Quantum phase transitions and critical behaviors in the two-mode three-level quantum Rabi model

Abstract

We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio $\eta$ of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant phases are of second order relating to the spontaneous breaking of the discrete $Z_2$ symmetry. On the other hand, the quantum phase transition between the two different superradiant phases is discontinuous with a phase boundary line relating to the continuous $U(1)$ symmetry. For a large enough but finite $\eta$, the scaling function and critical exponents are derived analytically and verified numerically, from which the universality class of the model is identified.

References in corpus (34)

• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Dark-State Polaritons in Electromagnetically Induced Transparency
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Security of quantum key distribution using d-level systems
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Ultrastrong coupling regimes of light-matter interaction
• On the Integrability of the Rabi Model
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime
• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Optimal eavesdropping in cryptography with three-dimensional quantum states
• Exploring Symmetry Breaking at the Dicke Quantum Phase Transition
• Non-adiabatic holonomic quantum computation
• Exact solvability of the quantum Rabi models within Bogoliubov operators
• Light-matter decoupling in the deep strong coupling regime: The breakdown of the Purcell effect
• Superradiance transition in a system with a single qubit and a single oscillator
• Universal scaling and critical exponents of the anisotropic quantum Rabi model
• Analytical eigenstates for the quantum Rabi model
• Anisotropic Rabi model
• Some remarks on 'superradiant' phase transitions in light-matter systems
• Single-photon-driven high-order sideband transitions in an ultrastrongly coupled circuit quantum electrodynamics system
• Theoretical methods for ultrastrong light-matter interactions
• Analytical solutions for the Rabi model
• Ground-state phase diagram of the quantum Rabi model
• Absence of Vacuum Induced Berry Phases without the Rotating Wave Approximation in Cavity QED
• Dynamics of a two-level system coupled to a quantum oscillator: Transformed rotating-wave approximation
• Phase transitions and dark-state physics in two-color superradiance
• Frequency-renormalized multipolaron expansion for the quantum Rabi model
• Polychromatic phase diagram for $n$-level atoms interacting with $\ell$ modes of electromagnetic field
• Chiral Light--Matter Interaction Beyond the Rotating-Wave Approximation
• Variational generalized rotating-wave approximation in the two-qubit quantum Rabi model

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