Nonlinear dynamics of driven superconductors with dissipation

Abstract

We study the out-of-equilibrium dynamics of a BCS superconductor in the presence of a periodic drive with a frequency ω d larger than the equilibrium superconducting gap and an external bath providing dissipation. Similar to the dissipationless case, a subset of quasiparticles, resonant with the drive, synchronizes and produces interesting non-linear phenomena. For small dissipation Rabi-Higgs oscillations [Collado et al. Phys. Rev. B 98, 214519 (2018)] can be observed as a transient effect. At long-times in contrast, dissipation leads to a steady state with a population imbalance that increases quadratically for small drives and saturates for large drives as in non-linear quantum optics. We show also that second harmonic generation is allowed for a drive which acts on the BCS coupling constant. We also compute the intensity of time-and angle-resolved photo-emission spectroscopy (tr-ARPES) and time-resolved tunneling spectra. The excited quasiparticle population appears as a decrease (increase) in the photo-emission intensity at energy −ω d 2 (+ω d 2) measured from the chemical potential. The tunneling intensity shows a time-dependent depression at ±ω d 2 due to the lacking of spectral density and population unbalance causing Pauli blockade. We predict that at short times, compared to the energy relaxation time, both experiments will show oscillations with the Rabi-Higgs frequency. arXiv:1909.12310v1 [cond-mat.supr-con]

Fate of dynamical phases of a BCS superconductor beyond the dissipationless regime

“…The case of a periodically driven or pumped superconductor is also very interesting. The order parameter shows a synchronization phenomena of Rabi oscillations of quasiparticles states which can be exploit to access all the aforementioned dynamical phases [20].…”

Non-equilibrium dynamics across the BEC-BCS crossover

“…Such population inversion in the momentum distribution function (J z k ) is characteristic of collective Rabi oscillations occurring in a superconductor subject to a periodic drive. 11,16 In the case of a pure BCS dynamics as considered in Ref. 16 and for a band width drive collective Rabi oscillations are due to states at 'resonant' energies…”

“…[6][7][8] These experiments have motivated the analysis of the BCS pairing problem with time-dependent interactions and several proposals based on the realization of a suitable out-of equilibrium dynamics (pump) which is then measured by a probe pulse. [9][10][11][12][13][14][15][16] Within the pseudospin formulation of Anderson 17 the problem can be mapped onto an effective spin Hamiltonian for which the Bloch dynamics can be solved exactly. [18][19][20][21][22] Upon considering the situation with a sudden change of the pairing interaction ("quench") the dynamics of the Cooper pair states either dephases or synchronizes.…”

Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics

“…The experiments mentioned above have motivated the analysis of the BCS pairing problem with time-dependent interactions and several proposals based on the realization of a suitable out-of equilibrium dynamics (pump) which is then measured by a probe pulse. [8][9][10][11][12][13][14][15][16][17][18] Within the pseudospin formulation of Anderson 19 the problem can be mapped onto an effective spin Hamiltonian for which the Bloch dynamics can be solved exactly. [20][21][22][23][24] In the present paper we investigate the case of adia-batically switching off the interaction in a BCS superconductor.…”