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Canadian Journal of Physics

Photonic analogue of boson Josephson junction in two coupled nonlinear cavities with pumping and dissipation

Xiaoyong Guo, Zhongzhou Ren, Guangjie Guo, Bo Zhou

Published Jan 1, 2012• 1 citation
Publisher

Abstract

In this paper, we propose a photonic Josephson junction in two coupled, Kerr-type, nonlinear cavities. In the coherent state representation, saddle point analysis of the system action yields a mean-field description of the coherent photon current. The photonic analogs of the Rabi oscillation, the AC effect as well as the Shapiro resonance are found. The tunneling dynamics dramatically change at a critical point that is determined by the relative value of on-site nonlinear strength versus intercavity tunneling rate. We discuss this critical behavior for various parameters in detail. Furthermore, the influences of the initial conditions and the environment-induced pumping–dissipation process on the system dynamics are also studied.

DOI
10.1139/p11-138

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In this paper, we propose a photonic Josephson junction in two coupled, Kerr-type, nonlinear cavities. In the coherent state representation, saddle point analysis of the system action yields a mean-field description of the coherent photon current. The photonic analogs of the Rabi oscillation, the AC effect as well as the Shapiro resonance are found. The tunneling dynamics dramatically change at a critical point that is determined by the relative value of on-site nonlinear strength versus intercavity tunneling rate. We discuss this critical behavior for various parameters in detail. Furthermore, the influences of the initial conditions and the environment-induced pumping–dissipation process on the system dynamics are also studied.
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We propose a bosonic Josephson junction (BJJ) in two nonlinear mechanical resonators coupled through two-phonon exchange interaction induced by quadratic optomechanical couplings. The nonlinear dynamical equations and effective Hamiltonian are derived to describe behaviors of the BJJ. We show that the BJJ can work in two different dynamical regimes: Josephson oscillation and macroscopic self-trapping. The system can transfer from one regime to the other one when the self-interaction and asymmetric parameters exceed their critical values. We show that the transition from Josephson oscillation to macroscopic self-trapping can be induced by the phonon damping of the asymmetric BJJ. Our results open up a way to demonstrate BJJ with two-phonon exchange interaction and might be applied to other systems.
We explore theoretically the nonequilibrium photonic phases of an array of coupled cavities in presence of incoherent driving and dissipation. In particular, we consider a Hubbard model system where each site is a Kerr nonlinear resonator coupled to a two-level emitter, which is pumped incoherently. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of such a system. We find that, at a critical value of the intercavity photon hopping rate, a second-order nonequilibrium phase transition associated with the spontaneous breaking of the U(1)\text{U}(1)U(1) symmetry occurs. The transition from an incompressible Mott-like photon fluid to a coherent delocalized phase is driven by commensurability effects and not by the competition between photon hopping and optical nonlinearity. The essence of the mean-field predictions is corroborated by finite-size simulations obtained with matrix product operators and corner-space renormalization methods.
We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes–Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect as described by the Bose–Hubbard (BH) model rather than a Jaynes–Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes–Cummings–Hubbard (JCH) model originating from the mixed nature of the excitations and investigate the regimes where the BH approximation would faithfully match the JCH physics. We find that the latter is true for values of the light–matter coupling and losses beyond the reach of current technology. Throughout the study we operate in the weak pumping, fully quantum mechanical regime where approaches such as mean field theory fail, and instead use a combination of quantum trajectories and the time evolving block decimation algorithm to compute the relevant steady state observables. In our study we have assumed small to medium size arrays (from 3 up to 16 sites) and values of the ratio of coupling to dissipation rate g / γ ∼ 20, which makes our results implementable with current designs in circuit QED and with near future photonic crystal set ups.
We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: The master equation for the model, which takes into account both a coherent continuous drive and radiative as well as nonradiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between 000 and 111, and divides the diagram identified by the two energy scales of the system---the tunneling and the nonlinear Kerr interaction---into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities, and the emitted light is coherent. In the opposite limit, photon blockade sets in, and the system shows an insulatorlike state with photons locked on each cavity, identified by antibunching of emitted light.
Abstract Josephson effects are commonly studied in quantum systems in which dissipation or noise can be neglected or do not play a crucial role. In contrast, here we discuss a setup where dissipative interactions do amplify a photonic Josephson current, opening a doorway to dissipation-enhanced sensitivity of quantum-optical interferometry devices. In particular, we study two coupled nanolasers subjected to phase coherent drivings and coupled by a coherent photon tunneling process. We describe this system by means of a Fokker–Planck equation and show that it exhibits an interesting non-equilibrium phase diagram as a function of the coherent coupling between nanolasers. As we increase that coupling, we find a non-equilibrium phase transition between a phase-locked (PL) and a non-phase-locked (NPL) steady-state, in which phase coherence is destroyed by the photon tunneling process. In the coherent, PL regime, an imbalanced photon number population appears if there is a phase difference between the nanolasers, which appears in the steady-state as a result of the competition between competing local dissipative dynamics and the Josephson photo-current. The latter is amplified for large incoherent pumping rates and it is also enchanced close to the lasing phase transition. We show that the Josephson photocurrent can be used to measure optical phase differences. In the quantum limit, the accuracy of the two nanolaser interferometer grows with the square of the photon number and, thus, it can be enhanced by increasing the rate of incoherent pumping of photons into the nanolasers.