The Quantum Monte Carlo method for spin 1/2 fermions at finite temperature is formulated for dilute systems with an s-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy and chemical potential as a function of temperature. We give upper bounds on the critical temperature T_c for the onset of superfluidity, obtained by studying the finite size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range -0.5 \le (k_F a)^{-1} \le 0.2, where a is the s-wave scattering length and k_F is the Fermi momentum of a non-interacting gas at the same density. In all cases our data is consistent with normal Fermi gas behavior above a characteristic temperature T_0 > T_c, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For T_c < T < T_0 we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low temperature results for the energy and the pairing gap are shown and compared with Green Function Monte Carlo results by other groups.
We study the Bogoliubov spectrum of an elongated Fermi superfluid confined in an one-dimensional superfluid along the Bose-Einstein-condensate (BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover. We derive analytic expressions for the sound velocity, effective mass and the Bogoliubov excitation spectrum of the axial quasiparticles long the crossover based on the hydrodynamic theory. Our investigation reveal interesting signatures of BEC-BCS crossover in an optical lattice which deserve experimental investigation.
We present the microscopic theory for the BEC-BCS crossover of an atomic Fermi gas in an optical lattice, showing that the Feshbach resonance underlying the crossover in principle induces strong multiband effects. Nevertheless, the BEC-BCS crossover itself can be described by a single-band model since it occurs at magnetic fields that are relatively far away from the Feshbach resonance. A criterion is proposed for the latter, which is obeyed by most known Feshbach resonances in ultracold atomic gases.
The ground-state fidelity has been introduced recently as a tool to investigate quantum phase transitions. Here, we apply this concept in the context of a crossover problem. Specifically, we calculate the fidelity susceptibility for the BCS ground-state wave function, when the intensity of the fermionic attraction is varied from weak to strong in an interacting Fermi system, through the BCS-BEC crossover. Results are presented for contact and finite-range attractive potentials and for both continuum and lattice models. We conclude that the fidelity susceptibility can be useful also in the cont…
We present the RPA theory of the BEC-BCS crossover in an atomic Fermi gas near a Feshbach resonance that includes the relevant two-body atomic physics exactly. This allows us to determine the probability $Z$ for the dressed molecules in the Bose-Einstein condensate to be in the closed channel of the Feshbach resonance and to compare with the recent experiments of Partridge {\it et al.} [cond-mat/0505353] with $^{6}$Li. We determine for this extremely broad resonance also the condensate density of the dressed molecules throughout the BEC-BCS crossover.
A comment on the letter by M. Machida and T. Koyama, Phys. Rev. Lett. {\bf 94}, 140401 (2005) and also on the preprint by Y. Kawaguchi and T. Ohmi, cond-mat/0411018.
We measure excitation spectra of an ultracold gas of fermionic $^{40}$K atoms in the BCS-BEC crossover regime. The measurements are performed with a novel spectroscopy that employs a small modulation of the B-field close to a Feshbach resonance to give rise to a modulation of the interaction strength. With this method we observe both a collective excitation as well as the dissociation of fermionic atom pairs in the strongly interacting regime. The excitation spectra reveal the binding energy / excitation gap for pairs in the crossover region.
We study the free expansion of a dilute two-component Fermi gas with attractive interspecies interaction in the BCS-BEC crossover. We apply a time-dependent parameter-free density-functional theory by using two choices of the equation of state: an analytic formula based on Monte Carlo data and the mean-field equation of state resulting from the extended BCS equations. The calculated axial and transverse radii and the aspect ratio of the expanding cloud are compared to experimental data on vapors of ^6Li atoms. Remarkably, the mean-field theory shows a better agreement with the experiments than…
We present a new many body formalism for BCS-BEC crossover, which represents a modification of the BCS-Leggett ground state to include 4-fermion, and higher correlations. In the BEC regime, we show how our approach contains the \textit{Petrov et al} 4-fermion behavior and associated scattering length $a_{dd}$ at short distances, and secondly reduces to composite-boson Bogoliubov physics at long distances. It reproduces the Lee-Yang term, whose numerical value is also fixed by $a_{dd}$. We have also examined the next term beyond the Lee-Yang correction in a phenomenological fashion, building on…
We report Bose-Einstein condensation of weakly bound $^6$Li$_2$molecules in a crossed optical trap near a Feshbach resonance. We measure a molecule-molecule scattering length of$170^{+100}_{-60}$ nm at 770 G, in good agreement with theory.We study the expansion of the cloud in the BEC-BCS crossoverregion.
We present a mean field approach based on pairs of fermionic atoms to describe condensates in the BEC-BCS crossover regime. By introducing an effective potential, the mean field equation allows us to calculate the chemical potential, the equation of states and the atomic correlation function. The results agree surprisingly well with recent quantum Monte Carlo calculations. We show that the smooth crossover from the bosonic mean field repulsion between molecules to the Fermi pressure among atoms is associated with the evolution of the atomic correlation function.
We discuss an integrable model of interacting Fermions in one dimension, that allows an exact description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 Fermions to the Lieb-Liniger model of repulsive Bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from minus infinity to plus infinity while the system evolves from a BCS-like state through a Tonks gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and sp…
We present the Bogoliubov theory for the Bose-Einstein condensation of Feshbach molecules in a balanced Fermi mixture. Because the Bogoliubov theory includes (Gaussian) fluctuations, we can in this manner accurately incorporate both the two-body and many-body aspects of the BEC-BCS crossover that occurs near a Feshbach resonance. We apply the theory in particular to the very broad Feshbach resonance in atomic Li-6 at a magnetic field of B_0 = 834 G and find good agreement with experiments in that case. The BEC-BCS crossover for more narrow Feshbach resonances is also discussed.
We investigate the non-universal behavior of the BCS-BEC crossover model at the normal to superfluid transition. By using a finite temperature quantum field theoretical approach due to Nozieres and Schmitt-Rink and by making the effective range expansion of the effective two-body interaction we numerically calculate the crossover transition temperature as a function of the scattering length, $a_{F},$ and the effective range parameter, $r_{\mathrm{e}}.$ In an ultracold two-component atomic Fermi gas BCS-BEC crossover physics is expected to appear near magnetic-field-induced Feshbach resonances.…
We investigate the Bose-Einstein condensation of Fermionic pairs in a uniform two-component Fermi gas obtaining an explicit formula for the condensate density as a function of the chemical potential and the energy gap. We analyze the condensate fraction in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly-interacting Cooper pairs to the Bose-Einstein Condensate (BEC) of molecular dimers. By using the local density approximation we study confined Fermi vapors of alkali-metal atoms for which there is experimental evidence of condensation also on the BCS side of the Feshbach …
The functional renormalisation group is used for the BCS-BEC crossover in gases of ultracold fermionic atoms. In a simple truncation, we see how universality and an effective theory with composite bosonic di-atom states emerge. We obtain a unified picture of the whole phase diagram. The flow reflects different effective physics at different scales. In the BEC limit as well as near the critical temperature, it describes an interacting bosonic theory.
The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length $a_{aa}$ displays a confinement-induced resonance. We compute the dimer-dimer scattering length $a_{dd}$, and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.
We study the macroscopic quantum tunneling of two weakly-linked superfluids made of interacting fermionic atoms. We derive atomic Josephson junction equations and find that zero-mode and pi-mode frequencies of coherent atomic oscillations depend on the tunneling coefficient and the sound velocity of the superfluid. By considering a superfluid of ^40K atoms, we calculate these oscillation frequencies in the crossover from the Bardeen-Cooper-Schrieffer state of weakly-bound Cooper pairs to the Bose-Einstein Condensate of strongly-bound molecular dimers.
Using mean-field theory for the Bardeen-Cooper-Schriefer (BCS) to the Bose-Einstein condensate (BEC) crossover we investigate the ground state thermodynamic properties of an interacting homogeneous Fermi gas. The interatomic interactions modeled through a finite range potential allows us to explore the entire region from weak to strong interacting regimes with no approximations. To exhibit the thermodynamic behavior as a function of the potential parameters in the whole crossover region, we concentrate in studying the contact variable, the thermodynamic conjugate of the inverse of the s-wave s…
