Dispersive regime of multiphoton qubit-oscillator interactions
arXiv:2503.21089 · doi:10.1103/hrc2-7nqg
Abstract
The dispersive regime of -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 -degree polynomial in the oscillator photon number operator, while the self-Kerr term is an -degree polynomial in the oscillator photon number operator. In addition to the higher-order Kerr terms, a qubit-conditional -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 various nonlinear effects.
Updated to match published version
References in corpus (39)
- Circuit Quantum Electrodynamics
- Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
- Universal Quantum Computation with Continuous-Variable Cluster States
- On the Integrability of the Rabi Model
- Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
- Quantum information processing with circuit quantum electrodynamics
- Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime
- Schrieffer-Wolff transformation for quantum many-body systems
- Dissipation and Ultrastrong Coupling in Circuit QED
- Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states
- A Schrodinger Cat Living in Two Boxes
- Exact solvability of the quantum Rabi models within Bogoliubov operators
- Two-photon and three-photon blockades in driven nonlinear systems
- Qubit-oscillator dynamics in the dispersive regime: analytical theory beyond rotating-wave approximation
- Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
- Two-resonator circuit QED: A superconducting quantum switch
- Two-photon quantum Rabi model with superconducting circuits
- Ultrastrong coupling phenomena beyond the Dicke model
- Observation of Three-Photon Spontaneous Parametric Downconversion in a Superconducting Parametric Cavity
- Improved Superconducting Qubit Readout by Qubit-Induced Nonlinearities
- Quantum control of bosonic modes with superconducting circuits
- Two-photon Rabi model: Analytic solutions and spectral collapse
- Exact Solvability of the two-photon Rabi Hamiltonian
- Beyond Strong Coupling in a Massively Multimode Cavity
- Multiphoton blockade in the two-photon Jaynes-Cummings model
- Superradiant phase transition in the ultrastrong coupling regime of the two-photon Dicke model
- Protected ultrastrong coupling regime of the two-photon quantum Rabi model with trapped ions
- Combinatorics and Boson normal ordering: A gentle introduction
- Ultrastrong coupling regime of non-dipolar light-matter interactions
- Observation of collective coupling between an engineered ensemble of macroscopic artificial atoms and a superconducting resonator
- Exact isolated solutions for the two-photon Rabi Hamiltonian
- Spectral Collapse in the two-photon quantum Rabi model
- Dissipative superradiant spin amplifier for enhanced quantum sensing
- Finite-size scaling analysis in the two-photon Dicke model
- State dependent motional squeezing of a trapped ion: new method and applications
- Driven Multiphoton Qubit-Resonator Interactions
- Exact -body representation of the Jaynes-Cummings interaction in the dressed basis: Insight into many-body phenomena with light
- Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator
- Superradiance phase transition in the presence of parameter fluctuations