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## Dipolar Bose-Einstein condensates in a PT-symmetric double-well potential

Rüdiger Fortanier, Dennis Dast, Daniel Haag, Holger Cartarius, Jörg Main, Günter Wunner

We investigate dipolar Bose-Einstein condensates in a complex external double-well potential that features a combined parity and time-reversal symmetry. On the basis of the Gross-Pitaevskii equation we study the effects of the long-ranged anisotropic dipole-dipole interaction on ground and excited states by the use of a time-dependent variational approach. We show that the property of a similar non-dipolar condensate to possess real energy eigenvalues in certain parameter ranges is preserved despite the inclusion of this nonlinear interaction. Furthermore, we present states that break the PT symmetry and investigate the stability of the distinct stationary solutions. In our dynamical simulations we reveal a complex stabilization mechanism for PT-symmetric, as well as for PT-broken states which are, in principle, unstable with respect to small perturbations.

http://arxiv.org/abs/1403.6742
Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Chaotic Dynamics (nlin.CD)

## Localized modes in dissipative lattice media: An overview

Yingji He, Boris A. Malomed, Dumitru Mihalache

We overview recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which include imaginary, real, or complex spatially periodic potentials. The imaginary potential represents periodic modulation of the local loss and gain. It is shown that the effective gradient force, induced by the inhomogeneous loss distribution, gives rise to three generic propagation scenarios for one-dimensional (1D) dissipative solitons: transverse drift, persistent swing motion, and damped oscillations. When the lattice-average loss/gain value is zero, and the real potential has spatial parity opposite to that of the imaginary component, the respective complex potential is a realization of the parity-time symmetry. Under the action of lattice potentials of the latter type, 1D solitons feature unique motion regimes in the form of transverse drift and persistent swing. In the 2D geometry, three types of axisymmetric radial lattices are considered, viz., ones based solely on the refractive-index modulation, or solely on the linear-loss modulation, or on a combination of both. The rotary motion of solitons in such axisymmetric potentials can be effectively controlled by varying the strength of the initial tangential kick.

http://arxiv.org/abs/1403.5436
Optics (physics.optics)

## Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain

James M. Hickey, Emanuele Levi, Juan P. Garrahan

We study the connection between the cumulants of a time-integrated observable of a quantum system and the PT-symmetry properties of the non-Hermitian deformation of the Hamiltonian from which the generating function of these cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of broken and of unbroken PT-symmetry, depending on the parameters of the problem and on the counting field that sets the strength of the non-Hermitian perturbation. This in turn determines the analytic structure of the long-time cumulant generating function (CGF) for the time-integrated observable. We consider in particular the case of the time-integrated (longitudinal) magnetisation in the one-dimensional Ising model in a transverse field. We show that its long-time CGF is singular on a curve in the magnetic field/counting field plane that delimits a regime where PT-symmetry is spontaneously broken (which includes the static ferromagnetic phase), from one where it is preserved (which includes the static paramagnetic phase). In the paramagnetic phase, conservation of PT -symmetry implies that all cumulants are sub-linear in time, a behaviour usually associated to the absence of decorrelation.

http://arxiv.org/abs/1403.4538
Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

## Bulk Vortex and Horseshoe Surface Modes in Parity-Time Symmetric Media

Huagang Li, Xing Zhu, Zhiwei Shi, Boris A. Malomed, Tianshu Lai, Chaohong Lee

We demonstrate that in-bulk vortex localized modes, and their surface half-vortex (“horseshoe”) counterparts (which were not reported before in truncated settings) self-trap in two-dimensional (2D) nonlinear optical systems with PT-symmetric photonic lattices (PLs). The respective stability regions are identified in the underlying parameter space. The in-bulk states are related to truncated nonlinear Bloch waves in gaps of the PL-induced spectrum. The basic vortex and horseshoe modes are built, severally, of four and three beams with appropriate phase shifts between them. Their stable complex counterparts, built of up to 12 beams, are reported too.

http://arxiv.org/abs/1403.4745
Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)

## Discrete spectrum of thin PT-symmetric waveguide

Denis Borisov

In a thin multidimensional layer we consider a second order differential PT-symmetric operator. The operator is of rather general form and its coefficients are arbitrary functions depending both on slow and fast variables. The PT-symmetry of the operator is ensured by the boundary conditions of Robin type with pure imaginary coefficient. In the work we determine the limiting operator, prove the uniform resolvent convergence of the perturbed operator to the limiting one, and derive the estimates for the rates of convergence. We establish the convergence of the spectrum of perturbed operator to that of the limiting one. For the perturbed eigenvalues converging to the limiting discrete ones we prove that they are real and construct their complete asymptotic expansions. We also obtain the complete asymptotic expansions for the associated eigenfunctions.

http://arxiv.org/abs/1403.4524

Spectral Theory (math.SP); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)

## PT-symmetry breaking with divergent potentials: lattice and continuum cases

Yogesh N. Joglekar, Derek D. Scott, Avadh Saxena

We investigate the parity- and time-reversal (PT)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, PT-symmetric potentials that remain finite or become divergent in the continuum limit. By scaling analysis of the fragile PT threshold for an open finite lattice, we show that continuum loss-gain potentials $$V_a(x)\sim i|x|^a{\rm sign}(x)$$ have a positive PT-breaking threshold for $$\alpha>−2$$, and a zero threshold for α≤−2. When α<0 localized states with complex (conjugate) energies in the continuum energy-band occur at higher loss-gain strengths. We investigate the signatures of PT-symmetry breaking in coupled waveguides, and show that the emergence of localized states dramatically shortens the relevant time-scale in the PT-symmetry broken region.

http://arxiv.org/abs/1403.4204
Quantum Physics (quant-ph); Optics (physics.optics)

## Giant Optomechanical Enhancement in the Presence of Gain and Loss

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)

## Three solvable matrix models of a quantum catastrophe

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)

## Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system

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)

## Mechanical PT symmetry in coupled optomechanical systems

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)