Mott insulator behavior and is suited to investigate finite-temperature effects. The equation of state of ultracold Bose and Fermi gases: a few examples 2
transition, critical parameters Abstract Strongly interacting Fermi gases provide a clean and controllable laboratory system for modeling strong interparticle interactions between fermions in nature, from high temperature superconductors to neutron matter and quark-gluon plasmas. Model-independent thermodynamic measurements, which do not require theoretical models for calibrations, are very important for exploring this important system experimentally, as they enable direct tests of predictions based on the best current non-perturbative many-body theories. At Duke University, we use all-optical methods to produce a strongly interacting Fermi gas of spin-1/2-up and spin-1/2-down 6 Li atoms that is magnetically tuned near a collisional (Feshbach) resonance. We conduct a series of measurements on the thermodynamic properties of this unique quantum gas, including the energy E, entropy S, and sound velocity c. Our model-independent measurements of E and S enable a precision study of the finite temperature thermodynamics. The E(S) data are directly compared to several recent predictions. The temperature in both the superfluid and normal fluid