The properties of two-component Fermi gases with zero-range interactions are universal. We use an explicitly correlated Gaussian basis set expansion approach to investigate small equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement. At unitarity, we determine the ground state energy for systems with up to ten particles interacting through finite-range two-body potentials for both even and odd number of particles. We extrapolate the energies to the zero-range limit using a novel scheme that removes the linear and, in some cases, also the quadratic dependence of the ground state energies on the two-body range. Our extrapolated zero-range energies are compared with results from the literature. We also calculate the two-body Tan contact and structural properties.
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases which are trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in $d=3$ and $d=2$. But more importantly we found that, the virial coefficients of bosons and fermions become equal (except the the second virial coefficient, where the sign is different) when we trap the gases under harmonic potential in $d=1$. This result suggests the equivalence between Bose and Fermi gases which is a…
We study the scissors modes of dipolar boson and fermion gases trapped in a spherically symmetric potential. We use the harmonic oscillator states to solve the time-dependent Gross-Pitaevskii equation for bosons and the time-dependent Hartree-Fock equation for fermions. It is pointed out that the scissors modes of bosons and fermions can be of quite different nature.
A unified description for the Bose and Fermi gases trapped in an external generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ is presented using the grandpotential of the system in $d$ dimensional space. The thermodynamic quantities of the quantum gases are derived from the grand potential. An equivalence between the trapped Bose and Fermi gases is constructed in one dimension ($d=1$) using the Landen relation. It is also found that the established equivalence between the ideal free Bose and Fermi gases in $d=2$ (M. H. Lee, Phys. Rev. E 55, 1518 (1997)) is lost when exter…
We develop a practical Hartree-Fock theory for trapped Bose and Fermi gases that interact with dipole-dipole interactions. This theory is applicable at zero and finite temperature. Our approach is based on the introduction of local momentum distortion fields that characterize the exchange effects in terms of a local effective potential. We validate our theory against existing theories, finding excellent agreement with full Hartree-Fock calculations.
We consider two separated pancake-shaped trapped gases interacting with a dipolar (either magnetic or electric) force. We study how the center of mass motion propagates from one cloud to the other as a consequence of the long-range nature of the interaction. The corresponding dynamics is fixed by the frequency difference between the in-phase and the out-of-phase center of mass modes of the two clouds, whose dependence on the dipolar interaction strength and the cloud separation is explicitly investigated. We discuss Fermi gases in the degenerate as well as in the classical limit and comment on…
Yoram Alhassid conjectured that the total energy of a harmonically trapped two-component Fermi gas with large scattering length is a linear functional of the occupation probabilities of single-particle energy eigenstates. We confirm his conjecture and derive the functional explicitly. We show that the functional applies to ALL smooth potentials having a minimum, not just harmonic traps. We also calculate the occupation probabilities of high energy states.
Ultracold atomic gases can be spined up either by confining them in rotating frame, or by introducing ``synthetic" magnetic field. In this paper, thermodynamics of rotating ideal Bose gases are investigated within truncated-summation approach which keeps to take into account the discrete nature of energy levels, rather than to approximate the summation over single-particle energy levels by an integral as does in semi-classical approximation. Our results show that Bose gases in rotating frame exhibit much stronger dependence on rotation frequency than those in ``synthetic" magnetic field. Conse…
We study the virial relations for ultracold trapped two component Fermi gases in the case of short finite range interactions. Numerical verifications for such relations are reported through the BCS-BEC crossover. As an intermediate step, it is necessary to evaluate the partial derivatives of the many body energy with respect to the inverse of the scattering length and with respect to the interaction range. They are found to have extreme values at the unitary limit. The virial results are used to check the quality of the variational wave function involved in the calculations.
We theoretically investigate the pair-superfluid phase of two-component ultracold gases with negative inter-species interactions in an optical lattice. We establish the phase diagram for filling $n=1$ at zero and finite temperature, by applying Bosonic Dynamical Mean-Field Theory, and confirm the stability of pair-superfluidity for asymmetric hopping of the two species. While the pair superfluid is found to be robust in the presence of a harmonic trap, we observe that it is destroyed already by a small population imbalance of the two species.
We theoretically address magnetic ordering at zero and finite temperature in both homogeneous and trapped Bose-Bose mixtures in optical lattices. By using Bosonic Dynamical Mean-Field Theory, we obtain the phase diagram of the homogeneous two-component Bose-Hubbard model in a three-dimensional (3D) cubic lattice, which features competing magnetic order of XY-ferromagnetic and anti-ferromagnetic type in addition to the Mott and superfluid states. We show that these magnetic phases persist also in the presence of a harmonic trap.
We analyze the macroscopic dynamics of a Bose gas axially confined in an optical lattice with a superimposed harmonic trap, taking into account weak tunneling effect. Our results show that upon transition to the quasi-two-dimensional (2D) regime of the trapped gas, the 3D equation of state and equilibrium density profile acquire corrections from 2D many-body effects. The corresponding frequency shift in the transverse breathing mode is accessible within current facilities, suggesting a direct observation of dimensional effects. Comparisons with other relevant effects are also presented.
An expression for the dynamic density response function has been obtained for an interacting quantum gas in Random Phase Approximation (RPA) including first order self and exchange contribution. It involves the single particle wave functions and eigen values. The expression simplifies when diagonal elements are considered. The diagonal elements of the imaginary part of Fourier transformed response function is relevant in the measurement of Bragg scattering cross-section and in several other applications.
We show that there exists the inverse Kibble-Zurek scenario, when we start with an equilibrium system with broken symmetry and, by imposing perturbations, transform it to a strongly nonequilibrium symmetric state through the sequence of states with spontaneously arising topological defects. We demonstrate the inverse Kibble-Zurek scenario both experimentally, by perturbing the Bose-Einstein condensate of trapped $^{87}$Rb atoms, and also by accomplishing numerical simulations for the same setup as in the experiment, the experimental and numerical results being in good agreement with each other…
It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One such example is the strongly-interacting Fermi gas with two imbalanced spin species, which has received a great amount of attention due to the possible presence of exotic superfluid phases. By employing novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov de-Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the v…
The highly controllable ultracold atoms in a one-dimensional (1D) trap provide a new platform for the ultimate simulation of quantum magnetism. In this regard, the Neel-antiferromagnetism and the itinerant ferromagnetism are of central importance and great interest. Here we show that these magnetic orders can be achieved in the strongly interacting spin-1/2 trapped Fermi gases with additional p-wave interactions. In this strong coupling limit, the 1D trapped Fermi gas exhibit an effective Heisenberg spin XXZ chain in the anisotropic p-wave scattering channels. For a particular p-wave attractio…
We show that the Bose-Hubbard Model exhibits an increase in density with temperature at fixed pressure in the regular fluid regime and in the superfluid phase. The anomaly at the Bose-Einstein condensate is the first density anomaly observed in a quantum state. We propose that the mechanism underlying both the normal phase and the superfluid phase anomalies is related to zero point entropies and ground state phase transitions. A connection with the typical experimental scales and setups is also addressed. This key finding opens a new pathway for theoretical and experimental studies of water-li…
I study vortex ring oscillations in a superfluid, trapped in an elongated trap, under the conditions of the Local Density Approximation. On the basis of the Hamiltonian formalism I develop a hydrodynamic theory, which is valid for an arbitrary superfluid and depends only on the equation of state. The problem is reduced to an ordinary differential equation for the ring radius. The cases of the dilute BEC and the Fermi gas at unitarity are investigated in detail. Simple analytical equations for the periods of small oscillations are obtained and the equations of non-linear dynamics are solved in …
Trapped two-component Fermi gases allow for the investigation of the so-called BCS-BEC crossover by tuning the interspecies atom-atom $s$-wave scattering length scattering $a^{(aa)}$ from attractive to repulsive, including vanishing and infinitely large values. Here, we numerically determine the energy spectrum of the equal-mass spin-balanced four-fermion system---the smallest few-particle system that exhibits BCS-BEC crossover-like behavior---as a function of $a^{(aa)}$ using the stochastic variational approach. For comparative purposes, we also treat the two- and three-particle systems. Stat…
By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time…
We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction $D/r^3$ favors an equilateral triangular arrangement of the molecules, which competes against the square symmetry of the underlying optical lattice with lattice constant $b$ and amplitude $V$. We find the minimal-energy states at the commensurate density $n = 1/b^2$ and establish the complete square-to-triangular transformation pathway of the lattice with decreasing $V$ involving period-doubled, solitonic, and distorted-triangular conf…
We study the transition from hydrodynamic to collisionless behavior in collective modes of ultracold trapped Fermi gases. To that end, we solve the Boltzmann equation for the trapped Fermi gas via the moments method. We showed previously that it is necessary to go beyond second-order moments if one wants to reproduce the results of a numerical solution of the Boltzmann equation. Here, we will give the detailed description of the method including fourth-order moments. We apply this method to the case of realistic parameters, and compare the results for the radial quadrupole and scissors modes a…
Trapped degenerate dipolar Bose and Fermi gases of cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose-Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using variational approximation and numerical solution of a mean-field model. In the disk shape, with the polarization vector perpendicular to the plane of the disk, the atoms experience an overall dipolar repulsion and this fact sho…
We study a harmonically confined atomic gas which is subjected to an additional external potential such as an optical lattice. Using a linear response formulation, we determine the response of the gas to a small, time-dependent displacement of the harmonic trap and derive a simple exact relation showing that the centre-of-mass position of the atomic cloud is directly related to the global optical conductivity of the system. We demonstrate the usefulness of this approach by calculating the optical conductivity of bosonic atoms in an optical lattice. In the Mott insulating phase, there is clear …
We examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. Direct interactions give rise to position space magnetostriction and exchange interactions give rise to momentum space magnetostriction. While the position space magnetostriction is similar in Bose and Fermi systems, the momentum space magnetostriction is markedly different: the Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short range correlations between the particles we discuss the …
We report on previously unobserved inter-system degeneracies in two-component equal-mass Fermi gases with interspecies zero-range interactions under isotropic harmonic confinement. Over the past 10 years, two-component Fermi gases consisting of $n_1$ spin-up and $n_2$ spin-down atoms with interspecies zero-range interactions have become a paradigm for modeling condensed matter systems, nuclear matter and neutron matter. We show that the eigen energies of the $(n_1+1,n_2-1)$ system are degenerate with the eigen energies of the $(n_1,n_2)$ system for any s-wave scattering length $a_s$, including…
We have studied the exotic superfluid phases of degenerated Fermi gases with spin-orbit coupling in a mixed dimensional system, where the motion of atoms are free in the x-direction and the tunneling between nearest tubes in the y-direction is permitted. Using the mean-field method, we obtain the phase diagrams of the system during the dimensional crossover between quasi one dimension to quasi two dimension. We find the existence of the topological state and Majorana edge mode in the weak tunneling case, and a rich phase diagram including two kinds of nodal superfluid phase and gapped superflu…
The striped state of ultracold bosons with Rashba spin-orbit coupling in a homogeneous infinite system has, as we show, a constant particle flow, which in a finite-size system would accumulate particles at the boundaries; it is thus not a physical steady state of the system. We propose, as a variational ansatz, a condensate wave function for a weakly trapped system which behaves similarly to the striped state near the center, but does not have particle flow at the boundaries. This state has a line of unquantized coreless vortices. We show, by minimizing the total energy, that our modified stri…
We theoretically study an interacting few-body system of Rashba spin-orbit coupled two-component Bose gases confined in a harmonic trapping potential. We solve the interacting Hamiltonian at large Rashba coupling strengths using Exact Diagonalization scheme, and obtain the ground state phase diagram for a range of interatomic interactions and particle numbers. At small particle numbers, we observe that the bosons condense to an array of topological states with n+1/2 quantum angular momentum vortex configurations, where n = 0, 1, 2, 3... At large particle numbers, we observe two distinct regime…
A system of identical bosons with short-range (contact) interactions is studied. Their motion is confined to one dimension by a tight lateral trapping potential and, additionally, subject to a weak harmonic confinement in the longitudinal direction. Finite delay time associated with penetration of quantum particles through each other in the course of a pairwise one-dimensional collision in the presence of the longitudinal potential makes the system non-integrable and, hence, provides a mechanism for relaxation to thermal equilibrium. To analyse this effect quantitatively in the limit of a non-…
We investigate the Zel'dovich effect in the context of ultra-cold, harmonically trapped quantum gases. We suggest that currently available experimental techniques in cold-atoms research offer an exciting opportunity for a direct observation of the Zel'dovich effect without the difficulties imposed by conventional condensed matter and nuclear physics studies. We also demonstrate an interesting scaling symmetry in the level rearragements which has heretofore gone unnoticed.
We measure the temporal pair correlation function $g^{(2)}(τ)$ of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed {\it in situ} using a local, time-resolved single-atom sensitive probing technique. Third and fourth order correlation functions are also extracted. We develop a theoretical model and compare it with our experimental data, finding good quantitative agreement and highlighting the role of interactions. Our results promote temporal correlations as new observables to study the dynamics of ultracold quantum ga…
The problem of particle fluctuations in arbitrary nonuniform systems with Bose-Einstein condensate is considered. This includes the case of trapped Bose atoms. It is shown that the correct description of particle fluctuations for any nonuniform system of interacting atoms always results in thermodynamically normal fluctuations.
Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of non-hydrodynamic modes. We review non-hydrodynamic modes in kinetic theory and gauge/gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data, we find hints of non-hydrodynamic modes in cold Fermi gases in two and three dimensions.
We present a dispersive imaging method for trapped quantum gases based on digital off-axis holography. Both phase delay and intensity of the probe field are determined from the same image. Due to the heterodyne gain inherent to the holographic method it is possible to retrieve the phase delay induced by the atoms at probe beam doses two orders of magnitude lower than phase-contrast imaging methods. Using the full field of the probe beam we numerically correct for image defocusing.
We use the Bogoliubov-de Gennes formalism to analyze harmonically trapped Fermi gases with Rashba-type spin-orbit coupling in two dimensions. We consider both population-balanced and -imbalanced Fermi gases throughout the BCS-BEC evolution, and study the effects of spin-orbit coupling on the spontaneously induced countercirculating mass currents and the associated intrinsic angular momentum. In particular, we find that even a small spin-orbit coupling destabilizes Fulde-Ferrel-Larkin-Ovchinnikov (FFLO)-type spatially modulated superfluid phases as well as the phase-separated states against the…
We find a new physical regime in the trapped Bose-Hubbard Hamiltonian using time-evolving block decimation. Between Mott-insulating and superfluid phases, the latter induced by trap compression, a spatially self-organized state appears in which non-local entropy signals entanglement between spatially distant superfluid shells. We suggest a linear rather than harmonic potential as an ideal way to observe such a self-organized system. We also explore both quantum information and thermal entropies in the superfluid regime, finding that while the former follows the density closely the latter can b…
We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose and Fermi gases with the short ranged (Fermi-Huang $δ^3_p$ [1]) interactions among the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature dependence in this regard. Coherent scattering even by a single boson or fermion in the finite geometry gives rise to new tool of determining energy eigenstate of the scatterer. Our predictions on the differential scattering cross-sections, can be tested within the present day experimental …
The prospect of controlling entanglement in interacting quantum systems offers a myriad of technological and scientific promises, given the progress in experimental studies in systems such as ultracold trapped gases. This control is often challenging because of decoherence, the process by which environmental interactions create spurious entanglements that can destroy the desired entanglement. Considering the collisional decoherence that is relevant for quantum measurements utilizing scattering in one-dimensional trapped gases, here we derive a relationship between particle masses and wave pack…
For the quantum kinetic system modelling the Bose-Einstein Condensate that accounts for interactions between condensate and excited atoms, we use the Chapman-Enskog expansion to derive its hydrodynamic approximations, include both Euler and Navier-Stokes approximations. The hydrodynamic approximations describe not only the macroscopic behavior of the BEC but also its coupling with the non-condensates, which agrees with Landau's two fluid theory.
We calculate the energy and the condensate fraction of a system of trapped bosons interacting via a short-range two-body potential with positive scattering length. The potential is attractive and has a two-body bound state. When the scattering length is small compared to the trap length the system is model independent: all potential models -- attractive, repulsive and zero-range -- provide similar results. When the scattering length is large the attractive model differs qualitatively from the repulsive and zero-range models. In this regime the system with attractive potential becomes independe…
We compute the fraction of closed-channel molecules in trapped atomic Fermi gases, over the entire range of accessible fields and temperatures. We use a two-channel model of BCS--Bose-Einstein condensation (BEC) crossover theory at general temperature $T$, and show that this fraction provides a measure of the $T$ dependent pairing gap. Our calculations, containing no free parameters, are in good quantitative agreement with recent low $T$ measurements in $^6$Li. We present readily testable predictions for the dependencies of the closed-channel fraction on temperature and Fermi momentum.
We address recent momentum resolved radio frequency (RF) experiments on ultracold trapped Fermi gases of $^{40}$K. We show that momentum resolved RF probes provide measurements of the centrally important fermionic spectral function. They also serve to remove ambiguity plaguing the interpretation of momentum integrated RF experiments by establishing a clear dispersion signature of pairing. We find that the temperature dependence of the spectral function is dramatic at unitarity, and, importantly, smooth from above to below $T_c$ throughout BCS-BEC crossover. This should be tested experimentally…
Density correlations unambiguously reveal the quantum nature of matter. Here, we study correlations between measurements of density in cold-atom clouds at different times at one position, and also at two separated positions. We take into account the effects of finite-size and -duration measurements made by light beams passing through the atom cloud. We specialise to the case of Bose gases in harmonic traps above critical temperature, for weakly-perturbative measurements. For overlapping measurement regions, shot-noise correlations revive after a trap oscillation period. For non-overlapping reg…
We present phase diagrams for population imbalanced, trapped Fermi superfluids near unitarity. In addition to providing quantitative values for the superfluid transition temperature, the pairing onset temperature and the transition line (separating the Sarma and phase separation regimes), we study experimental signatures of these transitions based on density profiles and density differences at the center. Predictions on the BCS side of resonance show unexpected behavior, which should be searched for experimentally.
Trapped ultracold Fermi gases provide a system that can be tuned between the BCS and BEC regimes by means of a magnetic-field Feshbach resonance. Condensation of fermionic atom pairs in a $^{40}$K gas was demonstrated experimentally by a sweep technique that pairwise projects fermionic atoms onto molecules. In this paper we examine previous data obtained with this technique that probed the phase boundary in the temperature-magnetic field plane. Comparison of the $^{40}$K data to a theoretically computed phase diagram demonstrates good agreement between the two.
We study the finite temperature $T$ behavior of trapped Fermi gases as they undergo BCS-Bose Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at $ T \neq 0$ and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Nevertheless a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we a…
In ultracold atoms settings, inelastic light scattering is a preeminent technique to reveal static and dynamic properties at nonzero momentum. In this work, we investigate an array of one-dimensional trapped Bose gases, by measuring both the energy and the momentum imparted to the system via light scattering experiments. The measurements are performed in the weak perturbation regime, where these two quantities - the energy and momentum transferred - are expected to be related to the dynamical structure factor of the system. We discuss this relation, with special attention to the role of in-tra…
We determine the temperature $T$ dependence of first and second sound mode frequencies for trapped Fermi gases undergoing BCS to Bose Einstein condensation (BEC) crossover. Our results are based on the two fluid equations in conjunction with a microscopic calculation of thermodynamical variables. As in experiment and at unitarity, we show that the lowest radial breathing mode is $T$ independent. At finite $T$, higher order breathing modes strongly mix with second sound. Their complex $T$ dependence should provide an alternative way of measuring the transition temperature, $T_c$.
We study, experimentally and theoretically, the controlled transfer of harmonically trapped ultracold gases between different quantum states. In particular we experimentally demonstrate a fast decompression and displacement of both a non-interacting gas and an interacting Bose-Einstein condensate which are initially at equilibrium. The decompression parameters are engineered such that the final state is identical to that obtained after a perfectly adiabatic transformation despite the fact that the fast decompression is performed in the strongly non-adiabatic regime. During the transfer the ato…
Vortex arrays in type-II superconductors admit the translational symmetry of an infinite system. There are cases, however, like ultra-cold trapped Fermi gases and the crust of neutron stars, where finite-size effects make it quite more complex to account for the geometrical arrangement of vortices. Here, we self-consistently generate these arrays of vortices at zero and finite temperature through a microscopic description of the non-homogeneous superfluid based on a differential equation for the local order parameter, obtained by coarse graining the Bogoliubov-de Gennes (BdG) equations. In thi…
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…
We theoretically investigate the itinerant ferromagnetic transition of a spherically trapped ultracold Fermi gas with spin imbalance under strongly repulsive interatomic interactions. Our study is based on a self-consistent solution of the Hartree-Fock mean-field equations beyond the widely used local density approximation. We demonstrate that, while the local density approximation holds in the paramagnetic phase, after the ferromagnetic transition it leads to a quantitative discrepancy in various thermodynamic quantities even with large atom numbers. We determine the position of the phase tra…
We study the spontaneous formation of vortices during the superfluid condensation in a trapped fermionic gas subjected to a rapid thermal quench via evaporative cooling. Our work is based on the numerical solution of the time dependent crossover Ginzburg-Landau equation coupled to the heat diffusion equation. We quantify the evolution of condensate density and vortex length as a function of a crossover phase parameter from BCS to BEC. The more interesting phenomena occur somewhat nearer to the BEC regime and should be experimentally observable; during the propagation of the cold front, the inc…
We study density profiles in trapped fermionic gases, near Feshbach resonances, at all $T \leq T_c$ and in the near-BEC and unitary regimes. For the latter, we quantify and characterize the generally neglected contribution from noncondensed Cooper pairs. As a consequence of these pairs, our profiles are rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature.
We calculate the density profiles of a trapped spin-imbalanced Fermi gas with attractive interactions in a one-dimensional optical lattice, using both the local density approximation (LDA) and density matrix renormalization group (DMRG) simulations. Based on the exact equation of state obtained by Bethe ansatz, LDA predicts that the gas phase-separates into shells with a partially polarized core and fully paired wings, where the latter occurs below a critical spin polarization. This behavior is also seen in numerically exact DMRG calculations at sufficiently large particle numbers. Unlike the …
We present a theoretical interpretation of radio-frequency (RF) pairing gap experiments in trapped atomic Fermi gases, over the entire range of the BCS-BEC crossover, for temperatures above and below $T_c$. Our calculated RF excitation spectra, as well as the density profiles on which they are based, are in semi-quantitative agreement with experiment. We provide a detailed analysis of the physical origin of the two different peak features seen in RF spectra, one associated with nearly free atoms at the edge of the trap, and the other with (quasi-)bound fermion pairs.
