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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.
Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum $k$-body Hamiltonian up to an absolute error $epsilon$. Typically, gadget constructions involve terms with large interaction stren
We extend the gauge choice problem Lamb noticed to include a time-dependent relativistic non-perturbative Coulomb field, which can be produced by a cluster of relativistic charged particles. If adiabatic conditions are carefully maintained, such a fi
We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the amplitude level. A
We theoretically study specific schemes for performing a fundamental two-qubit quantum gate via controlled atomic collisions by switching microscopic potentials. In particular we calculate the fidelity of a gate operation for a configuration where a
The interaction between the electromagnetic field inside a cavity and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies. Recently, new reg