Dispersive regime of multiphoton qubit-oscillator interactions

• URL: http://arxiv.org/abs/2503.21089v2
• Date: Sun, 20 Jul 2025 12:24:34 GMT
• Title: Dispersive regime of multiphoton qubit-oscillator interactions
• Authors: Mohammad Ayyash, Sahel Ashhab,
• Abstract summary: The dispersive regime of $n$-photon qubit-oscillator interactions is analyzed using Schrieffer-Wolff perturbation theory.<n>The spectral instabilities plaguing multiphoton qubit-oscillator models are treated by introducing stabilizing higher-order terms in the Hamiltonian.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The dispersive regime of $n$-photon qubit-oscillator interactions is analyzed using Schrieffer-Wolff perturbation theory. Effective Hamiltonians are derived up to the second order in the perturbation parameters. These effective descriptions reveal higher-order qubit-oscillator cross-Kerr and oscillator self-Kerr terms. The cross-Kerr term combines a qubit Pauli operator with an $n$-degree polynomial in the oscillator photon number operator, while the self-Kerr term is an $(n-1)$-degree polynomial in the oscillator photon number operator. In addition to the higher-order Kerr terms, a qubit-conditional $2n$-photon squeezing term appears in the effective non-rotating-wave-approximation Hamiltonian. Furthermore, perturbation theory is applied to the case of multiple qubits coupled to a shared oscillator. A photon-number-dependent qubit-qubit interaction emerges in this case, which can be leveraged to tune the effective multiqubit system parameters using the oscillator state. Results for the converse setup of multiple oscillators and a single qubit are also derived. In this case, a qubit-conditional oscillator-oscillator nonlinear interaction is found. The spectral instabilities plaguing multiphoton qubit-oscillator models are carefully treated by introducing stabilizing higher-order terms in the Hamiltonian. The stabilizing terms preserve low-photon subspaces, avoid negative infinite energies and facilitate reliable numerical calculations used to validate analytical predictions. The effective descriptions developed here offer a simple and intuitive physical picture of dispersive multiphoton qubit-oscillator interactions that can aid in the design of implementations harnessing their desired nonlinear effects.

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