We calculate the off-diagonal long range order (ODLRO) terms of the exciton--exciton correlation function of a semiconductor bilayer system with Coulomb interaction and a transverse magnetic field. We show that the formation of a BEC state is very sensitive to the width of the interaction in momentum space. This dependence is analytically derived and represents the key physical ingredient for the formation (or not) of an exciton condensate state.
We study the occurrence of excitonic superfluidity in electron-hole bilayers at zero temperature. We not only identify the crossover in the phase diagram from the BCS limit of overlapping pairs to the BEC limit of non-overlapping tightly-bound pairs but also, by varying the electron and hole densities independently, we can analyze a number of phases that occur mainly in the crossover region. With different electron and hole effective masses, the phase diagram is asymmetric with respect to excess electron or hole densities. We propose as the criterion for the onset of superfluidity, the jump of…
We study BCS-BEC crossover in the strongly correlated regime of two component rotating Fermi gases. We predict that the strong correlations induced by rotation will have the effect of modifying the crossover region relative to the non-rotating situation. We show via the two particle correlation function that the crossover smoothly connects the s-wave paired fermionic fractional quantum Hall state to the bosonic Laughlin state.
We present a reinterpretation of our previous results on the radial compression mode of a degenerate quantum gas in the BEC-BCS crossover in [1]. We show that our former data are consistent with other experimental and theoretical work, when the ellipticity of the optical trapping potential in [1] is properly taken into account.
The Josephson relation for the superfluid density is derived for a Fermi superfluid in the BCS-BEC crossover. This identity extends the original Josephson relation for Bose superfluids. It gives a simple exact relation between the superfluid density $ρ_s$ and the broken-symmetry Cooper pair order parameter $Δ_0$ in terms of the infrared limit of the pair fluctuation propagator. The same expression holds through the entire BCS-BEC crossover, describing the superfluid density of a weak-coupling BCS superfluid as well as the superfluid density of a Bose condensate of dimer molecules.
A review of recent BEC-BCS crossover experiments in ultracold Fermi gases is given with particular emphasis on the work performed with lithium-6 at the University of Innsbruck.
By using the diffusion Monte Carlo method we calculate the one- and two-body density matrix of an interacting Fermi gas at T=0 in the BCS-BEC crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of fermionic pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.
We derive an expression for the superfluid density of a uniform two-component Fermi gas through the BCS-BEC crossover in terms of the thermodynamic potential in the presence of an imposed superfluid flow. Treating the pairing fluctuations in a Gaussian approximation following the approach of Nozières and Schmitt-Rink, we use this definition of $ρ_s$ to obtain an explicit result which is valid at finite temperatures and over the full BCS-BEC crossover. It is crucial that the BCS gap $Δ$, the chemical potential $μ$, and $ρ_s$ all include the effect of fluctuations at the same level in a self-con…
Critical velocities have been observed in an ultracold superfluid Fermi gas throughout the BEC-BCS crossover. A pronounced peak of the critical velocity at unitarity demonstrates that superfluidity is most robust for resonant atomic interactions. Critical velocities were determined from the abrupt onset of dissipation when the velocity of a moving one dimensional optical lattice was varied. The dependence of the critical velocity on lattice depth and on the inhomogeneous density profile was studied.
We derive a path-integral description of the vortex state of a fermionic superfluid in the crossover region between the molecular condensate (BEC) regime and the Cooper pairing (BCS) regime. This path-integral formalism, supplemented by a suitable choice for the saddle point value of the pairing field in the presence of a vortex, offers a unified description that encompasses both the BEC and BCS limits. The vortex core size is studied as a function of the tunable interaction strength between the fermionic atoms. We find that in the BEC regime, the core size is determined by the molecular heali…
We develop a time-dependent mean-field theory to investigate the released momentum distribution and the released energy of an ultracold Fermi gas in the BCS-BEC crossover after the scattering length has been set to zero by a fast magnetic-field ramp. For a homogeneous gas we analyze the non-equilibrium dynamics of the system as a function of the interaction strength and of the ramp speed. For a trapped gas the theoretical predictions are compared with experimental results.
We consider cigar shaped Fermi superfluid in the BEC-BCS crossover. Using polytropic form of equation of state, we derive low energy multibranch bosonic excitations and the corresponding density fluctuations in three different regimes along the crossover, namely weak-coupling BCS, unitarity and molecular BEC regimes. Bragg spectroscopy can be used to probe the multibranch nature of the low energy bosonic excitations by measuring dynamic structure factor. Therefore, we calculate dynamic structure factor in those three different regimes. In the Bragg spectroscopy, an actual observable is momentu…
We observe dramatic changes in the atomic momentum distribution of a Fermi gas in the region of the BCS-BEC crossover. We study the shape of the momentum distribution and the kinetic energy as a function of interaction strength. The momentum distributions are compared to a mean-field crossover theory, and the kinetic energy is compared to theories for the two weakly interacting limits. The temperature dependence of the distribution is also presented.
Both the trapping geometry and the interatomic interaction strength of a dilute ultracold fermionic gas can be well controlled experimentally. When the interactions are tuned to strong attraction, Cooper pairing of neutral atoms takes place and a BCS superfluid is created. Alternatively, the presence of Feshbach resonances in the interatomic scattering allows populating a molecular (bound) state. These molecules are more tightly bound than the Cooper pairs and can form a Bose-Einstein condensate (BEC). In this contribution, we describe both the BCS and BEC regimes, and the crossover, from a fu…
We systematically study relativistic two-species fermions with tunable attractive interactions and number-density asymmetry at zero temperature. In general, a Bardeen-Cooper-Schrieffer (BCS) - Bose-Einstein Condensation (BEC) - relativistic BEC (RBEC) crossover is observed. A generalized BCS ground state and its stability are analyzed. The homogeneous superfluid phase can become unstable and we consider phase separation in real space for neutral systems. In the nonrelativistic limit, our results are consistent with well-known results. In addition to a BCS-BEC crossover similar to that in the n…
We have used optical molecular spectroscopy to probe the many-body state of paired $^6$Li atoms near a broad Feshbach resonance. The optical probe projects pairs of atoms onto a vibrational level of an excited molecule. The rate of excitation enables a precise measurement of the closed-channel contribution to the paired state. This contribution is found to be quite small, supporting the concept of universality for the description of broad Feshbach resonances. The dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover, and into the weakly interacting BCS regi…
We perform a detailed study of the collective mode across the whole BEC-BCS crossover in fermionic gases at zero temperature, covering the whole range of energy beyond the linear regime. This is done on the basis of the dynamical BCS model. We recover first the results of the linear regime in a simple form. Then specific attention is payed to the non linear part of the dispersion relation and its interplay with the continuum of single fermionic excitations. In particular we consider in detail the merging of collective mode into the continuum of single fermionic excitations. This occurs not onl…
Theoretical treatments of the BCS-BEC crossover need to provide as accurate as possible descriptions of the two regimes where the diluteness condition applies, either in terms of the constituent fermions (BCS limit) or of the composite bosons which form as bound-fermion pairs (BEC limit). This has to occur via a single fermionic theory that bridges across these two limiting representations. In this paper, we set up successive improvements of the fermionic theory, that result into composite bosons described at the level of either the Bogoliubov or the Popov approximations for point-like bosons.…
We explore the zero temperature phase behavior of a two-dimensional two-component atomic Fermi gas with population and mass imbalance in the regime of the BEC-BCS crossover. Working in the mean-field approximation, we show that the normal and homogeneous balanced superfluid phases are separated by an inhomogeneous superfluid phase of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type. We obtain an analytical expression for the line of continuous transitions separating the normal and inhomogeneous FFLO phases. We further show that the transition from the FFLO phase to the homogeneous balanced superflu…
Predictions for the chemical potential and the excitation gap recently obtained by our diagrammatic theory for the BCS-BEC crossover in the superfluid phase are compared with novel Quantum Monte Carlo results at zero temperature now available in the literature. A remarkable agreement is found between the results obtained by the two approaches
We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of Li-6 atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte-Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting BEC regime.
We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasi-molecules with finite orbital angular momenta $L_z=\pm1,0$, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper-pairs and mol…
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 study the stationary Josephson effect for neutral fermions across the BCS-BEC crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.
With reference to the broad and narrow Fano-Feshbach resonances of 6Li at about 822 G and 543 G, we show that for the broad resonance a molecular coupled-channel calculation can be mapped with excellent accuracy onto an effective single-channel problem with a contact interaction. This occurs for a wide enough range of the magnetic field, that the full BCS-BEC crossover can be realized with a typical trap. For the narrow resonance, the mapping onto a single-channel problem and the realization of the BCS-BEC crossover are restricted to too narrow a range of the magnetic field to obtain them in p…
We show that many hydrodynamical properties of the BEC/BCS crossover in the presence of a Feshbach resonance at T=0 can be derived easily from the derivative expansion of the (exact) fully renormalized one-loop effective action. In particular, we calculate the velocity of sound throughout the BCS and BEC regimes and derive the generalized superfluid continuity equations for the composite two-fluid system.
We study the crossover from BEC to BCS pairing for dilute systems but with a realistic finite-range interaction. We exhibit the changes in the excitation spectrum that provide a clean qualitative distinction between the two limits. We also study how the dilute system converges to the results from a zero-range pseudo-potential derived by Leggett.
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 subject of BCS - Bose Einstein condensation (BEC) crossover is particularly exciting because of its realization in ultracold Fermi gases and its possible relevance to high temperature superconductors. In the paper we review that body of theoretical work on this subject which represents a natural extension of the seminal papers by Leggett and by Nozieres and Schmitt-Rink (NSR). The former addressed only the ground state, now known as the "BCS-Leggett" wave-function and the key contributions of the latter pertain to calculations of the superfluid transition temperature $T_c$. These two paper…
We present a stability analysis on a driven-dissipative electron-hole condensate in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-condensation)-crossover region. Extending the combined BCS-Leggett theory with the generalized random phase approximation (GRPA) to the non-equilibrium case by employing the Keldysh formalism, we show that the pumping-and-decay of carriers causes a depairing effect on excitons. This phenomenon gives rise to an attractive interaction between excitons in the BEC regime, as well as a supercurrent that anomalously flows anti-parallel to $\nabla θ({\bf r})$ (whe…
The epsilon expansion (expansion around four spacial dimensions) developed by Nishida and Son for a cold fermi gas with infinite scattering length is extended to finite scattering length to study the BEC-BCS crossover. A resummation of higher order logarithms and a suitable extension of fermion coupling in d-dimensions are developed in order to apply the theory in the BCS regime. The ratio between the chemical potential and the Fermi energy, mu/eF, is computed to next-to-leading order in the epsilon expansion as a function of eta=1/(a kF), where a is the scattering length and kF is the Fermi m…
