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abstract: 'We show that the counter-rotating terms of the dispersive qubit-cavity Rabi model can produce relatively large and nonmonotonic Bloch–Siegert shifts in the cavity frequency as the system is driven through a quantum-to-classical transition. Using a weak microwave probe tone, we demonstrate experimentally this effect by monitoring the resonance frequency of a microwave cavity coupled to a transmon and driven by a microwave field with varying power. In the weakly driven regime (quantum phase), the Bloch–Siegert shift appears as a small constant frequency shift, while for strong drive (classical phase) it presents an oscillatory behaviour as a function of the number of photons in the cavity. The experimental results are in agreement with numerical simulations based on the quasienergy spectrum.'
author:
- 'I. Pietikäinen$^1$'
- 'S. Danilin$^2$'
- 'K. S. Kumar$^2$'
- 'A. Vepsäläinen$^2$'
- 'D. S. Golubev$^2$'
- 'J. Tuorila$^{1,3}$'
- 'G. S. Paraoanu$^2$'
title: 'Observation of the Bloch–Siegert shift in a driven quantum-to-classical transition'
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The Rabi Hamiltonian - describing a two-level system coupled to a cavity (resonator) mode - is a paradigmatic model in quantum physics. In the rotating-wave approximation (RWA) it leads to the well-known Jaynes–Cummings (JC) model. In the dispersive limit this model predicts 