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arXiv:1408.5239 · Physical Review Letters

Critical Velocity in the BEC-BCS Crossover

Wolf Weimer, Kai Morgener, Vijay Pal Singh, Jonas Siegl, Klaus Hueck, Niclas Luick, Ludwig Mathey, Henning Moritz

Published Mar 3, 2015• 98 citations
arXivHTMLPDF

Abstract

We map out the critical velocity in the crossover from Bose-Einstein condensation to Bardeen-Cooper-Schrieffer superfluidity with ultracold ^{6}Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity v_{c}. In the same samples, we measure the speed of sound v_{s} by exciting density waves and compare the results to the measured values of v_{c}. We perform numerical simulations in the Bose-Einstein condensation regime and find very good agreement, validating the approach. In the strongly correlated regime our measurements of v_{c} provide a testing ground for theoretical approaches.

DOI
10.1103/physrevlett.114.095301

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We map out the critical velocity in the crossover from Bose-Einstein condensation to Bardeen-Cooper-Schrieffer superfluidity with ultracold ^{6}Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity v_{c}. In the same samples, we measure the speed of sound v_{s} by exciting density waves and compare the results to the measured values of v_{c}. We perform numerical simulations in the Bose-Einstein condensation regime and find very good agreement, validating the approach. In the strongly correlated regime our measurements of v_{c} provide a testing ground for theoretical approaches.
Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid which are determined, e.g., by the interaction strength between the particles of the quantum liquid and their temperature. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation between the BEC, BCS and unitary regimes. Working with a quantum gas of ultracold fermionic 6^66Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. We gain deeper insights into sound propagation and excitation of second sound by varying the excitation procedure which ranges from a sudden force pulse to a gentle heating pulse at the cloud center. These measurements are accompanied by classical-field simulations which help with the interpretation of the experimental data. Furthermore, we determine the spatial extension of the superfluid phase and estimate the superfluid density. In the future, this may be used to construct the so far unknown equation of state throughout the crossover.
Abstract Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid, extending previous work at unitarity. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation in the crossover. Working with a quantum gas of ultracold fermionic 6Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. By varying the excitation procedure, we gain deeper insight on sound propagation. We compare our measurement results with classical-field simulations, which help with the interpretation of our experiments.
We study the effects of an external periodic potential on the critical velocity of a superfluid Fermi gas in the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and Bose-Einstein condensation (BEC). We numerically solve the Bogoliubov--de Gennes equations to model a three-dimensional gas of ultracold atoms in the superfluid phase flowing through a one-dimensional optical lattice. We find that when the recoil energy is comparable to the Fermi energy, the presence of the periodic potential reduces the effect of pair-breaking excitations. This behavior is a consequence of the peculiar band structure of the quasiparticle energy spectrum in the lattice. When the lattice height is much larger than the Fermi energy, the periodic potential makes pairs of atoms to be strongly bound, even in the BCS regime, and pair-breaking excitations are further suppressed. We have also found that when the recoil energy is comparable to or larger than the Fermi energy, the critical velocity due to long-wavelength phonon excitations shows a nonmonotonic behavior along the BCS-BEC crossover.
We investigate the linear and nonlinear sound propagations in a cigar-shaped superfluid Fermi gas with a large particle number. We first solve analytically the eigenvalue problem of linear collective excitations and provide explicit expressions of all eigenvalues and eigenfunctions, which are valid for all superfluid regimes in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. The linear sound speed obtained agrees well with that of a recent experimental measurement. We then consider a weak nonlinear excitation and show that the time evolution of the excitation obeys a Korteweg de Vries equation. Different from the result obtained in quasi-one-dimensional case studied previously, where subsonic dark solitons are obtained via the balance between quantum pressure and nonlinear effect, we demonstrate that bright solitons with supersonic propagating velocity can be generated in the present three-dimensional system through the balance between a waveguidelike dispersion and the interparticle interaction. The supersonic bright solitons obtained display different physical properties in different superfluid regimes and hence can be used to characterize superfluid features of the BCS-BEC crossover.
We theoretically investigate the specific heat at constant volume C V in the BCS(Bardeen-Cooper-Schrieffer)-BEC(Bose-Einstein-condensation)-crossover regime of an ultracold Fermi gas, below the superfluid phase transition temperature T c . Within the strong-coupling framework developed by Nozières and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6 Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.
We study, both analytically and numerically, the formation and propagation of dark solitons in a superfluid Fermi gas in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). Starting from a superfluid order-parameter equation, we derive a Korteweg--de Vries equation for weak nonlinear excitations under quasi-one-dimensional and long-wavelength approximations. We present dark soliton solutions valid for both BCS and BEC limits and also for the crossover, and show that dark solitons in different superfluid regimes possess different features. Particularly, a dark soliton in the BCS (BEC) regime has larger (smaller) propagating velocity and smaller (larger) spatial width. Upon moving to the boundary of the condensate, it generally decelerates and generates small radiations, which display different behavior in different superfluid regimes. We study also a head-on collision between two dark solitons and demonstrate that the phase shift due to the collision changes nonmonotonically along the BCS-BEC crossover. All analytical results are checked by numerical simulations, and good agreement between them is found.