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arXiv:2510.07398 · Physical review. B./Physical review. B

Measuring intrinsic relaxation rates in superconductors using nonlinear response

Wei-En Tseng, Rahul Nandkishore

Published Mar 5, 2026• 0 citations
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Abstract

This package includes the source code used for the simulations presented in the paper “Measuring intrinsic relaxation rates in superconductors using nonlinear response.” The code numerically solves the time-dependent Anderson pseudospin equations of motion for s- and d-wave superconductors driven by a short pump pulse, both with and without a phenomenological (energy- and momentum-dependent) damping of the pseudospins. From these simulations, the time-dependent superconducting gap and nonlinear current response are obtained.

DOI
10.1103/3j2n-tvvr

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This package includes the source code used for the simulations presented in the paper “Measuring intrinsic relaxation rates in superconductors using nonlinear response.” The code numerically solves the time-dependent Anderson pseudospin equations of motion for s- and d-wave superconductors driven by a short pump pulse, both with and without a phenomenological (energy- and momentum-dependent) damping of the pseudospins. From these simulations, the time-dependent superconducting gap and nonlinear current response are obtained.
The photoexcited state associated with superconducting fluctuations above the superconducting critical temperature Tc{T}_{c}Tc​ is studied based on the time-dependent Ginzburg-Landau approach. The excited state is created by an electric-field pulse and is probed by a weak secondary external field, which is treated by the linear response theory mimicking pump-probe spectroscopy experiments. The behavior is basically controlled by two relaxation rates: one is ${\ensuremath{\gamma}}_{1}$ proportional to the temperature measured from the critical point $T\ensuremath{-}{T}_{c}$, and the other is ${\ensuremath{\gamma}}_{2}$ proportional to the excitation intensity of the pump pulse. The excited state approaches the equilibrium state exponentially in a long time $t\ensuremath{\gg}{\ensuremath{\gamma}}_{1}^{\ensuremath{-}1}$, while in the intermediate-time domain we find a power-law or logarithmic decay with different exponents for $t\ensuremath{\ll}{\ensuremath{\gamma}}_{2}^{\ensuremath{-}1}$ and ${\ensuremath{\gamma}}_{2}^{\ensuremath{-}1}\ensuremath{\ll}t\ensuremath{\ll}{\ensuremath{\gamma}}_{1}^{\ensuremath{-}1}$, even though the system is located away from the critical point. This is interpreted as the critical point in equilibrium being extended to a finite region in the excited situation. The parameter dependences on both the pump and probe currents are also systematically studied in all dimensions.
Motivated by the generation by optical pulses of nonthermal distributions of nuclear spins in quantum dots we investigate the effect of optical pulses applied to Bardeen-Cooper-Schrieffer (BCS) superconductors. Using time-dependent mean-field theory formulated with Anderson pseudospins, we study the electronic configurations and the energy deposited in the system by optical pulses. The pulses are included by Peierls substitution and we study short rectangular pulses as well as idealized $\ensuremath{\delta}$ pulses. Already a few and even a single pulse generates highly nontrivial distributions of electron expectation values which we simulate numerically and explain analytically based on the linearization of the equations of motion. These results suggest so far unexplored experimental possibilities for the optical control of superconducting states.
The relaxation of a ddd-wave superconductor that has been driven out of equilibrium by an optical pulse is investigated. We consider a simple model for the low-energy nonequilibrium state, one in which the unpaired quasiparticles form Fermi spheres near the gap nodes, and calculate the decay rate of the quasiparticle population due to phonon-assisted recombination. In the high density limit for the photoinjected quasiparticles, the decay rate dn∕dtdn∕dtdn∕dt is found to vary as n5∕2{n}^{5∕2}n5∕2, which differs from the n2{n}^{2}n2 form commonly adopted in phenomenological models of the relaxation dynamics. In the low density limit, the decay is exponential. From numerical estimates, we determine that phonon-assisted recombination could play an important role over the picosecond time scales of current interest. We compare our results to pump-probe optical experiments on high TC{T}_{C}TC​ cuprates and find reasonable agreement for the decay rate in underdoped YBCO for low laser intensity.
Superconducting quantum interference devices (SQUIDs) are used across physics and engineering, from amplification to detecting tiny magnetic fields to quantum computing. In many applications the SQUID's steady-state response is of interest, but here the authors measure and model the $t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t$ response to short bursts of radiation. The resulting ringdown oscillations in voltage decay over time, with a rich structure that may be particularly useful in discriminating weak magnetic fluxes---in qubits, for example.