Theory of coherent phase modes in insulating Josephson junction chains

Abstract

Recent microwave reflection measurements of Josephson junction chains have suggested the presence of nearly coherent collective charge oscillations deep in the insulating phase. Here we develop a qualitative understanding of such coherent charge modes by studying the local dynamical polarizability of the insulating phase of a finite length sine-Gordon model. By considering parameters near the non-interacting fermion limit where the charge operator dominantly couples to solitonantisoliton pairs of the sine-Gordon model, we find that the local dynamical polarizability shows an array of sharp peaks in frequency representing coherent phase oscillations on top of an incoherent background. The strength of the coherent peaks relative to the incoherent background increases as a power law in frequency as well as exponentially as the Luttinger parameter approaches a critical value. The dynamical polarizability also clearly shows the insulating gap. We then compare the results in the high frequency limit to a perturbative estimate of phase-slip-induced decay of plasmons in the Josephson junction chain. arXiv:1811.07941v3 [cond-mat.supr-con]

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]. The other one consists of inelastic collisions of the probe photon with low-frequency thermal photons [13].…”

“…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.…”

Dual Fraunhofer interference and charge fluctuations in long quantum phase slip wires

“…The phase difference is, instead, pinned by the voltage source such thatφ R =φ L − 2eV b /h, where V b is the bias voltage. Here, on the same grounds, the restoring response to a 2π phase slip event in the chain would not contribute to the AC part of the action [22,35].…”

“…The AC effect has been considered extensively in systems of Josephson junctions in the phase slip regime (or analogously in nanowires with Josephson coupling between grains) [10][11][12][13][14][15][16][17]. In particular, the effects of disorder both due to background charge (parity) fluctuations [16][17][18][19][20][21][22][23] and spatial variations in junction parameters [15,[23][24][25] has been studied in detail. The AC effect has also been demonstrated experimentally for phase slips in Josephson junction rings [10] and networks [12,26] as well as for CQPS in devices made of continuous superconducting wires [27][28][29], yet the appearance of the direct dual to the diffraction effects in Josephson junctions is lacking.…”

Photon-Instanton Collider Implemented by a Superconducting Circuit

“…Recent experiments have exposed intriguing photon dynamics in a uniform Josephson junction array, in which phase slips may play an important role [13]. However, their interpretation is complicated due to the importance of disorder and charge fluctuations [14][15][16]. It has recently been realized theoretically [17][18][19][20][21][22][23][24][25][26][27] that controllable quantum simulation of many-body physics may be easier to achieve in "quantum impurity" setups, leading to initial experimental works [28][29][30][31].…”