Dissipation and noise in strongly driven Josephson junctions

TL;DR

This work shows that strong microwave driving can activate dissipation in Josephson junctions through multiphoton Cooper-pair breaking, even when single-photon energies are below the pair-breaking threshold. By formulating a microscopic model with a polarization operator in a Keldysh framework and deriving the driven admittance, the authors reveal phase- and drive-dependent dissipation and memory effects, including non-Markovian dynamics. They illustrate the consequences for a low-impedance LC resonator, finding non-Lorentzian spectra and drive-tunable quasitemperature, signaling potential for tunable dissipative elements and quantum heat-engine-like applications. The results highlight rich nonequilibrium physics in driven superconducting circuits and point to future work using fully quantum or hierarchical methods to capture quantum fluctuations and strong-coupling effects beyond the quasiclassical regime.

Abstract

In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.

Figures (7)

• Figure 1: Retarded components of the polarization operator (a, c, e) $\Pi^\mathrm R_\mathrm n$ and (b, d, f) $\Pi^\mathrm R_\mathrm s$ as functions of angular frequency $\omega$ for (a, b) cold $k_\mathrm B T_\mathrm s = 0.04\times \Delta_\Sigma$ and (c, d, e, f) hot $k_\mathrm B T_\mathrm s = 0.32\times \Delta_\Sigma$ junctions. Here, (a, b, c, d) $\Delta_\mathrm l = \Delta_\mathrm r$, (e, f) $\Delta_\mathrm l = 1.5 \times \Delta_\mathrm r$, and $\nu_\mathrm l = \nu_\mathrm r = 0$.
• Figure 2: Monochromatic drive $V_0\cos(\Omega t)$ and a weak probe voltage $v_\textrm{p}(t)$ applied to Josephson junction which is biased with a dc phase of $\varphi_0$. The bias, the drive, and the probe together lead to the current $I_\textrm{J}(t)$ through the junction.
• Figure 3: Admittance of a non-driven symmetric Josephson junction $Y_\textrm{J}$ as a function of angular frequency $\omega$ for the temperature of the superconducting leads at (a, b) $k_\mathrm B T_\mathrm s = 0.04\times \Delta_\Sigma$, (c, d) $k_\mathrm B T_\mathrm s = 0.32\times \Delta_\Sigma$ and the dc phase bias across the junction of (a, c) $\varphi_0=0$ and (b, d) $\varphi_0=\pi$.
• Figure 4: Frequency-preserving admittance component $Y_{\mathrm J, 0}$ of a driven symmetric Josephson junction as a function of angular frequency $\omega$. The temperature of the superconducting leads is $k_\mathrm B T_\mathrm s = 0.04\times \Delta_\Sigma$ and the drive angular frequency is $\Omega = 0.155\times \Delta_\Sigma/\hbar$. (a, b) Real and imaginary components of the admittance for the drive amplitude $e V_0 = 0.5\times\Delta_\Sigma$. The vertical black dotted lines highlight logarithmic singularities of the admittance at frequencies $\omega = \pm \Delta_\Sigma / \hbar + n \Omega$, where $n$ is an odd integer for (a) $\varphi_0=0$ and an even integer for (b) $\varphi_0=\pi$. (c, d) Real component of admittance as a function of angular frequency and drive amplitude.
• Figure 5: Diagram of an $LC$ circuit formed by an inductor $L_\mathrm r$, a capacitor $C_\mathrm r$, and a Josephson junction, driven by external voltage $V_\mathrm d(t)$. The circuit is coupled via the capacitor $C_\mathrm p$ to a probe formed by two semi-infinite transmission lines with impedance $Z_\mathrm p$ at temperature $T_\mathrm p$. The junction has a dc phase bias $\varphi_0$, the flux degrees of freedom of the $LC$ circuit and probe nodes are denoted by $\phi_\mathrm r$ and $\phi_\mathrm p$, respectively. From the probe side, an input signal $v_\mathrm i$ is sent to the $LC$ circuit and the output signal $v_\mathrm o$ is probed.