Trapped Two-component Fermi Gases Research Articles

Density response of a trapped Fermi gas: A crossover from the pair vibration mode to the Goldstone mode

We consider the density response of a trapped two-component Fermi gas. Combining the Bogoliubov-deGennes method with the random phase approximation allows the study of both collective and single-particle excitations. Calculating the density response across a wide range of interactions, we observe a crossover from a weakly interacting pair vibration mode to a strongly interacting Goldstone mode. The crossover is associated with a depressed collective mode frequency and an increased damping rate, in agreement with density response experiments performed in strongly interacting atomic gases.

Magnetism and Pairing of Two-Dimensional Trapped Fermions

The emergence of local phases in a trapped two-component Fermi gas in an optical lattice is studied using quantum Monte Carlo simulations. We treat temperatures that are comparable to or lower than those presently achievable in experiments and large enough systems that both magnetic and paired phases can be detected by inspection of the behavior of suitable short-range correlations. We use the latter to suggest the interaction strength and temperature range at which experimental observation of incipient magnetism and d-wave pairing are more likely and evaluate the relation between entropy and temperature in two-dimensional confined fermionic systems.

Virial relations for ultracold trapped Fermi gases with finite range interactions through the Bardeen–Cooper–Schrieffer Bose–Einstein-condensate crossover

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 Bardeen–Cooper–Schrieffer (BCS) Bose–Einstein-condensate (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. Once the binding energy of the formed molecules in the BEC side is subtracted, the corresponding energy derivatives are found to have extreme values at the unitary limit. The value of the derivative with respect to the potential range in that limit is large enough to yield measurable differences between the total energy and twice the trapping energy unless the interacting system is described by extremely short potential ranges. The virial results are used to check the quality of the variational wavefunction involved in the calculations.

New light on the intriguing history of superfluidity in liquid4He

Surprisingly, it was 30 years after the first liquefaction of4He in 1908 that thediscovery that liquid 4He is not just a ‘cold’ liquid was made. BelowT = 2.18 K, it is a ‘quantum’ liquid which exhibits spectacular macroscopic quantum behaviour thatcan be seen with the naked eye. Since the observation of superfluidity in liquid4He is one of the greatest discoveries in modern physics, we present a day-to-day chronology ofthe tangled events which preceded the seminal discovery of zero viscosity in 1938 byKapitza in Moscow and by Allen and Misener in Cambridge. On the theory side, Londonargued in 1938 that the microscopic basis for this new superfluid phase was theforgotten phenomenon of Bose–Einstein condensation (BEC) first suggested byEinstein in 1925. In 1941, Landau developed a very successful theory of superfluid4He, but it was not anchored in a microscopic theory of interacting atoms. It took another 20years for theorists to unify the two seemingly different theories of Landau and London.Experiments on trapped superfluid atomic gases since 1995 have shone new light on superfluid4He. Inthe mid-1930s, London had emphasized that superconductivity in metals and superfluidity in liquid4He were similar. Experiments on trapped two-component Fermi gases in the last fiveyears have shown that a Bose condensate is indeed the basis of both of thesesuperfluid phases. This confirms the now famous Bardeen–Cooper–Schrieffer–BECcrossover scenario developed for superfluidity by Leggett and Nozières in theearly 1980s but largely ignored until a few years ago. The study of superfluid4He will increasingly overlap with strongly interacting dilute quantum gases, perhaps openingup a new era of research on this most amazing liquid.

Energetics and structural properties of trapped two-component Fermi gases

Using two different numerical methods, we study the behavior of two-component Fermi gases interacting through short-range $s$-wave interactions in a harmonic trap. A correlated Gaussian basis-set expansion technique is used to determine the energies and structural properties, i.e., the radial one-body densities and pair distribution functions, for small systems with either even or odd $N$, as functions of the $s$-wave scattering length and the mass ratio $\ensuremath{\kappa}$ of the two species. Particular emphasis is put on a discussion of the angular momentum of the system in the BEC-BCS crossover regime. At unitarity, the excitation spectrum of the four-particle system with total angular momentum $L=0$ is calculated as a function of the mass ratio $\ensuremath{\kappa}$. The results are analyzed from a hyperspherical perspective, which offers unique insight into the problem. Additionally, fixed-node diffusion Monte Carlo calculations are performed for equal-mass Fermi gases with up to $N=30$ atoms. We focus on the odd-even oscillations of the ground-state energy of the equal-mass unitary system having up to $N=30$ particles, which are related to the excitation gap of the system. Furthermore, we present a detailed analysis of the structural properties of these systems.

BEC-BCS crossover of a trapped two-component Fermi gas with unequal masses

Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814(Dated: February 1, 2008)We determine the energetically lowest lying states in the BEC-BCS crossover regime of s-waveinteracting two-component Fermi gases under harmonic confinement by solving the many-bodySchr¨odinger equation using two distinct approaches. Essentially exact basis set expansion techniquesare applied to determine the energy spectrum of systems with N= 4 fermions. Fixed-node diffusionMonte Carlo methods are applied to systems with up to N = 20 fermions, and a discussion ofdifferent guiding functions used in the Monte Carlo approach to impose the proper symmetry of thefermionic system is presented. The energies are calculated as a function of the s-wave scatteringlength a

On the spin asymmetry of ground states in trapped two-component Fermi gases with repulsive interactions

We examine the spin asymmetry of ground states for two-dimensional, harmonically trapped two-component gases of fermionic atoms at zero temperature with weakly repulsive short-range interactions. Our main result is that, in contrast to the three-dimensional case, in two dimensions a non-trivial spin-asymmetric phase can only be caused by the shell structure. A simple, qualitative description is given in terms of an approximate single-particle model, comparing well to the standard results of Hartree–Fock or direct diagonalization methods.

Dynamics of trapped two-component Fermi gas: Temperature dependence of the transition from collisionless to collisional regime

We develop a numerical method to study the dynamics of a two-component atomic Fermi gas trapped inside a harmonic potential at temperature T well below the Fermi temperature Tf. We examine the transition from the collisionless to the collisional regime down to T=0.2 Tf and find good qualitative agreement with the experiments of B. DeMarco and D.S. Jin [Phys. Rev. Lett. vol. 88, 040405 (2002)]. We demonstrate a twofold role of temperature on the collision rate and on the efficiency of collisions. In particular we observe an hitherto unreported effect, namely that the transition to hydrodynamic behavior is shifted towards lower collision rates as temperature decreases.

Laser cooling of a trapped two-component Fermi gas

The collective Raman cooling of a trapped two-component Fermi gas is analyzed. We develop the quantum master equation that describes the collisions and the laser cooling, in the festina lente regime, where the heating due to photon reabsorption can be neglected. The numerical results based on Monte Carlo simulations show, that three-dimensional temperatures of the order of 0.008 T_F can be achieved. We analyze the heating related to the background losses, and conclude that our laser-cooling scheme can maintain the temperature of the gas without significant additional losses. Finally we derive an analytic expression for the temperature of a trapped Fermi gas heated by background collisions, that agrees very well with the data obtained from the numerical simulation.

Collective dynamics of fermion clouds in cigar-shaped traps

The propagation of zero sound in a spin-polarized Fermi gas under harmonic confinement is studied as a function of the mean-field interactions with a second Fermi gas. A local-density treatment is compared with the numerical solution of the Vlasov–Landau equations for the propagation of density distortions in a trapped two-component Fermi gas at temperature T=0.2 T F . The response of the gas to the sudden creation of a sharp hole at its centre is also studied numerically.