Analytical solutions of basic models in quantum optics
arXiv:1509.05748 · doi:10.1007/978-4-431-55342-7
Abstract
The recent progress in the analytical solution of models invented to describe theoretically the interaction of matter with light on an atomic scale is reviewed. The methods employ the classical theory of linear differential equations in the complex domain (Fuchsian equations). The linking concept is provided by the Bargmann Hilbert space of analytic functions, which is isomorphic to , the standard Hilbert space for a single continuous degree of freedom in quantum mechanics. I give the solution of the quantum Rabi model in some detail and sketch the solution of its generalization, the asymmetric Dicke model. Characteristic properties of the respective spectra are derived directly from the singularity structure of the corresponding system of differential equations.
arXiv commentTo appear in the Conference Proceedings of the Forum of Mathematics for Industry 2014
References in corpus (35)
- Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
- On the Integrability of the Rabi Model
- Towards Quantum Chemistry on a Quantum Computer
- Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
- Universal digital quantum simulation with trapped ions
- Deep Strong Coupling Regime of the Jaynes-Cummings model
- Time-reversal symmetry breaking in circuit-QED based photon lattices
- Digital quantum simulation of fermionic models with a superconducting circuit
- Remarks on the notion of quantum integrability
- Digital quantum simulation of spin models with circuit quantum electrodynamics
- From transistor to trapped-ion computers for quantum chemistry
- Ultrafast Quantum Gates in Circuit QED
- Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
- Digital Quantum Rabi and Dicke Models in Superconducting Circuits
- Digital Quantum Simulation of Spin Systems in Superconducting Circuits
- Exact Solvability of the two-photon Rabi Hamiltonian
- Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
- Topological states and braiding statistics using quantum circuits
- Full spectrum of the Rabi model
- Digital Quantum Simulation of the Holstein Model in Trapped Ions
- Integrability vs exact solvability in the quantum Rabi and Dicke models
- Many-Body Interactions with Tunable-Coupling Transmon Qubits
- Observing the Nonequilibrium Dynamics of the Quantum Transverse-Field Ising Chain in Circuit QED
- Analog Superconducting Quantum Simulator for Holstein Polarons
- Integrable spin-boson models descending from rational six-vertex models
- Toolbox of resonant quantum gates in Circuit QED
- Dicke simulators with emergent collective quantum computational abilities
- Continued Fractions and the Rabi Model
- Quantum Simulations of Relativistic Quantum Physics in Circuit QED
- Towards Outperforming Classical Algorithms with Analog Quantum Simulators
- Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits
- Fermionic Models with Superconducting Circuits
- Quantum phase transition in a multi-connected superconducting Jaynes-Cummings lattice
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