Session V14: BEC-BCS Crossover

Properties of a few-body trapped two-component Fermi gas at unitarity

We consider a trapped two-component Fermi system with even and odd number of fermions N. Unlike fermions interact with a short-range two-body potential which does not support a bound state and is characterized by an infinite scattering length. Using two different numerical techniques, i.e., a correlated Gaussians basis expansion method and a fixed-node diffusion Monte Carlo method, we solve the many-body Schrodinger equation and determine the spectrum and structural properties. Analyzing the excitation spectrum and the wavefunctions, we demonstrate that this system exhibits unique universal properties [1], in agreement with analytical predictions [2]. Furthermore, we determine the excitation gap up to N = 30 and we compare it with recent predictions. [1] D. Blume, J. von Stecher, and Chris H. Greene, e-print arXiv:cond-mat/0708.2734 [2] F. Werner and Y. Castin, Phys. Rev. A 74, 053604 (2006).   

Quantum and thermal fluctuations in the BCS-BEC crossover with unequal mass fermions

A lot of progress has been done in the study of the BCS-BEC crossover for equal-mass fermions in recent years by both theory and experimental groups. An extension of this problem which is starting to receive more attention is the study of mixtures of fermions with different masses, such as a mixture of $^{40}$K and $^6$Li. Using our functional integral method, which we have previously used to study the equal-mass case and which includes the effect of collective excitations (see R. B. Diener et al, cond-mat/0709.2653), we have studied the properties of a fermionic gas with unequal masses across the BCS-BEC crossover. We will present results for different thermodynamical quantities as a function of mass ratio and interaction strength: e.g. the beta parameter at unitarity, the ground state energy as a function of $1/(k_Fa_s)$, as well as the dimer scattering in the BEC limit as a function of mass ratio which agrees to within 20\% with the exact four-body calculation of D. Petrov et al., J. Phys. B At. Mol. Opt. Phys. {\bf 38}, S645 (2005).   

Critical temperature and thermodynamics of the BEC-BCS crosssover

The strongly-correlated regime of the BCS-BEC crossover can be realized by diluting a system of two-component fermions with a contact attractive interaction and an appropriate ultraviolet regularization. We investigate this system via a novel systematic-error-free continuous-space-time diagrammatic determinant Monte Carlo method. The results allow us to predict the universal curve $T_c/E_F$ as a function of the parameter $k_F a$ with the maximum on the BEC side. At unitarity, $T_c/E_F$ = 0.152(7). We also determine the thermodynamic functions and show how the Monte Carlo results can be used for accurate thermometry.   

First- and second-sound-like modes at finite temperature in trapped Fermi gases from BCS to BEC

We determine the temperature ($T$) dependence of first- and second-sound-like mode frequencies for trapped Fermi gases undergoing the BCS to Bose-Einstein condensation (BEC) crossover. Our results are based on numerical solution of 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 will also discuss collective mode frequancy for polarized Fermi gas.   

Transport Properties of a Fermi gas with attractive interactions in the BEC-BCS crossover

The transport phenomena of a two-component Fermi gas with attractive interactions are studied at finite temperatures focused on the normal state using a t-matrix formalism in the BEC-BCS crossover. We contrast the behavior of both charged and uncharged systems and address such varied coefficients as DC conductivity and shear viscosity. We show how the behavior above the pairing onset temperature $T^*$ appears to depend rather weakly on the scattering length. At lower temperatures by studying the appropriate Maki-Thompson and Aslamazov-Larkin diagrams, we find more pronounced fluctuation effects the closer the system is to the BCS limit. Interestingly, we observe that these fluctuation effects are more apparent in charged than in uncharged systems.   

Probing two-fluid hydrodynamics in a trapped Fermi superfluid at unitarity

We develop a variational approach to calculate the density response function at finite temperatures of the lowest-lying two-fluid dipole and breathing modes in a trapped two-component Fermi superfluid close to a Feshbach resonance. The out-of-phase oscillations, which are the analogue in trapped gases of second sound in uniform superfluids, have so far not been observed in cold-atom experiments. At unitarity, we show that these modes are observable at finite temperatures via two-photon Bragg scattering, whose spectrum is related to the imaginary part of density response function. This provides direct evidence for superfluidity and a promising way to test microscopic results for thermodynamics at unitarity. (arXiv:0709.0698, 0711.0561).   

Shear Viscosity and the Perfectness of Fluid

A recent calculation of the shear viscosity for a unitary gas is presented. Here unitary gas is defined as a non-relativistic Fermi gas with infinite scattering length. The unitary gas is a scale invariant strongly-interacting many-body system, and possesses universal properties that are of interest across subfields in physics. A unitary gas can be realized in cold atomic gas experiments near a Feshbach resonance. Conditions approximating the unitary gas emerge in low energy nuclear physics as well. From general principle, the shear viscosity of a strongly interacting gas should be small, however, quantum mechanics places a lower bound. A strict lower bound indicating how ``perfect'' a fluid can become has been conjectured from calculations in strongly coupled field theories that have a gravity dual. We test this conjecture with an explicit calculation in a unitary gas, the most strongly interacting non-relativistic system experimentally known.   

Spectroscopic Signatures of Nonequilibrium Pairing in Atomic Fermi Gases

We present the results of a theoretical description of the radio-frequency (RF) spectra for non-stationary states of a fermionic condensate. These states can be produced by a rapid switch of the scattering length. We show that the RF spectrum of the nonequilibrium state with constant BCS order parameter has two features in contrast to equilibrium where there is a single peak. The additional feature reflects the presence of excited pairs in the steady state. In the state characterized by periodically oscillating order parameter RF-absorption spectrum contains two sequences of peaks spaced by the frequency of oscillations. Satellite peaks appear due to a process where an RF photon in addition to breaking a pair emits/absorbs oscillation quanta.   

Mean Frequency Shift and Finite Width of RF Spectrum of Paired Fermions

Using sum rules we derived the mean frequency shift of the rf spectrum of paired fermions in terms of the derivative of free energy, and explained many features of experiments done at the unitarity point between the lowest hyperfine states of $^6$Li.\footnote{G. Baym, C. J. Pethick, Z. Yu, and M. W. Zwierlein, Phys. Rev. Lett. 99, 190407 (2007).} The calculated mean shifts are however some three times larger than the peak shift observed at the center of the trapped atomic cloud, a discrepency due to the long tail of the spectrum. Generating the rf spectrum function self-consistently within BCS-Hartree-Fock, we have determined the characteristic frequency where the behavior of the spectrum transits from $\omega^{-3/2}$ to $\omega^{-5/2}$ at large frequency. We discuss how to subtract out the long tail from the spectrum and give an improved estimate for the peak frequency shift from the sum rules.   

Final-state effects in radio-frequency spectrum of ultracold Fermions

We model the effects of final-state interaction on the radio-frequency spectrum of a two-component superfluid Fermi gas near resonance. We show how the spectrum evolves as one tunes from weak to strong interactions. Aside from the continuum resulting from the breaking of Cooper pairs, for certain interaction strengths, we predict a sharp peak resulting from converting a pair in one channel to a pair in another channel.   

Molecular production at a broad Feshbach resonance in Fermi-gas of cooled atoms

The problem of molecular production from a degenerate gas of fermions at a broad Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to the static problem, the close vicinity of the exact resonance does not play a substantial role. The two our main physical results are: i) The molecular production is sensitive to the initial magnetic field. ii) In the inverse process of molecule dissociation a large BCS condensate distributed over a broad range of momenta is generated.   

Bistability in Resonant Fermi Superfluid

The resonant two-channel Fermi superfluid model can be mapped to a quantum optics model that describes a single-mode laser field, subject to Kerr nonlinearity, interacting with an ensemble of inhomogeneously broadened two-level atoms. Using this analogy, we show that under proper conditions bistability will occur in resonant Fermi superfluids, a matter wave analog of a similar phenomenon encountered in nonlinear optical systems.   

Collective spin modes in a Fermionic atomic gas

We present our theoretical findings on the structure of the spin mode dispersion of a spin-population-imbalanced Fermionic atomic gas in the highly degenerate regime, but above the superfluid critical temperature, near a Feshbach resonance. We employ standard Fermi liquid theory to describe a gas consisting of two species of spin, up and down, existing in an external magnetic field, which models an atom gas of $^6Li$ atoms in the two lowest Zeeman states. The spin population imbalance creates a net magnetization, and as a result, the transverse magnetization propagates through the system. We find that a diverging scattering length, as occurs near a Feshbach resonance, affects the phenomenological Landau parameters of the system, whose relation to the scattering length is described by the induced interaction model, and thus in turn affects the structure of the collective spin modes, as well.