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arXiv:0909.4168 · Europhysics Letters (EPL)

Delayed response of a fermion pair condensate to a modulation of the interaction strength

Jesús Plata

Published Sep 1, 2009• 2 citations
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Abstract

The effect of a sinusoidal modulation of the interaction strength on a fermion pair condensate is analytically studied. The system is described by a generalization of the coupled fermion-boson model that incorporates a time-dependent intermode coupling induced via a magnetic Feshbach resonance. Nontrivial effects are shown to emerge depending on the relative magnitude of the modulation period and the relaxation time of the condensate. Specifically, a nonadiabatic modulation drives the system out of thermal equilibrium: the external field induces a variation of the quasiparticle energies, and, in turn, a disequilibrium of the associated populations. The subsequent relaxation process is studied and an analytical description of the gap dynamics is obtained. Recent experimental findings are explained: the delay observed in the response to the applied field is understood as a temperature effect linked to the condensate relaxation time.

DOI
10.1209/0295-5075/87/50001

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The effect of a sinusoidal modulation of the interaction strength on a fermion pair condensate is analytically studied. The system is described by a generalization of the coupled fermion-boson model that incorporates a time-dependent intermode coupling induced via a magnetic Feshbach resonance. Nontrivial effects are shown to emerge depending on the relative magnitude of the modulation period and the relaxation time of the condensate. Specifically, a nonadiabatic modulation drives the system out of thermal equilibrium: the external field induces a variation of the quasiparticle energies, and, in turn, a disequilibrium of the associated populations. The subsequent relaxation process is studied and an analytical description of the gap dynamics is obtained. Recent experimental findings are explained: the delay observed in the response to the applied field is understood as a temperature effect linked to the condensate relaxation time.
Heating induced by an oscillating modulation of the interaction strength in an atomic Fermion pair condensate is analyzed. The coupled fermion-boson model, generalized by incorporating a time-dependent intermode coupling through a magnetic Feshbach resonance, is applied. The dynamics is analytically characterized in a perturbative scheme. The results account for experimental findings which have uncovered a damped and delayed response of the condensate to the modulation. The delay is due to the variation of the quasiparticle energies and the subsequent relaxation of the condensate. The detected damping results from the excitations induced by a nonadiabatic modulation: for driving frequencies larger than twice the pairing gap, quasiparticles are generated, and, consequently, heating sets in.
Abstract Heating induced by an oscillating modulation of the interaction strength in an atomic Fermion pair condensate is analyzed. The coupled fermion-boson model, generalized by incorporating a time-dependent intermode coupling through a magnetic Feshbach resonance, is applied. The dynamics are analytically characterized in a perturbative scheme. The results account for experimental findings which have uncovered a damped and delayed response of the condensate to the modulation. The delay is due to the variation of the quasiparticle energies and the subsequent relaxation of the condensate. The detected damping results from the excitations induced by a nonadiabatic modulation: for driving frequencies larger than twice the pairing gap, quasiparticles are generated and, consequently, heating sets in.
The dynamics of pair condensate formation in a strongly interacting Fermi gas close to a Feshbach resonance was studied. We employed a phase-shift method in which the delayed response of the many-body system to a modulation of the interaction strength was recorded. The observable was the fraction of condensed molecules in the cloud after a rapid magnetic field ramp across the Feshbach resonance. The measured response time was slow compared to the rapid ramp, which provides final proof that the molecular condensates reflect the presence of fermion pair condensates before the ramp.
The effect of magnetic-field modulation on a Fermi gas of atoms in the BCS-BEC crossover is studied analytically. Recent experimental findings on the system response to a sinusoidal variation of the field are explained. Specifically, the dissociation processes induced by the modulation in the Bose-Einstein condensate regime are described. The role played by the frequency, amplitude, and application time of the perturbation in the emergence of the observed behavior is clarified. The results uncover also the relevance of the detuning from the Feshbach resonance to the appearance of particular spectral features. The applicability of the field modulation as a spectroscopic tool for probing the crossover is discussed.
We investigate a population-imbalanced two-species fermionic system where the resonantly-paired fermions combine to form bosonic molecules via Feshbach interaction. The natural dynamics of the system is studied and it is shown that the oscillation of the condensate fraction is periodic or quasi periodic, depending on the value of Feshbach coupling. We describe how a time dependent magnetic field can be used to study the natural frequencies and thus explore the momentum space structure of the population imbalanced system.
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.