Decay of plasmonic waves in Josephson junction chains

Abstract

We study the damping of plasma waves in linear Josephson junction chains as well as in two capacitively coupled chains. In the parameter regime where the ground capacitance can be neglected, the theory of the antisymmetric mode in the double chain can be mapped onto the theory of a single chain. We consider two sources of relaxation: the scattering from quantum phase slips (QPS) and the interaction among plasmons related to the nonlinearity of the Josephson potential. The contribution to the relaxation rate 1/τ from the nonlinearity scales with the fourth power of frequency ω, while the phase-slip contribution behaves as a power law with a non-universal exponent. In the parameter regime where the charging energy related to the junction capacitance is much smaller than the Josephson energy, the amplitude of QPS is strongly suppressed. This makes the relaxation mechanism related to QPS efficient only at very low frequencies. As a result, for chains that are in the infrared limit on the insulating side of the superconductor-insulator transition, the quality factor ωτ shows a strongly non-monotonic dependence on frequency, as was observed in a recent experiment.

Theory of coherent phase modes in insulating Josephson junction chains

“…We formally circumvent this problem by introducing an intrinsic broadening of the states. We find that the calculated decay rates that increase as one reduces wave-vector q consistent with both experiment [19] and recent theory [29]. However, it is not clear that the intrinsic source of broadening is justified at the low temperatures required to have an insulator.…”

“…Furthermore, we explicitly exclude disorder broadening of single-plasmon states. Such broadening is implicitly included in the replica-based disorder averaged partition function approach [29]. However, as shown in recent work [30], disorder-induced fluctuations can also lead to extrinsic broadening of the resonances.…”

“…In the last section of this work, we consider the perturbative decay of plasmons due to quantum phase slips, similar to recent work [29]. However, in contrast to previous work [29], we avoid analytic continuation and directly evaluate the self-energy with the quantum phase slip term in Eq. 1 being treated as a perturbation.…”

Quantum electrodynamics of a superconductor–insulator phase transition

“…Decoherence of the phase mode in a 1D Bose glass has been explored theoretically in response to our experiment [12][13][14]. One mechanism is that a single probe photon decays into lower-frequency photons [12].…”

“…By pushing the chain parameters deeper into the insulating state, we achieved propagation with the speed of light down to 8 × 10 5 m/s and the wave impedance up to 23 kΩ. The latter quantity exceeds the predicted critical impedance by an order of magnitude [6][7][8][9][10][11], which opens the problem of quantum electrodynamics of a Bose glass insulator for both theory and experiment [12][13][14]. Notably, the effective fine structure constant of such a 1D vacuum exceeds a unity, promising transformative applications to quantum science and technology.…”