Connecting active and passive $\mathcal{PT}$-symmetric Floquet modulation models

• URL: http://arxiv.org/abs/2008.01811v2
• Date: Wed, 9 Dec 2020 06:07:34 GMT
• Title: Connecting active and passive $\mathcal{PT}$-symmetric Floquet modulation models
• Authors: Andrew K. Harter and Yogesh N. Joglekar
• Abstract summary: We present a simple model of a time-dependent $mathcalPT$-symmetric Hamiltonian which smoothly connects the static case, a $mathcalPT$-symmetric Floquet case, and a neutral-$mathcalPT$-symmetric case. We show that slivers of $mathcalPT$-broken ($mathcalPT$-symmetric) phase extend deep into the nominally low (high) non-Hermiticity region.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Open systems with gain, loss, or both, described by non-Hermitian Hamiltonians, have been a research frontier for the past decade. In particular, such Hamiltonians which possess parity-time ($\mathcal{PT}$) symmetry feature dynamically stable regimes of unbroken symmetry with completely real eigenspectra that are rendered into complex conjugate pairs as the strength of the non-Hermiticity increases. By subjecting a $\mathcal{PT}$-symmetric system to a periodic (Floquet) driving, the regime of dynamical stability can be dramatically affected, leading to a frequency-dependent threshold for the $\mathcal{PT}$-symmetry breaking transition. We present a simple model of a time-dependent $\mathcal{PT}$-symmetric Hamiltonian which smoothly connects the static case, a $\mathcal{PT}$-symmetric Floquet case, and a neutral-$\mathcal{PT}$-symmetric case. We analytically and numerically analyze the $\mathcal{PT}$ phase diagrams in each case, and show that slivers of $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase extend deep into the nominally low (high) non-Hermiticity region.

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