Perturbative diagonalization for time-dependent strong interactions

Abstract

We present a systematic method to implement a perturbative Hamiltonian diagonalization based on the time-dependent Schrieffer-Wolff transformation. Applying our method to strong parametric interactions we show how, even in the dispersive regime, full Rabi model physics is essential to describe the dressed spectrum. Our results unveil several qualitatively new results including realization of large energy-level shifts, tunable in magnitude and sign with the frequency and amplitude of the pump mediating the parametric interaction. Crucially Bloch-Siegert shifts, typically thought to be important only in the ultra-strong or deep-strong coupling regimes, can be rendered large even for weak dispersive interactions to realize points of exact cancellation of dressed shifts (`blind spots') at specific pump frequencies. The framework developed here highlights the rich physics accessible with time-dependent interactions and serves to significantly expand the functionalities for control and readout of strongly-interacting quantum systems.

arXiv comment17+ pages, 5 figures

References in corpus (38)

• Charge insensitive qubit design derived from the Cooper pair box
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• The Flux Qubit Revisited to Enhance Coherence and Reproducibility
• Schrieffer-Wolff transformation for quantum many-body systems
• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Chiral groundstate currents of interacting photons in a synthetic magnetic field
• Black-box superconducting circuit quantization
• Demonstration of Universal Parametric Entangling Gates on a Multi-Qubit Lattice
• Suppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit
• Qubit-oscillator dynamics in the dispersive regime: analytical theory beyond rotating-wave approximation
• Generating and probing a two-photon Fock state with a single atom in a cavity
• Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields
• Josephson junction-embedded transmission-line resonators: from Kerr medium to in-line transmon
• Perfect quantum state transfer in a superconducting qubit chain with parametrically tunable couplings
• Tunable coupling in circuit quantum electrodynamics with a superconducting V-system
• Photon Shot Noise Dephasing in the Strong-Dispersive Limit of Circuit QED
• Suppression of photon shot noise dephasing in a tunable coupling superconducting qubit
• First-principles analysis of cross-resonance gate operation
• Universal stabilization of a parametrically coupled qubit
• Circuit QED with fluxonium qubits: theory of the dispersive regime
• Topological phase transitions and chiral inelastic transport induced by the squeezing of light
• Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise
• Suppression of Unwanted $ZZ$ Interactions in a Hybrid Two-Qubit System
• Analytical modeling of parametrically-modulated transmon qubits
• Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform
• Quantum to classical crossover of Floquet engineering in correlated quantum systems
• Parametric symmetry breaking in a nonlinear resonator
• Quantum heating of a parametrically modulated oscillator: spectral signatures
• Lifetime renormalization of driven weakly anharmonic superconducting qubits: II. The readout problem
• Coherent-State Storage and Retrieval Between Superconducting Cavities Using Parametric Frequency Conversion
• Josephson Metamaterial with a widely tunable positive/negative Kerr constant
• Quantum versus classical switching dynamics of driven-dissipative Kerr resonators
• High-fidelity dissipative engineering using parametric interactions
• Coherent Feedback Improved Qubit Initialization in the Dispersive Regime
• Adiabatic approximation, Gell-Mann and Low theorem and degeneracies: A pedagogical example
• Absence of Criticality in the Phase Transitions of Open Floquet Systems

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