PT-symmetric Rabi model: Perturbation theory

Abstract

We study a non-Hermitian version of the Rabi model, where a two-level system is periodically driven with an imaginary-valued drive strength, leading to alternating gain and loss. In the Floquet picture, the model exhibits PT symmetry, which can be broken when the drive is sufficiently strong. We derive the boundaries of the PT phase diagram for the different resonances by doing perturbation theory beyond the rotating-wave approximation. For the main resonance, we show that the non-Hermitian analog of the Bloch-Siegert shift corresponds to maximal PT-breaking. For the higher-order resonances, we capture the boundaries to lowest order. We also solve the regime of high frequency by mapping to the Wannier-Stark ladder. Our model can be experimentally realized in waveguides with spatially-modulated loss or in atoms with time-modulated spontaneous decay.

8 pages, 6 figures

References in corpus (11)

• The physics of exceptional points
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• PT spectroscopy of the Rabi problem
• Stabilizing Non-Hermitian Systems by Periodic Driving
• Tachyon physics with trapped ions
• Generation of Bell, W and GHZ states via exceptional points in non-Hermitian quantum spin systems
• Spin squeezing of the non-Hermitian one-axis twisting model
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions

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• Non-hermitian time evolution: from static to parametric instability
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• An attractor dynamics in a non-Hermitian two-level system
• Raising the $\mathcal{P}\mathcal{T}$ transition threshold by strong coupling to neutral chains
• Stability of time-periodic $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonians with different periodicities
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• Conserved quantities in non-Hermitian systems via vectorization method
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• Exceptional spectrum and dynamic magnetization
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems
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• Investigation of the Effect of Quantum Measurement on Parity-Time Symmetry
• Pursuing complex optical energy through Exceptional Points of Degeneracy (EPDs)
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• $\mathcal{P}\mathcal{T}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics
• Evolution operator for time-dependent non-Hermitian Hamiltonians