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Two-photon exchange interaction from Tavis-Cummings Hamiltonian under parametric modulation

G. Taian, Alexandre V. Dodonov

Published Mar 2, 2017• 1 citation
OpenAlex

Abstract

We consider the interaction of a single-mode cavity field and $N$ 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 $\sim 2|\Delta_-|$, where $\Delta_-$ is the bare atom-field detuning. The effective Hamiltonian and associated transition rate are derived analytically for $N\gg 1$, and a good agreement is found with numerical data even when $N \sim {\it O}(1)$.

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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 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) $2|{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{-}}|$, 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.
We propose a scheme to enhance the light-matter coupling in a cavity QED system where two $\mathrm{\ensuremath{\Lambda}}$ atoms are weakly coupled to a single-mode cavity via multiphoton interaction. By introducing a second-order nonlinear (parametric) driving of the cavity, the original NNN-photon exchanges between the atoms, and the cavity can be reduced to either an effective single- or two-photon transition depending on the odevity of NNN, with the effective atom-field interaction strength being significantly enhanced. This results in an NNN-dependent effective coupling strength on top of the exponential enhancement induced only by the parametric driving. As an example, we demonstrate that our proposal can be exploited for the preparation of high-fidelity steady-state entanglement. The proposed scheme could provide a feasible alternative for diverse applications in quantum technologies.
The interaction of an ensemble of NNN two-level quantum emitters with a single-mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by gN=Ng‾1{g}_{N}=\sqrt{N}{\overline{g}}_{1}gN​=N​g​1​, where g‾1{\overline{g}}_{1}g​1​ is the ensemble-averaged single-emitter coupling strength. This model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into noncavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive emitters. We show that the predictions of our cascaded model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.
We investigate a strongly correlated system of light and matter in two-dimensional cavity arrays. We formulate a multimode Tavis–Cummings (TC) Hamiltonian for two-level atoms coupled to cavity modes and driven by an external laser field which reduces to an effective spin Hamiltonian in the dispersive regime. In one-dimension we provide an exact analytical solution. In two-dimensions, we perform mean-field study and large scale quantum Monte Carlo simulations of both the TC and the effective spin models. We discuss the phase diagram and the parameter regime which gives rise to frustrated interactions between the spins. We provide a quantitative description of the phase transitions and correlation properties featured by the system and we discuss graph-theoretical properties of the ground states in terms of graph colourings using Pólya's enumeration theorem.
Abstract Entanglement between two identical two-level atoms (qubits) that interact nonresonantly with the thermal field of a single-mode ideal resonator via effective degenerate two-photon transitions is studied. Based on an exact solution for the time-dependent density matrix, negativity is calculated as a measure of atom entanglement. The effect detuning between the atomic frequencies and the doubled frequency of the resonator field has on the dynamics of qubit entanglement in cases of separable and entangled initial atomic states is investigated.
This work presents a pedagogical and self-contained derivation of the first-order effective Hamiltonian for the two-mode Jaynes-Cummings model in the dispersive regime. A perturbative unitary transformation removes nonresonant atom-field terms, revealing dispersive frequency shifts leading to an atom-induced effective beam-splitter interaction between the field modes. The resulting Hamiltonian is diagonalized through a simple geometric rotation in the two-mode bosonic space, providing a transparent interpretation of the underlying dynamics. The exposition emphasized clarity and physical insight, making effective Hamiltonian methods accessible for teaching and learning in multimode light-matter interactions.