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arXiv:0805.2798 · Europhysics Letters (EPL)

Cooper pair turbulence in atomic Fermi gases

M. Dzero, E. A. Yuzbashyan, B. L. Altshuler

Published Jan 1, 2009• 38 citations
arXivHTMLPDF

Abstract

We investigate under what conditions a uniform quench of a superfluid atomic Fermi gas leads to the emergence of spatial inhomogeneities. We demonstrate that, if the system is larger than the coherence length, the superfluid order parameter becomes spatially nonuniform. Spatial modulations develop through a parametric excitations of pairing modes with opposite momenta. Their growth is eventually suppressed by nonlinear effects resulting in a state characterized by a random superposition of wave packets of the superfluid order parameter. This state can be probed by measuring the molecular momentum distribution following a fast sweep to the BEC side of the Feshbach resonance.

DOI
10.1209/0295-5075/85/20004

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We investigate under what conditions a uniform quench of a superfluid atomic Fermi gas leads to the emergence of spatial inhomogeneities. We demonstrate that, if the system is larger than the coherence length, the superfluid order parameter becomes spatially nonuniform. Spatial modulations develop through a parametric excitations of pairing modes with opposite momenta. Their growth is eventually suppressed by nonlinear effects resulting in a state characterized by a random superposition of wave packets of the superfluid order parameter. This state can be probed by measuring the molecular momentum distribution following a fast sweep to the BEC side of the Feshbach resonance.
We investigate strong-coupling superfluidity in a uniform two-component gas of ultracold Fermi atoms attractively interacting via quasimolecular bosons associated with a Feshbach resonance. This interaction is tunable by the threshold energy $2\ensuremath{\nu}$ of the Feshbach resonance, becoming large as $2\ensuremath{\nu}$ is decreased (relative to $2{\ensuremath{\varepsilon}}_{\mathrm{F}},$ where ${\ensuremath{\varepsilon}}_{\mathrm{F}}$ is the Fermi energy of one component). In recent work, we showed that the enhancement of this tunable pairing interaction naturally leads to the BCS-BEC (Bose-Einstein condensation) crossover, where the character of the superfluid phase transition changes from the BCS type to a BEC of composite bosons consisting of preformed Cooper-pairs and Feshbach-induced molecules. In this paper, we extend our previous work and study both the quasiparticles and the collective dynamics of the superfluid phase below the phase-transition temperature Tc,{T}_{\mathrm{c}},Tc​, limiting ourselves to a uniform gas. We show how the superfluid order parameter changes from the Cooper-pair amplitude $\ensuremath{\Delta}$ to the square root of the number of condensed molecules $({\ensuremath{\varphi}}_{\mathrm{m}})$ associated with the Feshbach resonance, as the threshold energy $2\ensuremath{\nu}$ is lowered. In the intermediate coupling regime, the superfluidity is shown to be characterized by an order parameter consisting of a superposition of $\ensuremath{\Delta}$ and ${\ensuremath{\varphi}}_{\mathrm{m}}.$ We also discuss the Goldstone mode associated with superfluidity, and show how its character smoothly changes from the Anderson-Bogoliubov phonon in the BCS regime to the Bogoliubov phonon in the BEC regime in the BCS-BEC crossover. The velocity of this Goldstone phonon mode is shown to strongly depend on the value of $2\ensuremath{\nu}.$ We also show that this Goldstone mode appears as a resonance in the spectrum of the density-density correlation function, which is experimentally accessible.
We study an ultra-cold atomic Fermi Gas with the atom-atom interaction modulated periodically in space. A novel ground state with cooper pairs occupying non-zero center of mass momenta is found. Such a state is closely related to the state proposed by Fulde, Ferrell, Larkin, and Ovchinnikov(FFLO). The resultant single particle excitations with momenta along the direction of the modulation shows multiple-gap structures. Such a system can be realized in experiment with a spatially modulated Feshbach resonance. Experimental signatures of such a state are discussed.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the sss-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
We report observations of quasiparticle pair production by a modulational instability in an atomic superfluid and present a measurement technique that enables direct characterization of quasiparticle quantum entanglement. By quenching the atomic interaction to attractive and then back to weakly repulsive, we produce correlated quasiparticles and monitor their evolution in a superfluid through evaluating the in situ density noise power spectrum, which essentially measures a "homodyne" interference between ground-state atoms and quasiparticles of opposite momenta. We observe large amplitude growth in the power spectrum and subsequent coherent oscillations in a wide spatial frequency band within our resolution limit, demonstrating coherent quasiparticle generation and evolution. The spectrum is observed to oscillate below a quantum limit set by the Peres-Horodecki separability criterion of continuous-variable states, thereby confirming quantum entanglement between interaction quench-induced quasiparticles.
We study the superfluid flow in a quasi-one-dimensional Fermi gas with spatially modulated interactions induced by an optical Feshbach resonance. Due to the competition between the periodicity of the modulated interaction and the nonlinearity of the background interaction, an interesting swallowtail structure emerges in the energy spectrum under appropriate parameters. As the interaction strengths are tuned, the swallowtail structure may disappear, giving rise to various different states on a rich phase diagram. We investigate the spatial distribution of the order parameter and the particle density under various parameters, which are useful for the experimental detection of the interesting phases in these systems.
Abstract We discuss the possible signatures of superfluidity induced by the Feshbach resonance in the ultracold gas of fermion atoms. Optically or magnetically trapped atoms such as 6Li or 40K are used in two hyperfine states where part of them is converted into the diatomic molecules. These fermion and boson entities get coupled in a presence of the external magnetic field. Eventually, at critical Tc, they simultaneously undergo transition to the superfluid state. Approaching this transition from above there appear various signatures manifesting a gradually emerging order parameter, but yet the long range coherence is not established due to the strong quantum fluctuations. Fermion atoms are characterized by the gapped excitation spectrum (pseudogap) up to temperature Tp (larger than Tc) while boson molecules exhibit collective features such as first sound showing up above a certain critical momentum q.crit (T) Upon lowering temperature to Tc this critical value shifts to zero and hence there appears the Goldstone mode signaling the symmetry broken superfluid state. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)