Josephson effect in fermionic superfluids across the BEC-BCS crossover

Abstract

We report on the observation of the Josephson effect between two strongly interacting fermionic superfluids coupled through a thin tunneling barrier. We prove that the relative population and phase are canonically conjugate dynamical variables, coherently oscillating throughout the entire crossover from molecular Bose-Einstein condensates (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluids. We measure the plasma frequency and we extract the Josephson coupling energy, both exhibiting a non-monotonic behavior with a maximum near the crossover regime. We also observe the transition from coherent to dissipative dynamics, which we directly ascribe to the propagation of vortices through the superfluid bulk. Our results highlight the robust nature of resonant superfluids, opening the door to the study of the dynamics of superfluid Fermi systems in the presence of strong correlations and fluctuations.The Josephson effect is a pristine example of a macroscopic quantum phenomenon, disclosing the broken symmetry associated with the superfluid state [1]. On a very fundamental level, it allows to pinpoint the most elusive part of the superfluid order parameter, the phase, through a measurable quantity, a particle current [2]. Furthermore, being based on tunneling processes, Josephson dynamics provides fundamental insights into the microscopic properties of superfluids and their robustness against dissipative phenomena [3]. Since its discovery, Josephson effect has been demonstrated for a variety of fermionic and bosonic systems [3][4][5][6][7][8][9][10][11][12]. However, it has so far eluded observation in BEC-BCS crossover superfluids [13,14] realized by ultracold Fermi gas mixtures close to a Feshbach resonance [15,16]. The interest in these systems is twofold: on the one hand, they encompass the two paradigmatic aspects of superfluidity within a single framework: Bose-Einstein condensation of tightly bound molecules and BCS superfluidity of long-range fermion pairs [13]. Moreover, in the resonant regime where the pair size matches the interparticle spacing, they exhibit universal properties, sharing analogies with other exotic strongly-correlated fermionic superfluids, from cuprate superconductors to nuclear and quark matter [17,18].In this work, we report on the observation of the Josephson effect in ultracold gases of 6 Li atom pairs across the BEC-BCS crossover. Our Josephson junction consists of two superfluid reservoirs, weakly coupled through a thin tunneling barrier. For all interaction regimes, we detect coherent oscillations of both the pair population imbalance ∆N = N L −N R and the relative phase ϕ = ϕ L −ϕ R across * Permanent address: Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México Distrito Federal, Mexico.the junction, measured in situ and after time-of-flight expansion respectively. We prove these two observables to be dynamically conjugate [2], directly unveiling macroscopic phase coherence in these strongly-correlated fermionic superfluids. We measure th...

Spin-asymmetric Josephson plasma oscillations

“…has to be on the order of a few percent [8,12]. This gives an upper bound to the Josephson frequency ω J =δ ↓ +δ ↑ in the plasma oscillation regime.…”

“…Motivated by the experiment in [8], we now ask how the small-amplitude Josephson plasma oscillations are affected by the presence of spin-dependent potentials. Detecting spinasymmetric Josephson plasma oscillations offers an alternative and perhaps an experimentally more feasible means to establish the spin-asymmetric Josephson effect with presentday techniques.…”

“…Note that in the spin-symmetric case, we have the standard formula ω p = √ E ch E J , where E J = I C ↑ + I C ↓ = I C is the Josephson energy [8,54] (recall that h = 1). However, in general, we expect the plasma frequency in the presence of spin-dependent potentials to differ from the standard case, as can be seen, for example, with the toy calculation presented in Sec.…”

“…Thus, the arrangement that we propose can be realized with existing techniques in ultracold-atom setups. The plasma oscillation regime corresponds to a relative number difference on the order of a few percent across the junction [8,12]. This limits the possible values of the spin-dependent potentials (see Sec.…”

“…Recently [8], the observation of Josephson plasma oscillations throughout the BCS-Bose-Einstein condensate (BEC) crossover has been reported in ultracold Fermi gases. Here, motivated by these experimental advances in Josephson dynamics, we consider the possibility to observe the spinasymmetric Josephson effect via spin-dependent plasma oscillations in a superfluid Fermi gas forming a Josephson junction with a spin-dependent potential.…”