Analytical solutions for the Rabi model

Abstract

The Rabi model that describes the fundamental interaction between a two-level system with a quantized harmonic oscillator is one of the simplest and most ubiquitous models in modern physics. However, this model has not been solved exactly because it is hard to find a second conserved quantity besides the energy. Here we present a unitary transformation to map this unsolvable Rabi model into a solvable Jaynes-Cummings-like model by choosing a proper variation parameter. As a result, the analytical energy spectrums and wavefunctions including both the ground and the excited states can be obtained easily. Moreover, these explicit results agree well with the direct numerical simulations in a wide range of the experimental parameters. In addition, based on our obtained energy spectrums, the recent experimental observation of Bloch-Siegert in the circuit quantum electrodynamics with the ultrastrong coupling can be explained perfectly. Our results have the potential application in the solid-state quantum information processing.

5 pages, 4 figures

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• Hidden Single-Qubit Topological Phase Transition without Gap Closing in Anisotropic Light-Matter Interactions
• Nonperturbative cavity quantum electrodynamics: is the Jaynes-Cummings model still relevant?
• Variational generalized rotating-wave approximation in the two-qubit quantum Rabi model
• Nodes and Spin Windings for Topological Transitions in Light-Matter Interactions: \\ Anisotropic Quantum Rabi Model as a Born Abstract Artist
• Quantized resonator field coupled to a current-biased Josephson junction in circuit QED
• Non-orthogonal qubit states expansion for the asymmetric quantum Rabi model
• Robust topological feature against non-Hermiticity in Jaynes-Cummings Model
• Characterizing Superradiant Phase of the Quantum Rabi Model
• Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models
• Spin Winding and Topological Nature of Transitions in Jaynes-Cummings Model with Stark Non-linear Coupling
• Ground state of the asymmetric Rabi model in the ultrastrong coupling regime
• Quantum Fisher information and polaron picture for identification of transition coupling in quantum Rabi model
• Quantum phase transitions and critical behaviors in the two-mode three-level quantum Rabi model
• An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime
• On the rotating wave approximation in the adiabatic limit
• Ground state of three qubits coupled to a harmonic oscillator with ultrastrong coupling
• Adiabatic approximation for three qubits ultrastrongly coupled to a harmonic oscillator
• Effective Hamiltonians in the Quantum Rabi Problem
• Plateau dynamics with quantized oscillations of a strongly driven qubit
• Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators
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• Dynamic sensitivity of quantum Rabi model with quantum criticality
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• Low-temperature Quantum Metrology Enhanced by Strong Couplings
• Polarized Fock States for Polariton Photochemistry