Convergence of the multimode quantum Rabi model of circuit quantum electrodynamics

Abstract

Circuit quantum electrodynamics (QED) studies the interaction of artificial atoms, open transmission lines and electromagnetic resonators fabricated from superconducting electronics. While the theory of an artificial atom coupled to one mode of a resonator is well studied, considering multiple modes leads to divergences which are not well understood. Here, we introduce a first-principles model of a multimode resonator coupled to a Josephson junction atom. Studying the model in the absence of any cutoff, in which the coupling rate to mode number $n$ scales as $\sqrt{n}$ for $n$ up to $\infty$, we find that quantities such as the Lamb shift do not diverge due to a natural rescaling of the bare atomic parameters that arises directly from the circuit analysis. Introducing a cutoff in the coupling from a non-zero capacitance of the Josephson junction, we provide a physical interpretation of the decoupling of higher modes in the context of circuit analysis. In addition to explaining the convergence of the quantum Rabi model with no cutoff, our work also provides a useful framework for analyzing the ultra-strong coupling regime of multimode circuit QED.

References in corpus (20)

• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Charge insensitive qubit design derived from the Cooper pair box
• State preservation by repetitive error detection in a superconducting quantum circuit
• Resolving photon number states in a superconducting circuit
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Schrieffer-Wolff transformation for quantum many-body systems
• Controlling the spontaneous emission of a superconducting transmon qubit
• Black-box superconducting circuit quantization
• Nonlinear response of the vacuum Rabi resonance
• Detecting bit-flip errors in a logical qubit using stabilizer measurements
• Light-matter decoupling in the deep strong coupling regime: The breakdown of the Purcell effect
• Demonstration of weight-four parity measurements in the surface code architecture
• Ultrastrong coupling phenomena beyond the Dicke model
• Circuit QED with fluxonium qubits: theory of the dispersive regime
• Beyond Strong Coupling in a Massively Multimode Cavity
• Multi-mode mediated exchange coupling in cavity QED
• Blackbox Quantization of Superconducting Circuits using exact Impedance Synthesis
• Light-matter decoupling and $A^2$ term detection in superconducting circuits
• Origin and Implications of $A^2$-like Contribution in the Quantization of Circuit-QED Systems
• Microwave quantum optics and electron transport through a metallic dot strongly coupled to a transmission line cavity

Cited by in corpus (47)

• Ultrastrong coupling between light and matter
• Resolution of Gauge Ambiguities in Ultrastrong-Coupling Cavity QED
• Breakdown of gauge invariance in ultrastrong-coupling cavity QED
• Electromagnetic coupling in tight-binding models for strongly correlated light and matter
• Cavity Quantum Electrodynamics at Arbitrary Light-Matter Coupling Strengths
• Multi-mode ultra-strong coupling in circuit quantum electrodynamics
• A tunable Josephson platform to explore many-body quantum optics in circuit-QED
• Cutoff-free Circuit Quantum Electrodynamics
• Resolution of superluminal signalling in non-perturbative cavity quantum electrodynamics
• Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits
• Quantum Networks in Divergence-free Circuit QED
• Reduced Density-Matrix Approach to Strong Matter-Photon Interaction
• QuCAT: Quantum Circuit Analyzer Tool in Python
• Engineering dissipation with resistive elements in circuit quantum electrodynamics
• Simple Impedance Response Formulas for the Dispersive Interaction Rates in the Effective Hamiltonians of Low Anharmonicity Superconducting Qubits
• Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions
• Non-perturbative treatment of giant atoms using chain transformations
• Approaching ultra-strong coupling in Transmon circuit-QED using a high-impedance resonator
• Ab initio few-mode theory for quantum potential scattering problems
• Canonical circuit quantization with linear nonreciprocal devices
• Optimal gauge for the multimode Rabi model in circuit QED
• Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator
• Algebraic canonical quantization of lumped superconducting networks
• Floquet stroboscopic divisibility in non-Markovian dynamics
• Canonical quantisation of telegrapher's equations coupled by ideal nonreciprocal elements
• Lecture Notes on Quantum Electrical Circuits
• Toolbox for nonreciprocal dispersive models in circuit QED
• Light-dressing of a diatomic superconducting artificial molecule
• Equation of motion approach to black-box quantization: taming the multi-mode Jaynes-Cummings model
• Three-qubit direct dispersive parity measurement with Tunable Coupling Qubits
• Matrix product states and numerical mode decomposition for the analysis of gauge-invariant cavity quantum electrodynamics
• Shortcuts to adiabaticity in superconducting circuits for fast multi-partite state generation
• Light-dressed states under intense optical near fields
• Floquet analysis of extended Rabi models based on high-frequency expansion
• Transmon in a semi-infinite high-impedance transmission line -- appearance of cavity modes and Rabi oscillations
• Saturable Purcell filter for circuit quantum electrodynamics
• Variational approach to atom-membrane dynamics
• Escaping Local Minima with Quantum Coherent Cooling
• Dressed bound states and non-Markovian dynamics with a whispering-gallery-mode microcavity coupled to a two-level atom and a semi-infinite photonic waveguide
• High-frequency suppression of inductive coupling between flux qubit and transmission line resonator
• Inducing nontrivial qubit coherence through a controlled dispersive environment
• Purcell-enhanced quantum adsorption
• Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits
• Neutral atom entangling gate in the ultrastrong coupling regime
• Universal deterministic quantum operations in microwave quantum links
• Dynamics of a dispersively coupled transmon qubit in the presence of a noise source embedded in the control line
• Quantum Zeno effect in the multimode quantum Rabi model