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Register a new userRobust photon transmission in nonlinear parity-time-symmetric cavities
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We explore the photon transfer in the nonlinear parity-time-symmetry system of two coupled cavities, which contains nonlinear gain and loss dependent on the intracavity photons. Analytical solution to the steady state gives a saturated gain, which satisfy the parity-time symmetry automatically. The eigen-frequency self-adapts the nonlinear saturated gain to reach the maximum efficiency in the steady state. We find that the saturated gain in the weak coupling regime does not match the loss in the steady state, exhibiting an appearance of a spontaneous symmetry-breaking. The photon transmission efficiency in the parity-time-symmetric regime is robust against the variation of the coupling strength, which improves the results of the conventional methods by tuning the frequency or the coupling strength to maintain optimal efficiency. Our scheme provides an experimental platform for realizing the robust photon transfer in cavities with nonlinear parity-time symmetry.
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The nonlinear dynamics of a balanced parity-time symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain-thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time symmetric systems. Unlike other saturable parity time symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.
Classical open systems with balanced gain and loss, i.e. parity-time ($mathcal{PT}$) symmetric systems, have attracted tremendous attention over the past decade. Their exotic properties arise from exceptional point (EP) degeneracies of non-Hermitian Hamiltonians that govern their dynamics. In recent years, increasingly sophisticated models of $mathcal{PT}$-symmetric systems with time-periodic (Floquet) driving, time-periodic gain and loss, and time-delayed coupling have been investigated, and such systems have been realized across numerous platforms comprising optics, acoustics, mechanical oscillators, optomechanics, and electrical circuits. Here, we introduce a $mathcal{PT}$-symmetric (balanced gain and loss) system with memory, and investigate its dynamics analytically and numerically. Our model consists of two coupled $LC$ oscillators with positive and negative resistance, respectively. We introduce memory by replacing either the resistor with a memristor, or the coupling inductor with a meminductor, and investigate the circuit energy dynamics as characterized by $mathcal{PT}$-symmetric or $mathcal{PT}$-symmetry broken phases. Due to the resulting nonlinearity, we find that energy dynamics depend on the sign and strength of initial voltages and currents, as well as the distribution of initial circuit energy across its different components. Surprisingly, at strong inputs, the system exhibits self-organized Floquet dynamics, including $mathcal{PT}$-symmetry broken phase at vanishingly small dissipation strength. Our results indicate that $mathcal{PT}$-symmetric systems with memory show a rich landscape.
Optical systems combining balanced loss and gain profiles provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity-time- (PT-) symmetric Hamiltonians and to originate new synthetic materials with novel properties. To date, experimental works on PT-symmetric optical systems have been limited to waveguides in which resonances do not play a role. Here we report the first demonstration of PT-symmetry breaking in optical resonator systems by using two directly coupled on-chip optical whispering-gallery-mode (WGM) microtoroid silica resonators. Gain in one of the resonators is provided by optically pumping Erbium (Er3+) ions embedded in the silica matrix; the other resonator exhibits passive loss. The coupling strength between the resonators is adjusted by using nanopositioning stages to tune their distance. We have observed reciprocal behavior of the PT-symmetric system in the linear regime, as well as a transition to nonreciprocity in the PT symmetry-breaking phase transition due to the significant enhancement of nonlinearity in the broken-symmetry phase. Our results represent a significant advance towards a new generation of synthetic optical systems enabling on-chip manipulation and control of light propagation.
In this work, we propose a PT-symmetric coupler whose arms are birefringent waveguides as a realistic physical model which leads to a so-called quadrimer i.e., a four complex field setting. We seek stationary solutions of the resulting linear and nonlinear model, identifying its linear point of PT symmetry breaking and examining the corresponding nonlinear solutions that persist up to this point, as well as, so-called, ghost states that bifurcate from them. We obtain the relevant symmetry breaking bifurcations and numerically follow the associated dynamics which give rise to growth/decay even within the PT-symmetric phase. Our obtained stationary nonlinear solutions are found to terminate in saddle-center bifurcations which are analogous to the linear PT-phase transition.
Non-Hermitian systems with parity-time ($mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second or higher order EPs have been proposed or realized. In contrast, quantum information studies of $mathcal{PT}$-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here by using a single-photon interferometry setup, we simulate quantum dynamics of a four-dimensional $mathcal{PT}$-symmetric system across a fourth-order exceptional point. By tracking the coherent, non-unitary evolution of the density matrix of the system in $mathcal{PT}$-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional $mathcal{PT}$-symmetric systems, and our results point towards the rich dynamics and critical properties.
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