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arXiv:cond-mat/0411626

Thermodynamic properties and phase transition of strongly interacting two-component Fermi gases

Hongwei Xiong, Shujuan Liu, Mingsheng Zhan

Published Nov 25, 2004• 0 citations
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Abstract

The thermodynamic properties of two-component Fermi gases with divergent scattering length is investigated and the transition temperature for the emergence of a stable dimeric gas is obtained by a simple theoretical model where the unique property of the dimers (i.e. fermionic atom pairs) with divergent scattering length is considered. Below the transition temperature, through the investigation of the overall entropy for the mixture gas of fermionic atoms and dimers, we calculate the relation between the energy and temperature of the system. In the limit of zero temperature, based on the chemical equilibrium condition, the fraction of the dimers is investigated and the role of the dimers in the collective excitations of the system is also discussed. It is found that our theoretical results agree with the condensate fraction, collective excitations, transition temperature and heat capacity investigated by the recent experiments about the strongly interacting two-component Fermi gases.

DOI
10.48550/arxiv.cond-mat/0411626

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The thermodynamic properties of two-component Fermi gases with divergent scattering length is investigated and the transition temperature for the emergence of a stable dimeric gas is obtained by a simple theoretical model where the unique property of the dimers (i.e. fermionic atom pairs) with divergent scattering length is considered. Below the transition temperature, through the investigation of the overall entropy for the mixture gas of fermionic atoms and dimers, we calculate the relation between the energy and temperature of the system. In the limit of zero temperature, based on the chemical equilibrium condition, the fraction of the dimers is investigated and the role of the dimers in the collective excitations of the system is also discussed. It is found that our theoretical results agree with the condensate fraction, collective excitations, transition temperature and heat capacity investigated by the recent experiments about the strongly interacting two-component Fermi gases.
Fermionic matter is ubiquitous in nature, from the electrons in metals and semiconductors or the neutrons in the inner crust of neutron stars, to gases of fermionic atoms, like 40K or 6Li that can be created and studied under laboratory conditions. It is especially interesting to study these systems at very low temperatures, where we enter the world of quantum mechanical phenomena. Due to the Fermi-Dirac statistics, a dilute system of spin-polarised fermions exhibits no interactions and can be viewed as an ideal Fermi gas. However, interactions play a crucial role for fermions of several spin species. This thesis addresses several questions concerning interacting Fermi gases, in particular the transition between the normal and the superfluid phase and dynamical properties at higher temperatures. First we will look at the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. This system is particularly interesting as it exhibits universal behaviour. Due to the strong interactions perturbation theory is inapplicable and no exact theoretical description is available. I will describe the Determinant Diagrammatic Monte Carlo algorithm with which the unitary Fermi gas can be studied from first principles. This algorithm fails in the presence of a spin imbalance (unequal number of particles in the two components) due to a sign problem. I will show how to apply reweighting techniques to generalise the algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. These are the first numerical results for the imbalanced unitary Fermi gas at finite temperature. I will also show how temperatures beyond the critical point can be accessed and present results for the equation of state and the temperature dependence of the contact density. At sufficiently high temperatures a semiclassical description captures all relevant physical features of the system. The dynamics of an interacting Fermi gas can then be studied via a numerical simulation of the Boltzmann equation. I will describe such a numerical setup and apply it to study the collision of two spin-polarised fermionic clouds. When the two components are separated in an elongated harmonic trap and then released, they collide and for sufficiently strong interactions can bounce off each other several times. I will discuss the different types of the qualitative behaviour, show how they can be interpreted in terms of the equilibrium properties of the system, and explain how they relate to the coupling between different excitation modes. I will also demonstrate how transport coefficients, for instance the spin drag, can be extracted from the numerical data.
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Strongly interacting gases of ultracold fermions have become an amazingly rich test-bed for many-body theories of fermionic matter. Here we present our recent experiments on these systems. Firstly, we discuss high-precision measurements on the thermodynamics of a strongly interacting Fermi gas across the superfluid transition. The onset of superfluidity is directly observed in the compressibility, the chemical potential, the entropy, and the heat capacity. Our measurements provide benchmarks for current many-body theories on strongly interacting fermions. Secondly, we have studied the evolution of fermion pairing from three to two dimensions in these gases, relating to the physics of layered superconductors. In the presence of p-wave interactions, Fermi gases are predicted to display toplogical superfluidity carrying Majorana edge states. Two possible avenues in this direction are discussed, our creation and direct observation of spin-orbit coupling in Fermi gases and the creation of fermionic molecules of 23Na 40K that will feature strong dipolar interactions in their absolute ground state.