H. Jing, Sahin K. Ozdemir, Xin-You Lv, Jing Zhang, F. Nori
The parity-time-symmetric structure was experimentally accessible very recently in coupled optical resonators with which, for normal or non-PT-symmetric cases, a phonon laser device had also been realized. Here we study cavity optomechanics of this system now with tunable gain-loss ratio. We find that nonlinear behaviors emerge for cavity-photon populations around balanced point, resulting giant enhancement of both optical pressure and phonon-lasing action. Potential applications range from enhancing mechanical cooling to designing highly-efficient phonon-laser amplifier.
http://arxiv.org/abs/1403.0657
Quantum Physics (quant-ph); Optics (physics.optics)
Geza Levai, Frantisek Ruzicka, Miloslav Znojil
Three classes of finite-dimensional models of quantum systems exhibiting spectral degeneracies called quantum catastrophes are described in detail. Computer-assisted symbolic manipulation techniques are shown unexpectedly efficient for the purpose.
http://arxiv.org/abs/1403.0723
Quantum Physics (quant-ph); Mathematical Physics (math-ph)
Mohammad Hasan, Ananya Ghatak, Bhabani Prasad Mandal
We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system.
http://arxiv.org/abs/1403.0539
Quantum Physics (quant-ph)
Xun-Wei Xu, Yu-xi Liu, Chang-Pu Sun, Yong Li
We propose to observe mechanical PT symmetry in the coupled optomechanical systems. In order to provide gain to one mechanical resonator and equivalent amount of damp to another, we drive the two optical cavities with a blue and a red detuned laser fields respectively. After adiabatically eliminating the freedom of the cavity modes, we develop a formalism for describing mechanical PT-symmetric system. Moreover, we discuss the experimental feasibility of our scheme and show that the observation of mechanical PT-symmetric transition in the coupled optomechanical systems is within the reach of resent experiments.
http://arxiv.org/abs/1402.7222
Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics)
K. Nireekshan Reddy, Subhrajit Modak, Kumar Abhinav, Prasanta K. Panigrahi
Systems governed by the Non-linear Schroedinger Equation (NLSE) with various external PT-symmetric potentials are considered. Exact solutions have been obtained for the same through the method of ansatz, some of them being solitonic in nature. It is found that only the unbroken PT-symmetric phase is realized in these systems, characterized by real energies.
http://arxiv.org/abs/1402.5762
Quantum Physics (quant-ph)
Cale M. Gentry, Milos A. Popovic
We propose a new type of laser resonator based on imaginary “energy-level splitting” (imaginary coupling, or quality factor Q splitting) in a pair of coupled microcavities. A particularly advantageous arrangement involves two microring cavities with different free-spectral ranges (FSRs) in a configuration wherein they are coupled by “far-field” interference in a shared radiation channel. A novel Vernier-like effect for laser resonators is designed where only one longitudinal resonant mode has a lower loss than the small signal gain and can achieve lasing while all other modes are suppressed. This configuration enables ultra-widely tunable single-frequency lasers based on either homogeneously or inhomogeneously broadened gain media. The concept is an alternative to the common external cavity configurations for achieving tunable single-mode operation in a laser. The proposed laser concept builds on a high-Q “dark state” that is established by radiative interference coupling and bears a direct analogy to parity-time (PT) symmetric Hamiltonians in optical systems. Variants of this concept should be extendable to parametric-gain based oscillators, enabling use of ultrabroadband parametric gain for widely tunable single-frequency light sources.
http://arxiv.org/abs/1402.4767
Optics (physics.optics)
Francisco M. Fernández
The purpose of this paper is the discussion of a pair of coupled linear oscillators that has recently been proposed as a model of a system of two optical resonators. By means of an algebraic approach we show that the frequencies of the classical and quantum-mechanical interpretations of the optical phenomenon are exactly the same. Consequently, if the classical frequencies are real, then the quantum-mechanical eigenvalues are also real.
http://arxiv.org/abs/1402.4473
Quantum Physics (quant-ph)
Carl M. Bender, Daniel W. Hook
Complex trajectories for Hamiltonians of the form H=p^n+V(x) are studied. For n=2 time-reversal symmetry prevents trajectories from crossing. However, for n>2 trajectories may indeed cross, and as a result, the complex trajectories for such Hamiltonians have a rich and elaborate structure. In past work on complex classical trajectories it has been observed that turning points act as attractors; they pull on complex trajectories and make them veer towards the turning point. In this paper it is shown that the poles of V(x) have the opposite effect — they deflect and repel trajectories. Moreover, poles shield and screen the effect of turning points.
http://arxiv.org/abs/1402.3852
Mathematical Physics (math-ph)
S. Longhi, G. Della Valle
The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including PT-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here we show that exceptional points in the continuum can arise in non-Hermitian (yet admitting and entirely real-valued energy spectrum) optical lattices with engineered defects. At an exceptional point, the lattice sustains a bound state with an energy embedded in the spectrum of scattered states, similar to the von-Neumann Wigner bound states in the continuum of Hermitian lattices. However, the dynamical and scattering properties of the bound state at an exceptional point are deeply different from those of ordinary von-Neumann Wigner bound states in an Hermitian system. In particular, the bound state in the continuum at an exceptional point is an unstable state that can secularly grow by an infinitesimal perturbation. Such properties are discussed in details for transport of discretized light in a PT-symmetric array of coupled optical waveguides, which could provide an experimentally accessible system to observe exceptional points in the continuum.
http://arxiv.org/abs/1402.3764
Quantum Physics (quant-ph); Optics (physics.optics)
Stefano Longhi
Bound states in the continuum (BIC), i.e. normalizable modes with an energy embedded in the continuous spectrum of scattered states, are shown to exist in certain optical waveguide lattices with PT-symmetric defects. Two distinct types of BIC modes are found: BIC states that exist in the broken PT phase, corresponding to exponentially-localized modes with either exponentially damped or amplified optical power; and BIC modes with sub-exponential spatial localization that can exist in the unbroken PT phase as well. The two types of BIC modes at the PT symmetry breaking point behave rather differently: while in the former case spatial localization is lost and the defect coherently radiates outgoing waves with an optical power that linearly increases with the propagation distance, in the latter case localization is maintained and the optical power increase is quadratic.
http://arxiv.org/abs/1402.3761
Quantum Physics (quant-ph); Optics (physics.optics)