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arXiv:2108.05859 · Physica A Statistical Mechanics and its Applications

Enhancement of photon creation through the pseudo-Hermitian Dynamical Casimir Effect

Danilo Cius, Fabiano M. Andrade, Antonio S. M. de Castro, M. H. Y. Moussa

Published Jan 20, 2022• 13 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2022.126945

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Here we first present an alternative formulation of the Lewis & Riesenfeld theorem for solving the Schrödinger equation with nonautonomous Hermitian and pseudo-Hermitian Hamiltonians. We then employ this framework to characterize the spontaneous breaking of time-dependent antilinear symmetries of these Hamiltonians. We demonstrate that, under unbroken antilinear symmetries, the Lewis & Riesenfeld phases are real and odd functions of time, which allows us to recover the well-known real spectra of time-independent pseudo-Hermitian Hamiltonians. However, in the spontaneously broken regime, imaginary components of the Lewis & Riesenfeld phases arise, leading to coalescence effects analogous to those in the time-independent scenario. Finally, we present an illustrative example of unbroken and broken PT-symmetry for a time-dependent Hamiltonian modeling the non-Hermitian dynamical Casimir effect.
Abstract Real photon pairs can be created in a dynamic cavity with an oscillating boundary or temporally modulated refractive index of the constituent medium. This effect is called dynamic Casimir effect (DCE), which represents one of the most amazing predictions of quantum field theory. The DCE has been experimentally observed in Josephson metamaterials embedded in a microwave cavity. However, the efficiency of the observed DCE is extremely weak, entailing a complex external signal enhancement process to detect the signal. Here, it is shown that the DCE can be drastically enhanced in a dynamic 1D cavity consisting of a superconducting quantum interference device (SQUID)‐based Josephson transmission line with both temporal and spatial modulation on the effective inductance profile through flux‐biasing. Such a system can resonantly generate photons at driving frequencies equal to even or odd integer times of that of the fundamental cavity mode governed by the symmetry of the spatial modulation. Interesting spectral and scaling behaviors for photons excited at the band edge are further observed. The discovery introduces a new degree of freedom—spatial modulation—to enhance the efficiency of DCE.