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

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 ($\mathcal{P}\mathcal{T}$) 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 $\mathcal{P}\mathcal{T}$-symmetric system to a periodic (Floquet) driving, the regime of dynamical stability can be dramatically affected, leading to a frequency-dependent threshold for the $\mathcal{P}\mathcal{T}$-symmetry breaking transition. We present a simple model of a time-dependent $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian which smoothly connects the static case, a $\mathcal{P}\mathcal{T}$-symmetric Floquet case, and a neutral-$\mathcal{P}\mathcal{T}$-symmetric case. We analytically and numerically analyze the $\mathcal{P}\mathcal{T}$ phase diagrams in each case, and show that slivers of $\mathcal{P}\mathcal{T}$-broken ($\mathcal{P}\mathcal{T}$-symmetric) phase extend deep into the nominally low (high) non-Hermiticity region.

arXiv comment9 pages, 3 figures

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• Non-Hermitian dynamics and $\mathcal{P}\mathcal{T}$-symmetry breaking in interacting mesoscopic Rydberg platforms
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• On-demand Parity-Time symmetry in a lone oscillator through complex, synthetic gauge fields
• Unified entropies and quantum speed limits for nonunitary dynamics
• Constraining work fluctuations of non-Hermitian dynamics across the exceptional point of a superconducting qubit
• Stability of time-periodic $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonians with different periodicities
• Quantum Speed Limits Based on the Sharma-Mittal Entropy