Nonequilibrium Quasiparticle and Phonon Dynamics in Superconductors.

A. G. Aronov, Boris Z. Spivak

Han Huang, Samuel M. Kielar, Zhiting Tian

Phonon-induced Cooper pair breaking, inciting nonequilibrium quasiparticle (QP) bursts, is known to deteriorate the performance of superconducting devices. However, a detailed understanding of QP-phonon dynamics is lacking due to the absence of a well-established theoretical framework. This paper presents a fully ab initio scheme of calculating nonequilibrium, polarization-dependent QP-phonon dynamics in superconductors. The authors find that with only an 8% deviation from the equilibrium phonon Bose–Einstein distribution, the resulting nonequilibrium QP population is 83 times larger than the equilibrium Fermi–Dirac distribution, and the longitudinal acoustic (LA) phonon polarization is most responsible for QP generation. The authors demonstrated that the qubit transition rate in Josephson junction-based transmon qubits is increased by orders of magnitude when taking these nonequilibrium distributions into account, compared to equilibrium distributions. This framework allows an in-depth exploration of nonequilibrium QP-phonon dynamics in various Josephson-junction-based superconducting devices. It paves the way for formulating advanced phonon shielding strategies to target the LA polarization, potentially leading to enhanced device performance, such as increased coherence time of transmon qubits or reduced thermal noise in cryogenics.

Karwan Rostem, Pieter de Visser, Edward J. Wollack

When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at $2\mathrm{\ensuremath{\Delta}}$. We show that a phonon band gap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon band gap can be realized and matched to the recombination energy with a phononic crystal, a periodically patterned dielectric membrane. We discuss in detail the nonequilibrium quasiparticle and phonon distributions that arise in a superconductor due to a phonon band gap and a pair-breaking photon signal. Although intrinsically a nonequilibrium effect, the lifetime enhancement in the small-signal regime is remarkably similar to an estimate from an equilibrium formulation. The equilibrium estimate closely follows $exp({\mathrm{\ensuremath{\Omega}}}_{bg}/{k}_{B}{T}_{b})$, where ${\mathrm{\ensuremath{\Omega}}}_{bg}$ is the phonon band gap energy bandwidth above $2\mathrm{\ensuremath{\Delta}}$ and ${T}_{b}$ is the phonon bath temperature of the coupled electron-phonon system. We discuss the impact of a phononic band gap on the performance of a superconducting circuit element and propose a microwave resonator to measure the enhancement in the quasiparticle lifetime.

Andreas P. Schnyder

Yuta Murakami, Philipp Werner, Naoto Tsuji +1 more

We study the effect of strong electron-phonon interactions on the damping of the Higgs amplitude mode in superconductors by means of nonequilibrium dynamical mean-field simulations of the Holstein model. In contrast to the BCS dynamics, we find that the damping of the Higgs mode strongly depends on the temperature, becoming faster as the system approaches the transition temperature. The damping at low temperatures is well described by a power law, while near the transition temperature the damping shows exponential-like behavior. We explain this crossover in terms of a temperature-dependent quasiparticle lifetime caused by the strong electron-phonon coupling, which smears the superconducting gap edge and makes the relaxation of the Higgs mode into quasiparticles more efficient at elevated temperatures. We also reveal that the phonon dynamics can soften the Higgs mode, which results in a slower damping.