Perturbative diagonalization for time-dependent strong interactions

TL;DR

This paper introduces a systematic perturbative method using time-dependent Schrieffer-Wolff transformation to analyze strong parametric interactions, revealing new phenomena like large tunable energy shifts and 'blind spots' in dressed spectra.

Contribution

The authors develop a novel perturbative diagonalization technique for time-dependent Hamiltonians, enabling detailed analysis of strong interactions beyond traditional approximations.

Findings

Large energy-level shifts tunable by pump parameters

Identification of 'blind spots' where dressed shifts cancel

Revealing the importance of full Rabi model physics in dispersive regimes

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.