Squeezed Displaced Schr\"odinger-cat state as a signature of the PT-symmetry phase transition

TL;DR

This paper demonstrates that the emergence of a Squeezed Displaced Schrödinger-cat state in a cavity coupled to a non-Hermitian SSH chain can serve as a signature of PT-symmetry phase transition, linking quantum states to phase changes.

Contribution

It introduces a novel method to detect PT-symmetry phase transitions in electronic systems via cavity quantum states and quantum Fisher information.

Findings

SDSc state appears with high fidelity when PT symmetry is broken.

Fidelity sharply drops as PT symmetry is restored.

Quantum Fisher information declines sharply at exceptional points.

Abstract

Parity-time (PT ) symmetric systems are gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with degeneracies at exceptional-points (EPs) and has been studied in various photonic, electrical, mechanical systems, and so on. However, it is still an open question how to capture PT symmetry phase transition in electronic system where the transport properties of electron will be dramatically effected. Fortunately, the hybridization between photon and electron offers a novel way not only to control but also probe material properties. Here, we investigate a cavity coupled to a non-Hermitian Su-Schrieffer-Heeger (SSH) chain within mean-field ansatzs. We find that Squeezed Displaced Schrodinger cat (SDSc) will emerge with high fidelity in cavity ground state when PT -symmetry is broken and the fidelity will experience a sharp drop from almost 1 to 0 as PT symmetry recovers. Additionally, in semiclassical limit, we find that there exists local extrema at two sides of $x=0$ in semiclassical photon Hamiltonian $H_{\rm eff}(x, p)$, a clear signature of the emergence of SDSc state in cavity ground state. Thus, the appearance of SDSc state can be used to capture PT-symmetry phase transition which can not be modified by cavity mode. Besides, we exploit the cavity ground state to estimate the phase in the optical interferometer, and show that the quantum Fisher information and nonclassicality will sharply decline at EPs. This reveals that PT-symmetry breaking in electronic materials can also be captured by the quantum Fisher information and nonclassicality in phase estimation.