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arXiv:1112.2033

Two-photon emission from thin superconducting rings irradiated by coherent microwave fields

A. I. Agafonov

Published Dec 9, 2011• 0 citations
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Abstract

Superconducting current instability in thin rings, irradiated by a coherent microwave electromagnetic field, is studied. On the regular circular motion of the Cooper pairs in the supercurrent states the field imposes coherent oscillations of the condensate as a whole. The oscillating condensate should emit photons with the energies determined mainly by the discrete values of the superconducting ring energy. For the first time the probability of the supercurrent decay accompanied by the two- photon emission, is derived. The ring thickness is less than both the field skin-depth and the London penetration depth. Numerical results for the energy-angular distributions of the photons, as well as the waiting time of the stimulated two-photon transition depending on both the ring sizes and fluxoid number in the initial current state, are presented.

DOI
10.48550/arxiv.1112.2033

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Superconducting current instability in thin rings, irradiated by a coherent microwave electromagnetic field, is studied. On the regular circular motion of the Cooper pairs in the supercurrent states the field imposes coherent oscillations of the condensate as a whole. The oscillating condensate should emit photons with the energies determined mainly by the discrete values of the superconducting ring energy. For the first time the probability of the supercurrent decay accompanied by the two- photon emission, is derived. The ring thickness is less than both the field skin-depth and the London penetration depth. Numerical results for the energy-angular distributions of the photons, as well as the waiting time of the stimulated two-photon transition depending on both the ring sizes and fluxoid number in the initial current state, are presented.
When a thin-film ring with supercurrent is irradiated by coherent microwave field, the field induces coherent oscillations of all the Cooper pairs involved in the supercurrent. The oscillating charged condensate will emit photons with energies determined by the difference of quantized energy levels of the superconducting ring. This effect can be observed only in the rings, the thickness of which is less than both the field skin-depth and the London penetration depth. The probability of the microwave field-induced single-photon and two-photon emission is calculated. The energy - angle distributions of the emitted photons as a function of both the ring sizes and the fluxoid number trapped in the ring, are explored.
Abstract Microwave dressed states are found to emerge within the superconducting condensate when coupled to a quantized electromagnetic field due to photon-Cooper pair entanglement. This renormalized energy separation exceeds the prediction of BCS theory, yielding an enhancement that depends on the number of photons and persists even in the presence of electromagnetic vacuum fluctuations. Our work introduces an equilibrium quantum model of microwave-enhanced superconductivity, representing a significant departure from the standard non-equilibrium Eliashberg theory. We further demonstrate that the superconducting condensate exerts a back-action on the electromagnetic field, suppressing electric field fluctuations, including those from the vacuum state. This result is consistent with Glauber and Lewenstein’s field quantization in dielectric media.
In this paper we consider the interaction of a quantum-mechanical superconducting quantum interference device (SQUID) with a classical monochromatic electromagnetic (EM) field. We solve the time-dependent Schrödinger equation for the SQUID ring in this EM field. We demonstrate that non-perturbative transitions between the low-lying states of the ring, due to coherent multiphoton absorption processes, dominate, even when the single-photon energy is small compared with the energy separation between these states. We present experimental data on small-capacitance SQUID rings, interacting with microwave fields, which point to the existence of such non-perturbative transitions.
We present an extensive theoretical analysis of the supercurrent of a superconducting point contact of arbitrary transparency in the presence of a microwave field. Our paper is mainly based on two different approaches: a two-level model that describes the dynamics of the Andreev bound states in these systems and a fully microscopic method based on the Keldysh--Green function technique. This combination provides both a deep insight into the physics of irradiated Josephson junctions and quantitative predictions for arbitrary range of parameters. The main predictions of our analysis are: (i) for weak fields and low temperatures, the microwaves can induce transitions between the Andreev states, leading to a large suppression of the supercurrent at certain values of the phase; (ii) at strong fields, the current-phase relation is strongly distorted and the corresponding critical current does not follow a simple Bessel-function-like behavior; and (iii) at finite temperatures, the microwave field can enhance the critical current by means of transitions connecting the continuum of states outside the gap region and the Andreev states inside the gap. Our paper is of relevance for a large variety of superconducting weak links as well as for the proposals of using the Andreev bound states of a point contact for quantum computing applications.
Inducing interactions between individual photons is key for photonic quantum information and studying many-body photon states. Superconducting circuits are well suited to combine strong interactions with low losses. Typically, microwave photons are stored in an LC oscillator shunted by a Josephson junction, where the zero-point phase fluctuations across the junction determine the strength and order of photon interactions. Most superconducting nonlinear oscillators operate with small phase fluctuations, where two-photon Kerr interactions dominate. In our experiment, we shunt a high-impedance LC oscillator with a dipole element favoring the tunneling of paired Cooper pairs. This leads to large phase fluctuations of 3.4, accessing a regime where transition frequencies shift non-monotonically with excitation number. From spectroscopy, we extract two-, three-, and four-photon interaction energies, all of similar strength and exceeding the photon loss rate. Our results open a new regime of high-order photon interactions in microwave quantum optics. In superconducting circuits, the nonlinearity of Josephson junctions mediates photon interactions, but they are typically dominated by two-photon processes. Here the authors observe multi-photon interactions in a superconducting circuit with Cooper-pair pairing, revealing a new regime of microwave quantum optics.