Nonperturbative Approach to Circuit Quantum Electrodynamics

Abstract

We outline a rigorous method which can be used to solve the many-body Schroedinger equation for a Coulomb interacting electronic system in an external classical magnetic field as well as a quantized electromagnetic field. Effects of the geometry of the electronic system as well as the polarization of the quantized electromagnetic field are explicitly taken into account. We accomplish this by performing repeated truncations of many-body spaces in order to keep the size of the many particle basis on a manageable level. The electron-electron and electron-photon interactions are treated in a nonperturbative manner using "exact numerical diagonalization". Our results demonstrate that including the diamagnetic term in the photon-electron interaction Hamiltonian drastically improves numerical convergence. Additionally, convergence with respect to the number of photon states in the joint photon-electron Fock space basis is fast. However, the convergence with respect to the number of electronic states is slow and is the main bottleneck in calculations.

Revtex, pdflatex, 8 pages, with 5 included pdf figures

References in corpus (17)

• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Quantum nature of a strongly-coupled single quantum dot-cavity system
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Observation of the Dynamical Casimir Effect in a Superconducting Circuit
• Exciton photon strong-coupling regime for a single quantum dot in a microcavity
• The photon blockade effect in optomechanical systems
• Quantum vacuum properties of the intersubband cavity polariton field
• Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System
• Generalized rotating-wave approximation for arbitrarily large coupling
• The photon shuttle: Landau-Zener-Stueckelberg dynamics in an optomechanical system
• Superconducting Phase Qubit Coupled to a Nanomechanical Resonator: Beyond the Rotating-Wave Approximation
• Solutions to the Jaynes-Cummings model without the rotating-wave approximation
• Time-dependent transport of electrons through a photon cavity
• Analytical ground state for the Jaynes-Cummings model with the ultrastrong coupling
• Non-adiabatic current generation in a finite width semiconductor ring
• High speed spatially multimode atomic memory
• Quantum magneto-electrodynamics of electrons embedded in a photon cavity

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• Optical switching of electron transport in a waveguide-QED system
• Time-dependent current into and through multilevel parallel quantum dots in a photon cavity
• The photocurrent generated by photon replica states of an off-resonantly coupled dot-cavity system
• Generalized Master Equation Approach to Time-Dependent Many-Body Transport
• Cavity-photon induced high order transitions between ground states of quantum dots
• Competition of static magnetic and dynamic photon forces in electronic transport through a quantum dot
• Thermoelectric inversion in a resonant quantum dot-cavity system in the steady-state regime
• Controlling the excitation spectrum of a quantum dot array with a photon cavity
• Magneto-optical properties of a quantum dot array interacting with a far-infrared photon mode of a cylindrical cavity
• Back-action effects in cavity-coupled quantum conductors
• Symmetric excitation and de-excitation of a cavity QED system