Parity-Time Symmetric Adiabatic Elimination

Demetrios N. Christodoulides, Jianke Yang

Rahman Sharaf, Mojgan Dehghani, Hamidreza Ramezani

We investigate the influence of non-Hermiticity on the adiabatic elimination in coupled waveguides. We show that although the total norm of the system is not conserved in parity-time symmetric phase, the dark state intensity remains constant. However, in broken phase the eliminated waveguide loses its darkness, i.e., its field amplitude starts increasing. In both exact and broken phases, the effective Hamiltonian derived from the adiabatic elimination condition describes the dynamics of all states except the dark state. Specifically, it cannot predict the amplification in the intensity of the dark state. Our results can strengthen the control of the dynamics in cavities with active elements and improve the design of controllable absorbers.

Wenlin Li, Chong Li, He‐Shan Song

In the existing parity-time ($\mathcal{PT}$) symmetry with the balanced gain and loss, the gain is derived from semiclassical but not full quantum theories, which significantly restricts the applications of $\mathcal{PT}$ symmetry in quantum fields. In this work, we propose and analyze a theoretical scheme to realize full quantum oscillator $\mathcal{PT}$ symmetry. The quantum gain is provided by a dissipation optical cavity with a blue-detuned laser field. After adiabatically eliminating the cavity modes, we give an effective master equation, which is a complete quantum description compared with the non-Hermitian Hamiltonian, to reveal the quantum behaviors of such a gain oscillator. This kind of $\mathcal{PT}$ symmetry can eliminate the dissipation effect in the quantum regime. As an example, we apply $\mathcal{PT}$-symmetric oscillators to enhance optomechanically induced transparency.

Federico Casagrande, L. A. Lugiato, G. Strini

Luc Bouten, Andrew Silberfarb

Lan Xu, Qiong Wang, Zhi He

Abstract We investigate precision of phase estimation without and with decoherence using a non-Hermitian operation, i.e. parity-time ( ) symmetric operation. We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. Special attention is paid to the two schemes, i.e. pre-and post- symmetric operations, to show the performance of symmetric operation on QFI dynamics. By investigation, we find that pre- symmetric operator process could completely eliminate the effect of decoherence to improve the parameters estimation, while with the help of the post- symmetric operator process can potentially enhance and preserve the QFI by choosing appropriate non-Hermitian operator parameters.