Analytical comparison of the first- and second-order resonances for implementation of the dynamical Casimir effect in nonstationary circuit QED

Abstract

We investigate analytically and numerically the nonstationary circuit QED setup in which $N$ independent qubits interact with a single mode of the Electromagnetic field confined in a resonator. We consider the harmonic time modulation of some parameter (atomic transition frequency or the atom-field coupling strength) and derive the unitary dynamics up to the second order in the modulation depth for $N=1$ and $N\gg 1$. It is shown that all the resonant phenomena that occur for modulation frequencies $\sim 2{\omega }_0$ (where ${\omega }_0$ is the cavity frequency) also occur for the halved frequencies. However, in the latter case the associated transition rates are significantly smaller and the modulation of the coupling strength is less effective. The transition rates are evaluated explicitly and the prospects of employing the second-order resonances in the phenomena related to the dynamical Casimir effect are examined.

arXiv comment13 pages, 3 figures

References in corpus (43)

• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Charge insensitive qubit design derived from the Cooper pair box
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Quantum state engineering with Josephson-junction devices
• Coupling Superconducting Qubits via a Cavity Bus
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Cold and Ultracold Molecules: Science, Technology, and Applications
• Atomic physics and quantum optics using superconducting circuits
• Observation of the Dynamical Casimir Effect in a Superconducting Circuit
• Resolving photon number states in a superconducting circuit
• On the Integrability of the Rabi Model
• Coherent dynamics of a flux qubit coupled to a harmonic oscillator
• Quantum information processing with circuit quantum electrodynamics
• Quantum vacuum properties of the intersubband cavity polariton field
• Qubit architecture with high coherence and fast tunable coupling
• Observation of quantum state collapse and revival due to the single-photon Kerr effect
• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits
• Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime
• Dissipation and Ultrastrong Coupling in Circuit QED
• Dynamical Casimir effect in a Josephson metamaterial
• Deterministic entanglement of superconducting qubits by parity measurement and feedback
• Motion Induced Radiation from a Vibrating Cavity
• Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements
• Numerical methods for computing Casimir interactions
• An acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate
• Extracavity quantum vacuum radiation from a single qubit
• Dynamical Casimir effect entangles artificial atoms
• Tunable coupling in circuit quantum electrodynamics with a superconducting V-system
• Density correlations and dynamical Casimir emission of Bogoliubov phonons in modulated atomic Bose-Einstein condensates
• Microwave-Induced Amplitude and Phase Tunable Qubit-Resonator Coupling in Circuit Quantum Electrodynamics
• Quantum control and long-range quantum correlations in dynamical Casimir arrays
• Fluctuations, dissipation and the dynamical Casimir effect
• Relativistic Motion with Superconducting Qubits
• Spectrum and entanglement of phonons in quantum fluids of light
• Entangling polaritons via dynamical Casimir effect in circuit quantum electrodynamics
• Dynamical Casimir Effect in Quantum Information Processing
• Origin and Implications of $A^2$-like Contribution in the Quantization of Circuit-QED Systems
• Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles
• Microscopic toy model for Cavity dynamical Casimir effect
• Dynamical Casimir Effect in cavity with N-level detector or N-1 two-level atoms
• Effective Landau-Zener transitions in circuit dynamical Casimir effect with time-varying modulation frequency
• Continuous intracavity monitoring of the dynamical Casimir effect

Cited by in corpus (8)

• Anti-Dynamical Casimir Effect as a Resource for Work Extraction
• Dynamical Casimir effect via four- and five-photon transitions using a strongly detuned atom
• Speeding up antidynamical Casimir effect with nonstationary qutrits
• Dynamical Casimir effect via modulated Kerr or higher nonlinearities
• 1- and 3-photon dynamical Casimir effects using nonstationary cyclic qutrit
• Generation of photons from vacuum in cavity via time-modulation of a qubit invisible to the field
• Comparison of Quantum and Semiclassical Rabi models near multiphoton resonances in the presence of parametric modulation
• Two-photon exchange interaction from Dicke Hamiltonian under parametric modulation