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Journal of Telecommunications and Information Technology

Optical Josephson effects using phase-conjugating mirrors: an analogy with superconductors

M. Blaauboer, Daan Lenstra, A. Lodder

Published Jun 30, 2000• 1 citation
Publisher

Abstract

Motivated by the analogy between a phase-conjugating mirror (PCM) and a superconductor, we search for optical counterparts of the well-known DC and AC Josephson effects. We show that in a system consisting of two PCM`s separated by vacuum an ,,optical supercurrent`` arises as a function of an applied phase difference between the PCM`s, which is the optical analogue of the DC supercurrent flowing in a superconducting weak link. The corresponding AC effect occurs when the two PCM`s are pumped by light of a different frequency, causing the phase difference to oscillate in time with the frequency difference.

DOI
10.26636/jtit.2000.1-2.17

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Motivated by the analogy between a phase-conjugating mirror (PCM) and a superconductor, we search for optical counterparts of the well-known DC and AC Josephson effects. We show that in a system consisting of two PCMs separated by vacuum an ,,optical supercurrent`` arises as a function of an applied phase difference between the PCMs, which is the optical analogue of the DC supercurrent flowing in a superconducting weak link. The corresponding AC effect occurs when the two PCM`s are pumped by light of a different frequency, causing the phase difference to oscillate in time with the frequency difference.
We describe an optical system that allows for direct observation of the photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms. We show that, by moving the ultracold atoms within one cavity, we could simulate an analogous superconducting circuit and realize both the alternating- and direct-current (ac and dc) photonic Josephson effects. This provides a strategy for constructing novel interference devices of coherent photons and enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems.
Josephson effects were predicted theoretically by B. D. Josephson in 1962. Josephson effects occur in weak links, structures which link two bulk superconductors 1 and 2, capable of carrying a supercurrent but not as strongly superconducting as the bulk materials. This chapter applies a specified voltage to the weak link, but many weak links have impedances at the relevant microwave frequencies of a few ohms or less. The surprising appearance of the oscillatory current is the d.c. Josephson effect. The ability of weak links to provide tunable oscillator power at very high frequencies can be very useful, but the power available from a single junction is of order RIJ2 typically less than 1 μW, and from a low-impedance source which is difficult to match; practical applications usually therefore make use of a suitable array of weak links.
This is a theoretical study of the interplay of optical phase conjugation and multiple scattering. We calculate the intensity of light reflected by a phase-conjugating mirror when it is placed behind a disordered medium. We compare the results of a fully phase-coherent theory with those from the theory of radiative transfer. Both methods are equivalent if the dwell time ${\ensuremath{\tau}}_{\mathrm{dwell}}$ of a photon in the disordered medium is much larger than the inverse of the frequency shift $2\ensuremath{\Delta}\ensuremath{\omega}$ acquired at the phase-conjugating mirror. When ${\ensuremath{\tau}}_{\mathrm{dwell}}\ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\lesssim}1$, in contrast, phase coherence drastically affects the reflected intensity. In particular, a minimum in the dependence of the reflectance on the disorder strength disappears when $\ensuremath{\Delta}\ensuremath{\omega}$ is reduced below $1/{\ensuremath{\tau}}_{\mathrm{dwell}}.$ The analogies and differences with Andreev reflection of electrons at the interface between a normal metal and a superconductor are discussed.
This paper is the second in a series describing propagation of electromagnetic radiation in phase-conjugate oscillators. We apply the formulation developed in the first paper to study the phase-conjugate resonator (PCR) and the Fabry–Perot cavity with an intracavity phase-conjugate mirror (PCM). Our results show that nondegenerate oscillation occurs in the PCR for large parametric gains and fixed separation between the conventional reflector and the PCM. The bandwidth is considerably reduced from that of a PCM alone. In the phase-conjugate oscillator, oscillation will occur at the pump frequency only if there is no separation between the conventional mirrors and the phase-conjugate element and if the nonlinear medium fills the entire Fabry–Perot cavity.