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arXiv:1703.00836 · Physical Review A

Two-photon exchange interaction from the Dicke Hamiltonian under parametric modulation

Alexandre V. Dodonov

Published Feb 12, 2018• 0 citations
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Abstract

We consider the nonstationary circuit QED architecture in which a single-mode cavity interacts with $N>1$ identical qubits, and some system parameters undergo a weak external perturbation. It is shown that in the dispersive regime one can engineer the two-photon exchange interaction by adjusting the frequency of harmonic modulation to (approximately) $2|{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}|$, where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}$ is the average atom-field detuning. A closed analytic description is derived for the weak atom-field coupling regime, and the system dynamics under realistic conditions is studied numerically.

DOI
10.1103/physreva.97.023816

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We consider the nonstationary circuit QED architecture in which a single-mode cavity interacts with N>1N>1N>1 identical qubits, and some system parameters undergo a weak external perturbation. It is shown that in the dispersive regime one can engineer the two-photon exchange interaction by adjusting the frequency of harmonic modulation to (approximately) 2∣\ensuremathΔ\ensuremath−∣2|{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}|2∣\ensuremathΔ\ensuremath−​∣, where \ensuremathΔ\ensuremath−{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}\ensuremathΔ\ensuremath−​ is the average atom-field detuning. A closed analytic description is derived for the weak atom-field coupling regime, and the system dynamics under realistic conditions is studied numerically.
We consider the interaction of a single-mode cavity field and NNN identical qubits in the scenario when one or several system parameters undergo a weak external modulation. It is shown that in the dispersive regime of light-matter coupling one can engineer the effective two-photon exchange interaction when the frequency of harmonic modulation is ∼2∣Δ−∣\sim 2|\Delta_-|∼2∣Δ−​∣, where Δ−\Delta_-Δ−​ is the bare atom-field detuning. The effective Hamiltonian and associated transition rate are derived analytically for N≫1N\gg 1N≫1, and a good agreement is found with numerical data even when N∼O(1)N \sim {\it O}(1)N∼O(1).
We have studied the nonstationary circuit QED system in which N qubits or a ( N + 1)-level ladder atom interact with a single mode of the cavity field in the presence of external one- and two-photon drivings. It is assumed that all the system parameters can be simultaneously time-modulated by arbitrary external modulations. We have derived new analytical expressions for the system dynamics in the dressed-states basis and have shown that one can implement different regimes of light–matter interaction by adjusting the modulation form.
We study theoretically the nonstationary circuit QED system in which the artificial atom transition frequency, or the atom-cavity coupling, have a small periodic time modulation, prescribed externally. The system formed by the atom coupled to a single cavity mode is described by the Rabi Hamiltonian. We show that, in the dispersive regime, when the modulation periodicity is tuned to the 'resonances', the system dynamics presents the dynamical Casimir effect, resonant Jaynes-Cummings or resonant Anti-Jaynes-Cummings behaviors, and it can be described by the corresponding effective Hamiltonians. In the resonant atom-cavity regime and under the resonant modulation, the dynamics is similar to the one occurring for a stationary two-level atom in a vibrating cavity, and an entangled state with two photons can be created from vacuum. Moreover, we consider the situation in which the atom-cavity coupling, the atomic frequency, or both have a small non-periodic time modulation, and show that photons can be created from vacuum in the dispersive regime. Therefore, an analog of the dynamical Casimir effect can be simulated in circuit QED, and several photons, as well as entangled states, can be generated from vacuum due to the anti-rotating term in the Rabi Hamiltonian.
We consider a nonstationary circuit quantum electrodynamics setup in which a three-level artificial atom in the $\mathrm{\ensuremath{\Delta}}$ configuration interacts with a single-mode cavity field of natural frequency $\ensuremath{\omega}$. It is demonstrated that when some atomic energy level(s) undergoes a weak harmonic modulation, photons can be generated from vacuum via effective one- and three-photon transitions, while the atom remains approximately in the ground state. These phenomena occur in the dispersive regime when the modulation frequency is accurately tuned near $\ensuremath{\omega}$ and $3\ensuremath{\omega}$, respectively, and the generated field states exhibit strikingly different statistics from the squeezed vacuum state attained in the standard cavity dynamical Casimir effect.
We study a circuit QED setup involving a single cavity mode and a cyclic qutrit whose parameters are time modulated externally. It is shown that in the dispersive regime this system behaves as a versatile platform to implement effective nnn-photon Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) models by suitably setting the modulation frequency. The atomic levels and the cavity Fock states involved in the effective Hamiltonians can be controlled through adjustment of the system parameters, and different JC and AJC interactions can be implemented simultaneously using multitone modulations. Moreover, one can implement some models that go beyond simple JC and AJC-like interaction, such as multiphoton coupling between certain entangled states. We estimate analytically the associated transition rates and study numerically the dynamics in the presence of Markovian dissipation, demonstrating that lower-order effective Hamiltonians can be implemented with current technology.
Abstract We consider the nonstationary circuit quantum electrodynamics (circuit QED) architecture, where a single artificial two-level atom interacts with a cavity field mode under external modulation of one or more system parameters. Two different approaches are employed to study the effects of Markovian dissipation on modulation-induced transitions between the atom–field dressed states: the standard master equation of quantum optics and the recently formulated dressed-picture master equation. We estimate the associated transition rates and show that photon generation from vacuum (‘dynamical Casimir effect’, DCE) and coherent photon annihilation from nonvacuum states (‘anti-DCE’) are possible with the current state-of-the-art parameters.