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arXiv:2208.02739 · Physical Review A

Dissipative dynamics of a fermionic superfluid with two-body losses

Giacomo Mazza, Marco Schirò

Published May 12, 2023• 26 citations
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Abstract

A sudden change of pairing interaction leads to coherent solitonlike oscillations of the superfluid order parameter. Here, the authors study the effect of pair losses on the dynamics of a quenched fermionic superfluid and reveal that even a tiny dissipation leads to a large renormalization of the soliton period. They explain the effect through a dissipative soliton model and a variational approach for the Markovian quantum dynamics.

DOI
10.1103/physreva.107.l051301

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A sudden change of pairing interaction leads to coherent solitonlike oscillations of the superfluid order parameter. Here, the authors study the effect of pair losses on the dynamics of a quenched fermionic superfluid and reveal that even a tiny dissipation leads to a large renormalization of the soliton period. They explain the effect through a dissipative soliton model and a variational approach for the Markovian quantum dynamics.
We predict a new mechanism to induce collective excitations and a nonequilibrium phase transition of fermionic superfluids via a sudden switch on of two-body loss, for which we extend the BCS theory to fully incorporate a change in particle number. We find that a sudden switch on of dissipation induces an amplitude oscillation of the superfluid order parameter accompanied by a chirped phase rotation as a consequence of particle loss. We demonstrate that when dissipation is introduced to one of the two superfluids coupled via a Josephson junction, it gives rise to a nonequilibrium dynamical phase transition characterized by the vanishing dc Josephson current. The dissipation-induced collective modes and nonequilibrium phase transition can be realized with ultracold fermionic atoms subject to inelastic collisions.
We revisit the study of amplitude oscillations in a pair condensate of fermions after an interaction quench, and generalize it to nonzero temperature. For small variations of the order parameter, we show that the energy transfer during the quench determines both the asymptotic pseudo-equilibrated value of the order parameter and the magnitude of the oscillations, after multiplication by, respectively, the static response of the order parameter and spectral weight of the pair-breaking threshold. Since the energy transferred to the condensed pairs decreases with temperature as the superfluid contact, the oscillations eventually disappear at the critical temperature. For deeper quenches, we generalize the regimes of persistent oscillations and monotonic decay to nonzero temperatures, and explain how they become more abrupt and are more easily entered at high temperatures when the ratio of the initial to final gap either diverges, when quenching towards the normal phase, or tends to zero, when quenching towards the superfluid phase. Our results are directly relevant for existing and future experiments on the non-equilibrium evolution of Fermi superfluids near the phase transition.
We investigate nonequilibrium dynamics of a triad of fermionic superfluids connected via Josephson junctions, following sudden switch-on of two-body loss in one of the three superfluids. By formulating the dissipative BCS theory for the Lindblad equation, we find that the superfluid order parameter exhibits a phase rotation, thereby giving rise to three types of dc Josephson currents corresponding to different junctions. We demonstrate that, when the tunneling amplitude V31V_{31}V31​ between superfluids without two-body loss is weak, a two-step nonequilibrium phase transition characterized by the vanishing dc Josephson currents occurs: dissipation first induces the nonequilibrium phase transition by making one dc Josephson current finite, while further increasing dissipation makes this remaining dc Josephson current vanish. By contrast, when V31V_{31}V31​ is strong, dissipation induces the nonequilibrium phase transition in which all dc Josephson currents simultaneously vanish. An analytical study based on a simplified model further supports this observation.
Quench dynamics of fermionic superfluids are an active topic both experimentally and theoretically. Using the BCS theory, such non-equilibrium problems can be reduced to nearly independent spin dynamics, only with a time-dependent mean-field pairing term. This results in persisting oscillations of the pairing strength in certain parameter regimes. However, experiments have observed that the oscillations decay rapidly when the interaction becomes strong, such as in the unitary Fermi gas [Phys. Rev. Res. 3, 023205 (2021)]. Theoretical analysis on this matter is still absent. In this work, we construct an SYK-like model to analyze the effect of strong interactions in a one-dimensional BCS system. We employ the large- N N approximation and a Green’s function-based technique to solve the equilibrium problem and quench dynamics. Our findings reveal that a strong SYK interaction suppresses the pairing order. Additionally, we verify that the system quickly thermalizes with SYK interactions, whether it involves intrinsic pairing order or proximity effect, resulting in a rapid decay of the oscillation strength. The decay rates exhibit different scaling laws against SYK interaction, which can be understood in terms of the Boltzmann equation. This work represents a first step towards understanding the attenuating dynamics of strongly interacting fermionic superfluids.
The key feature of time-dependent dynamics in a paired Fermi superfluid is the presence of a large number of independent degrees of freedom---the pairing amplitudes of fermions with different momenta. We argue that useful prototypes of this dynamics come from D-brane constructions of string theory. Using a specific example of that kind, we identify the mechanism by which a strongly coupled Fermi superfluid relaxes to equilibrium; it involves a wave of excitation in the momentum space, propagating from the Fermi surface towards the ultraviolet. For a sudden quench induced by a change in the fermion coupling, we find that the relaxation occurs rapidly, over only a few oscillations of the quasiparticle gap.
Driven-dissipative open quantum many-body systems exhibit rich phases that are characterized by the steady states in the long-time dynamics. However, lossy open systems inevitably decay to the vacuum, making their transient evolution the primary focus. Assuming the Hartree-Fock-Bogoliubov ansatz, we derive a generalized time-dependent Hartree-Fock-Bogoliubov equation based on the least action principle for open quantum systems. By solving the quench dynamics after abruptly introducing inelastic scattering or one-body loss in the Bardeen-Cooper-Schrieffer limit, we reveal a generic dynamical phase transition: the superfluid order parameter vanishes non-analytically while the superfluid fraction's first-order time derivative undergoes a discontinuous change at a finite critical time. This marks a new paradigm of dynamical phase transitions, distinct from those in closed systems, where the initial state must be finely tuned.