We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. Exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of groundstates occur, associating with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist for the open chain within unbroken time-reversal symmetric region, demonstrating the bulk-edge correspondence in such a non-Hermitian system.
We study the directional amplification of an optical probe field in a three-mode optomechanical system, where the mechanical resonator interacts with two linearly-coupled optical cavities and the cavities are driven by strong optical pump fields. The optical probe field is injected into one of the cavity modes, and at the same time, the mechanical resonator is subject to a mechanical drive with the driving frequency equal to the frequency difference between the optical probe and pump fields. We show that the transmission of the probe field can be amplified in one direction and deamplified in the opposite direction. This directional amplification or de-amplification results from the constructive or destruction interference between different transmission paths in this three-mode optomechanical system.
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.
Periodically driven non-Hermitian systems can exhibit rich topological band structure and non-Hermitian skin effect, without analogs in their static or Hermitian counterparts. In this work we investigate the exceptional band-touching points in the Floquet quasi-energy bands, the topological characterization of such exceptions points and the Floquet non-Hermitian skin effect (FNHSE). Specifically, we exploit the simplicity of periodically quenched two-band systems in one dimension or two dimensions to analytically obtain the Floquet effective Hamiltonian as well as locations of the many exceptional points possessed by the Floquet bulk bands. Two different types of topological winding numbers are used to characterize the topological features. Bulk-edge correspondence (BBC) is naturally found to break down due to FNHSE, which can be drastically different among different bulk states. Remarkably, given the simple nature of our model systems, recovering the BBC is doable in practice only for certain parameter regime where a low-order truncation of the characteristic polynomial (which determines the Floquet band structure) becomes feasible. Furthermore, irrespective of which parameter regime we work with, we find a number of intriguing aspects of Floquet topological zero modes and π modes. For example, under the open boundary condition zero edge modes and π edge modes can individually coalesce and localize at two different boundaries. These anomalous edge states can also switch their accumulation boundaries when certain system parameter is tuned. These results indicate that non-Hermitian Floquet topological phases, though more challenging to understand than their Hermitian counterparts, can be extremely rich in the presence of FNHSE. arXiv:1909.10234v1 [cond-mat.mes-hall]
Complex potential and non-Hermitian hopping amplitude are building blocks of a non-Hermitian quantum network. Appropriate configuration, such as PT -symmetric distribution, can lead to a full real spectrum. To investigate the underlying mechanism of this phenomenon, we study the phase diagrams of a semi-infinite non-Hermitian systems. They consist of finite non-Hermitian clusters and semi-infinite leads. Based on the analysis of the solutions of the concrete systems, it is shown that they can have full real spectra without any requirements on the symmetry and the wave function within the leads becomes unidirectional plane waves at the exceptional point. This universal dynamical behavior is demonstrated as the persistent emission and reflectionless absorption of wave packets in the typical non-Hermitian systems containing the complex on-site potentials and non-Hermitian hopping amplitudes.
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