Perfect state transfer inPT-symmetric non-Hermitian networks

Abstract

We systematically study the PT (parity-time reversal)-symmetric non-Hermitian version of a quantum network proposed in the work of Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)]. The exclusive nature of this model show that it is a nice paradigm to demonstrate the complex quantum mechanics theory for the relationship between the pseudo-Hermitian Hamiltonian and its Hermitian counterpart, as well as a candidate in experimental realization to simulate the PT symmetry breaking. We also show that this model allows conditional perfect state transfer within the unbroken PT symmetry region, but not arbitrary. This is due to the fact that the evolution operator at certain period is equivalent to the PT operator for the real-valued wavefunction in the elaborate PT -symmetric Hilbert space.

Non-Hermitian anisotropicXYmodel with intrinsic rotation-time-reversal symmetry

“…Then for a Hermitian matrix, the non-analytic behavior is not from the Jordan block but from the divergence of derivatives of matrix elements. The similar situation also occurs in another model 27 , which may imply a general conclusion.…”

$\mathcal {PT}$-symmetric optical superlattices

“…Complex crystals show rather unusual scattering and transport properties as compared to ordinary crystals, such as violation of the Friedel's law of Bragg scattering [37,38,44], double refraction and nonreciprocal diffraction [17], unidirectional Bloch oscillations [47], unidirectional invisibility [48,49,50,51,52], and invisible defects [53,54]. Complex crystals described by tight-binding Hamiltonians with complex site energies and/or hopping rates have been investigated in several recent works (see, for instance, [8,9,10,11,27,29,53,55,56,57,58,59,60,61] and references therein). Most of previous studies on non-Hermitian lattices have been limited to consider periodic or bi-periodic crystals, inhomogenous lattices, or lattices in presence of localized defects or disorder.…”

Cyclic permutation-time symmetric structure with coupled gain-loss microcavities

“…One category that has attracted wide research interest in the past decade is with properly balanced gain-loss profiles for the coupling optical modes, as it is regarded as a realization of optical analog for parity-time (PT)-symmetric quantum mechanics [1,2], These proposed systems include optical waveguides [3][4][5], optical lattices [4][5][6], microcavities [7,8], and others [9,10]. So far most of the research on these systems is concerned with properties such as light transportation, and some of the interesting features of the systems have been demonstrated by the experiments with different setups [11][12][13][14][15], An important characteristic of a PT-symmetric system is the existence of the threshold known as the exceptional point [16,17], across which the optical modes undergo a "phase transition" between periodic oscillation and exponential growth or decay.…”

“…In addition to the above-mentioned properties, the quantum features of linear PT systems have received attention recently [8,10,19], The quantum dynamics of these systems should be well understood in view of the potential applications. On the one hand, the dynamics of these systems has been studied with PT-symmetric non-Hermitian Hamiltonians, which have real and complex eigenvalues, respectively, across the exceptional point where there is the unit ratio of amplification (dissipation) rate over coupling strength.…”