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arXiv:1006.4579 · Physical Review A

Dynamics of a quantum quench in an ultracold atomic BCS superfluid

Chih-Chun Chien, Bogdan Damski

Published Dec 14, 2010• 4 citations
arXivHTMLPDF

Abstract

We study dynamics of an ultracold atomic BCS superfluid driven toward the BCS superfluid--Fermi-liquid quantum critical point by a gradual decrease of the pairing interaction. We analyze how the BCS superfluid falls out of equilibrium and show that the nonequilibrium gap and Cooper pair size reflect critical properties of the transition. We observe three stages of evolution: adiabatic where the Cooper pair size is inversely proportional to the equilibrium gap, weakly nonequilibrium where it is inversely proportional to the nonequilibrium gap, and strongly nonequilibrium where it decouples from both equilibrium and nonequilibrium gap. These phenomena should stimulate future experimental characterization of nonequilibrium ultracold atomic BCS superfluids.

DOI
10.1103/physreva.82.063616

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We study dynamics of an ultracold atomic BCS superfluid driven toward the BCS superfluid--Fermi-liquid quantum critical point by a gradual decrease of the pairing interaction. We analyze how the BCS superfluid falls out of equilibrium and show that the nonequilibrium gap and Cooper pair size reflect critical properties of the transition. We observe three stages of evolution: adiabatic where the Cooper pair size is inversely proportional to the equilibrium gap, weakly nonequilibrium where it is inversely proportional to the nonequilibrium gap, and strongly nonequilibrium where it decouples from both equilibrium and nonequilibrium gap. These phenomena should stimulate future experimental characterization of nonequilibrium ultracold atomic BCS superfluids.
A new field of research, which gained interest in the past years, is the field of non- equilibrium physics of strongly interacting fermionic systems. In this thesis we present a novel apparatus to study an ultracold strongly interacting superfluid Fermi gas driven out of equilibrium. In more detail, we study the excitation of a collective mode, the Higgs mode, and the dynamics occurring after a rapid quench of the interaction strength. Ultracold gases are ideal candidates to explore the physics of strongly interacting Fermi gases due to their purity and the possibility to continuously change many different system parameters, such as the interaction strength. The novel apparatus enabling the experiments outlined below is built from scratch. The setup is described and characterized in detail. We produce a fermionic superfluid of 4 × 10^6 6Li atoms at a temperature of T/T_F = 0.07 ± 0.02, where T_F is the Fermi temperature. This is achieved within 23 s by a combination of laser cooling, radio frequency evaporation of 23Na and simultaneous sympathetic cooling of 6Li in an optical plugged magnetic trap and subsequent evaporative cooling of 6Li in a dipole trap. In this thesis we provide the first experimental evidence of the Higgs mode in a strongly interacting Fermi gas in the crossover from a BCS superfluid to a molecular Bose-Einstein condensate. We develop a novel excitation method, which directly couples to the amplitude of the order parameter. This is achieved by continuously changing the population of one spin component by driving a radio frequency transition to a previously unoccupied third hyperfine state. This effectively modulates the interaction strength and the amplitude of the order parameter. We spectroscopically observe a resonance behavior at twice the gap frequency. For strong coupling, the peak width broadens and eventually the Higgs mode disappears when the Cooper pairs turn into tightly bound dimers signaling the instability of the Higgs mode. It has been suggested that the Higgs mode frequency is a precise measure of the superconducting gap in the BEC-BCS crossover, where the exact value of the gap is yet unknown and numerical calculations are challenging. Hence, our novel method provides a unique technique to determine the superconducting gap. Moreover, we perform rapid variations of the interaction parameter and vary both the initial interaction strength and the amplitude of the quench. The rapid quenches are performed by rapidly transferring one spin component of a two-component spin mixture into a third state with a different interaction strength by using a radio frequency transition. Using this novel method, we can perform the quenches in half the Fermi time, which is experimentally very close to a sudden change and to date faster than any other research group performing interaction quenches with ultra cold gases. In the experiment, we observe a fast relaxation to a zero order parameter for large quenches, whereas for small quenches we observe, after a sudden drop, a revival of the order parameter and equilibration to a long-term superfluid steady state. Our measurement provides the first evidence of the collapse and subsequent revival of order in a strongly interacting fermionic system.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the nonequilibrium steady state, being coupled with two fermion baths. By developing a nonequilibrium strong-coupling theory based on the combined TTT-matrix approximation with the Keldysh Green's function technique, we show that the chemical potential bias applied by the two baths gives rise to the anomalous enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing fluctuations (although the system has no spin imbalance), resulting in the re-entrant behavior of the nonequilibrium superfluid phase transition in the Bardeen-Cooper-Schrieffer unitary regime. These pairing fluctuations are also found to anomalously enhance the pseudogap phenomenon. Since various nonequilibrium phenomena have recently been measured in ultracold Fermi gases, our nonequilibrium strong-coupling theory would be useful to catch up with this experimental development in this research field.
Within the time-dependent Gutzwiller approximation applied to the negative-UUU Hubbard model, we investigate the dynamics of a superconductor after an interaction quench for different values of the final interaction from weak to strong coupling. The equilibrium BCS-BEC crossover becomes a sharp transition in the out-of-equilibrium dynamics between weak- and strong-coupling dynamical phases. Two different frequencies (${\mathrm{\ensuremath{\Omega}}}_{J}<{\mathrm{\ensuremath{\Omega}}}_{U}$) dominate the order parameter dynamics. In the weak coupling phase, ${\mathrm{\ensuremath{\Omega}}}_{J}$ follows twice the asymptotic average value of the gap (${\mathrm{\ensuremath{\Omega}}}_{J}\ensuremath{\approx}2{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\infty}}$) and ${\mathrm{\ensuremath{\Omega}}}_{U}$ is much larger but hardy visible in the anomalous density. At long times the BCS dynamics is recovered but surprisingly differences remain during the transient phase. In the strong coupling phase, the dynamics decouples from the asymptotic value of the order parameter except at exactly half filling and close to the dynamical transition where ${\mathrm{\ensuremath{\Omega}}}_{U}\ensuremath{\approx}2{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\infty}}$. The out-of-equilibrium transient spectral density and optical conductivity are presented and discussed in relation to pump probe experiments. Both ${\mathrm{\ensuremath{\Omega}}}_{J}$ and ${\mathrm{\ensuremath{\Omega}}}_{U}$ give rise to a complex structure of self-driven slow Rabi oscillations which are visible in the nonequilibrium optical conductivity where also sidebands appear due to the modulation of the double occupancy by superconducting amplitude oscillations. Analogous results apply to CDW and SDW systems. Our results show that in systems with long coherence times, pump-probe experiments allow us to characterize the regime (BCS vs preformed pairs) through very specific out-of-equilibrium fingerprints.
This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) \nto Bose-Einstein condensation (BEC) evolution in ultracold superfluid \nFermi gases when the interaction between atoms is varied. The tuning of \nattractive interactions permits the ground state of the system to evolve from a weak \nfermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs \nto a strong fermion attraction limit of tightly bound small bosonic molecules \nwhich undergo BEC. \nThis evolution is accompanied by anomalous behavior of many superfluid \nproperties, and reveals several quantum phase transitions. \nThis thesis has two parts: \nIn the first part, I analyze zero and nonzero orbital angular momentum \npairing effects, and show that a quantum phase transition occurs for \nnonzero angular momentum pairing, unlike the sss-wave case where the BCS \nto BEC evolution is just a crossover. \nIn the second part, I analyze two-species fermion mixtures with mass and \npopulation imbalance in continuum, trap and lattice models. In contrast with \nthe crossover physics found in the mass and population balanced mixtures, \nI demonstrate the existence of phase transitions between normal and \nsuperfluid phases, as well as phase separation between superfluid (paired) \nand normal (excess) fermions in imbalanced mixtures as a function of scattering \nparameter and mass and population imbalance.
With an eye toward the interpretation of so-called ``cosmological'' experiments performed on the low-temperature phases of 3He^{3}\mathrm{He}3He, in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter $\ensuremath{\lambda}$. In 3He^{3}\mathrm{He}3He, the quenches induced by the rapid cooling of the ``hot spots'' back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches that fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady state with a gap ${\ensuremath{\Delta}}_{\ensuremath{\infty}}={ϵ}_{C}{({e}^{2∕N(0)\ensuremath{\lambda}}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$. In weak coupling, this is only half the BCS gap, the extra energy being taken up by the residual collective motion of the pairs.