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Register a new userParity-time symmetric optical coupler with birefringent arms
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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.
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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.
We consider a dual-core nonlinear waveguide with the parity-time (PT) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and explore possibilities for the development of dynamical control of the solitons, we introduce management in the form of periodic sinusoidal variation of the loss-gain (LG) coefficients, along with synchronous variation of the inter-core coupling (ICC) constant. This system, which can be realized in optics (in the temporal and spatial domains alike), features strong robustness when amplitudes of the variation of the LG and ICC coefficients keep a ratio equal to that of their constant counterparts, allowing one to find exact solutions for PT-symmetric solitons. A stability region for the solitons is identified in terms of the management amplitude and period, as well as the solitons amplitude. In the long-period regime, the solitons evolve adiabatically, making it possible to predict their stability boundaries in an analytical form. The system keeping the Galilean invariance, collisions between moving solitons are considered too.
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.
We show that the no-signaling principle can be violated with classical inseparable beams in the presence of a parity-time (PT) symmetric subsystem. Thus, the problems associated to PT-symmetric quantum theories recently discovered by Lee et al. [Phys. Rev. Lett. 112, 130404 (2014)] are not exclusive to quantum mechanics, but already exist in the classical case. The possibility to implement local optical PT-symmetric subsystems via light-matter interactions enables the experimental exploration of local PT symmetry and subtle quantum concepts via classical analogues.
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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