We theoretically investigate the isothermal compressibility $κ_{T}$ in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent $T$-matrix approximation (SCTMA), we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While $κ_T$ in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect $κ_T$ near the superfluid phase transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multi-body correlations between Cooper-pair molecules.
We apply the global thermodynamic variables approach to experimentally determine the isothermal compressibility parameter $κ_T$ of a trapped Bose gas across the phase transition. We demonstrate the behavior of $κ_T$ around the critical pressure, revealing the second order nature of the phase transition. Compressibility is the most important susceptibility to characterize the system. The use of global variables shows advantages with respect to the usual local density approximation method and can be applied to a broad range of situations.
Fermi gases with repulsive interactions are characterized by measuring their compressibility as a function of interaction strength. The compressibility is obtained from in-trap density distributions monitored by phase contrast imaging. For interaction parameters k_F a > 0.25 fast decay of the gas prevents the observation of equilibrium profiles. For smaller interaction parameters, the results are adequately described by first-order perturbation theory. A novel phase contrast imaging method compensates for dispersive distortions of the images.
We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in-situ imaging to extract the central density of the gas, and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interacti…
The spin-orbit coupling (SOC) in degenerate Fermi gases can fundamentally change the fate of $s$-wave superfluids with strong Zeeman field and give rise to topological superfluids and associated Majorana zero modes. It also dramatically changes the thermodynamic properties of the superfluids. Here we report the anomalous isothermal compressibility $κ_T$ in this superfluids with both SOC and Zeeman field. We formulate this quantity from the Gibbs-Duhem equation and show that the contribution of $κ_T$ comes from the explicit contribution of chemical potential and implicit contribution of order p…
We discuss the thermodynamic signatures for the topological phase transitions into Majorana and Weyl superfluid phases in ultracold Fermi gases in two and three dimensions in the presence of Rashba spin-orbit coupling and a Zeeman field. We analyze the thermodynamic properties exhibiting the distinct nature of the topological phase transitions linked with the Majorana fermions (2D Fermi gas) and Weyl fermions (3D Fermi gas) which can be observed experimentally, including pressure, chemical potential, isothermal compressibility, entropy, and specific heat, as a function of the interaction and t…
We describe the relation between the isothermal atomic compressibility and density fluctuations in mixtures of two-component fermions with population or mass imbalance. We derive a generalized version of the fluctuation-dissipation theorem which is valid for both balanced and imbalanced Fermi-Fermi mixtures. Furthermore, we show that the compressibility, its critical exponents, and phase boundaries can be extracted via an analysis of the density fluctuations as a function of population imbalance, interaction parameter or temperature. Lastly, we demonstrate that in the presence of trapping pote…
We describe the relation between the isothermal atomic compressibility and density fluctuations in mixtures of two-component fermions with population or mass imbalance. We derive a generalized version of the fluctuation-dissipation theorem which is valid for both balanced and imbalanced Fermi-Fermi mixtures. Furthermore, we show that critical exponents for the compressibility can be extracted via an analysis of the density fluctuations when phase transitions occur as a function of population imbalance or interaction parameter. In addition, we demonstrate that in the presence of trapping potent…
Itinerant ferromagnetism in cold Fermi gases with repulsive interactions is studied applying the Jastrow-Slater approximation generalized to finite polarization and temperature. For two components at zero temperature a second order transition is found at $ak_F\simeq0.90$ compatible with QMC. Thermodynamic functions and observables such as the compressibility and spin susceptibility and the resulting fluctuations in number and spin are calculated. For trapped gases the resulting cloud radii and kinetic energies are calculated and compared to recent experiments. Spin polarized systems are recomm…
We present a direct measurement of the density profile of a two-dimensional Mott Insulator formed by ultracold atoms in an optical lattice. High resolution absorption imaging is used to probe the "wedding-cake" structure of a trapped gas as it crosses the boundary from a unit-filled Mott insulating phase to the superfluid phase at finite temperature. Detailed analysis of images yields measurements of temperature and local compressibility; for the latter we observe a strong suppression deep in the Mott-insulating phase, which is recovered for the superfluid and normal phases. Furthermore, we me…
We analyze theoretically the transport properties of a weakly-interacting ultracold Bose gas enclosed in two reservoirs connected by a constriction. We assume that the transport of the superfluid part is hydrodynamic, and we describe the ballistic transport of the normal part using the Landauer-Buttiker formalism. Modeling the coupled evolution of the phase, atom number, and temperature mismatches between the reservoirs, we predict that Helmholtz (plasma) oscillations, induced by an initial imbalance in atom numbers, can be observed at non-zero temperatures below Tc. We show that, because of i…
We have theoretically studied the effect of disorder on ultracold alkaline-earth atoms governed by the Kondo lattice model in an optical lattice via simplified double-well model and hybridization mean-field theory. Disorder-induced narrowing and even complete closure of hybridization gap have been predicted and the compressibility of the system has also been investigated for metallic and Kondo insulator phases in the presence of the disordered potential. To make connection to the experimental situation, we have numerically solved the disordered Kondo lattice model with an external harmonic tra…
We study the effects of anisotropic hopping amplitudes on quantum phases of ultracold fermions in optical lattices described by the repulsive Fermi-Hubbard model. In particular, using dynamical mean-field theory (DMFT) we investigate the dimensional crossover between the isotropic square and the isotropic cubic lattice. We analyze the phase transition from the antiferromagnetic to the paramagnetic state and observe a significant change in the critical temperature: Depending on the interaction strength, the anisotropy can lead to both a suppression or increase. We also investigate the localizat…
Recent experimental progresses allow for exploring some important physical quantities of ultracold Fermi gases, such as the compressibility, spin susceptibility, viscosity, optical conductivity and spin diffusivity. Theoretically, these quantities can be evaluated from suitable linear response theories. For BCS superfluid, it has been found that the gauge invariant linear response theories can be fully consistent with some stringent consistency constraints. When the theory is generalized to stronger-than-BCS regime, one may meet serious difficulties to satisfy the gauge invariance conditions. …
A one-dimensional Bose-Einstein condensate may experience nonlinear periodic modulations known as "cnoidal waves". We argue that such structures represent promising candidates for the study of supersolidity-related phenomena in a non-equilibrium state. A mean-field treatment makes it possible to rederive Leggett's formula for the superfluid fraction of the system and to estimate it analytically. We determine the excitation spectrum, for which we obtain analytical results in the two opposite limiting cases of (i) a linearly modulated background and (ii) a train of dark solitons. The presence of…
The mechanism of fermionic pairing is the key to understanding various phenomena such as high-temperature superconductivity and the pseudogap phase in cuprate materials. We study the pair correlations in the attractive Hubbard model using ultracold fermions in a two-dimensional optical lattice. By combining the fluctuation-dissipation theorem and the compressibility equation of state, we extract the interacting pair correlation functions and deduce a characteristic length scale of pairs as a function of interaction and density filling. At sufficiently low filling and weak on-site interaction, …
We investigate the thermodynamic properties of a superfluid Fermi gas subject to Rashba spin-orbit coupling and effective Zeeman field. We adopt a T-matrix scheme that takes beyond-mean-field effects, which are important for strongly interacting systems, into account. We focus on the calculation of two important quantities: the superfluid transition temperature and the isothermal compressibility. Our calculation shows very distinct influences of the out-of-plane and the in-plane Zeeman fields on the Fermi gas. We also confirm that the in-plane Zeeman field induces a Fulde-Ferrell superfluid be…
We calculate the renormalized Fermi surface and the quasiparticle properties in the Fermi liquid phase of three-dimensional dipolar fermions to second order in the dipole-dipole interaction. Using parameters relevant to an ultracold gas of erbium atoms, we find that the second-order corrections typically renormalize the Hartree-Fock results by less than one percent. On the other hand, if we use the second-order correction to the compressibility to estimate the regime of stability of the system, the point of instability is already reached for a significantly smaller interaction strength than in…
We discuss the evolution from BCS to BEC superfluids in the presence of spin-orbit coupling, and show that this evolution is just a crossover in the balanced case. The dependence of several thermodynamic properties, such as the chemical potential, order parameter, pressure, entropy, isothermal compressibility and spin susceptibility tensor on the spin-orbit coupling and interaction parameter at low temperatures are analyzed. We studied both the case of equal Rashba and Dresselhaus (ERD) and the Rashba-only (RO) spin-orbit coupling. Comparisons between the two cases reveal several striking diff…
We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state. This directly confirms Pauli blocking in momentum space. For the spin-balanced unitary Fermi gas, we observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid tran…
By a novel reciprocal space analysis of the measurement, we report a calibrated in situ observation of the bunching effect in a 3D ultracold gas. The calibrated measurement with no free parameters confirms the role of the exchange symmetry and the Hanbury Brown-Twiss effect in the bunching. Also, the enhanced fluctuations of the bunching effect give a quantitative measure of the increased isothermal compressibility. We use 2D images to probe the 3D gas, using the same principle by which computerized tomography reconstructs a 3D image of a body. The powerful reciprocal space technique presented…
We investigate thermodynamics and quantum criticality of strongly attractive Fermi gases confined in a one-dimensional (1D) harmonic trap. Finite temperature density profiles, entropy, compressibility and susceptibility of the trapped gas are studied using analytic results for the thermodynamics within the local density approximation. We demonstrate that current experiments are capable of measuring universal Tomonaga-Luttinger liquid physics and quantum criticality of 1D strongly interacting Fermi gases. The results provide insights on recent measurements of key features of the phase diagram o…
Using a multiple-image reconstruction method applied to a harmonically trapped Bose gas, we determine the equation of state of uniform matter across the critical transition point, within the local density approximation. Our experimental results provide the canonical description of pressure as a function of the specific volume, emphasizing the dramatic deviations from the ideal Bose gas behavior caused by interactions. They also provide clear evidence for the non-monotonic behavior with temperature of the chemical potential, which is a consequence of superfluidity. The measured thermodynamic qu…
We discuss the thermodynamics of a non-relativistic gas of bosons with a local repulsive interaction. In particular, we compute the temperature and density dependence of pressure, energy and entropy-density, superfluid and condensate-fraction, correlation length, specific heat, isothermal and adiabatic compressibility and various sound velocities. The T->0 limit approaches the quantum phase transition, while the universal critical behavior of a classical second order phase transition in the O(2) universality class determines the region around the critical temperature. Our non-perturbative flow…
The effects of low dimensionality on the thermodynamics of a Fermi gas trapped by isotropic power law potentials are analyzed. Particular attention is given to different characteristic temperatures that emerge, at low dimensionality, in the thermodynamic functions of state and in the thermodynamic susceptibilities (isothermal compressibility and specific heat). An energy-entropy argument that physically favors the relevance of one of these characteristic temperatures, namely, the non vanishing temperature at which the chemical potential reaches the Fermi energy value, is presented. Such an arg…
The thermodynamic properties of a nonrelativistic free-electron Fermi gas is of fundamental interest in condensed matter physics. Properties previously studied in three-dimensions (3D) in the low- and high-temperature limits include the internal energy, heat capacity, zero-field magnetic spin susceptibility, and pressure. Here we report solutions for the temperature dependence spanning these two temperature regimes of the chemical potential, internal energy, magnetic susceptibility, and the heat capacity at constant volume in 1D, 2D, and 3D. Also calculated are the pressure, enthalpy, heat cap…
