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Physical Review Letters

Josephson Effect for Photons in Two Weakly Linked Microcavities

An-Chun Ji, Qing Sun, X. C. Xie, W.M. Liu

Published Jan 15, 2009• 126 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.102.023602

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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.
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In cavity quantum electrodynamics (QED), the key physical systems include Fabry-Pérot cavity resonators and multilevel cold atoms. Since ultra-strong electromagnetic interaction between photons and quantized cavity modes occurs in cavity QED, many novel quantum optical effects such as optical Rabi oscillation, quantum collapse/revival of atomic-level population and atom-field quantum entanglement can be realized in such quantum microcavities. As is known in quantum optics, these schemes can be generalized to circuit QED, which is a circuit analog of cavity QED. Fundamental devices in circuit QED are superconducting coplanar waveguide microwave resonators and mesoscopic Cooper-pair boxes. Here, the coplanar waveguide resonator with photons stored can be identified as a resonant cavity and the Cooper-pair boxes with large electric dipoles play the role of multilevel cold atoms. Thus, all the quantum optical effects in conventional cavity QED can also be exhibited in the present superconducting circuit QED system. We consider the theoretical working mechanism of superconducting charge qubits based on tunable Josephson junction coupling. It can be found that an analog of optical Rabi oscillation in Cooper-pair boxes can be achieved by tuning an applied external magnetic field. Time evolution of energy levels in a Cooper-pair box, which is manipulated by a time-dependent magnetic flux through its Josephson-junction ring, is studied within the framework of time-dependent quantum mechanics.
Superconducting electronic devices have reemerged as contenders for both classical and quantum computing due to their fast operation speeds, low dissipation, and long coherence times. An ultimate demonstration of coherence is lasing. We use one of the fundamental aspects of superconductivity, the ac Josephson effect, to demonstrate a laser made from a Josephson junction strongly coupled to a multimode superconducting cavity. A dc voltage bias applied across the junction provides a source of microwave photons, and the circuit's nonlinearity allows for efficient down-conversion of higher-order Josephson frequencies to the cavity's fundamental mode. The simple fabrication and operation allows for easy integration with a range of quantum devices, allowing for efficient on-chip generation of coherent microwave photons at low temperatures.
In this paper we investigate the photonic tunneling effect between two coupled one-atom laser cavities. The physical system consists of two coupled photonic crystal microcavities and each cavity contains a coherently pumped two-level atom. The dynamics of the system can be described by the master equation in terms of the reduced density operator. It is shown that the photonic tunneling behavior depends on certain physical conditions of the system. In the absence of the pumping field and without dissipations, the coherent photon number imbalance between two cavities exhibits the alternating-current Josephson effect. However, when the pumping effect and losses of the system are taken into account, the mean photon number imbalance displays a damped oscillation. In addition, the influence of tunneling amplitude and photonic band-gap structure on the oscillations is also studied. The research gives a further insight into the correlated dynamics of two coupled one-atom laser systems and provides an idea for constructing novel photon tunnel devises.
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.
We propose an experiment that would demonstrate the dc and ac Josephson effects in two weakly linked Bose-Einstein condensates. We consider a time-dependent barrier, moving adiabatically across the trapping potential. The phase dynamics are governed by a "driven-pendulum" equation, as in current-driven superconducting Josephson junctions. At a critical velocity of the barrier (proportional to the critical tunneling current), there is a sharp transition between the dc and ac regimes. The signature is a sudden jump of a large fraction of the relative condensate population. Analytical results are compared with a numerical integration of the Gross-Pitaevskii equation, in an experimentally realistic situation.