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Optics Communications

Non-perturbational calculation of the Bloch-Siegert effect in semiclassical and quantum approaches

Guy Oliver

Published Dec 1, 1973• 0 citations
Publisher
DOI
10.1016/0030-4018(73)90279-4

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We revisit the theoretical description of the ultrastrong light-matter interaction in terms of exactly solvable effective Hamiltonians. A perturbative approach based on polaronic and spin-dependent squeezing transformations provides an effective Hamiltonian for the quantum Rabi model up to the second order in the expansion parameter. The model consistently includes both rotating and counter-rotating terms, going therefore beyond the rotating-wave approximation. Analytical and numerical results show that the proposed Hamiltonian performs better than the Bloch-Siegert model when calculating operator averages (e.g., the mean photon number and number of excitations). This improvement is due to a refined calculation of the dressed states within the present model. Regarding the frequency shift induced by the qubit-photon interaction, we find a different sign from the Bloch-Siegert value. This influences the structure of the eigenstates in a nontrivial way and ensures the correct calculation of the number of excitations associated with a given dressed state. As a consistency check, we show that the exactly solvable independent boson model is reproduced as a special limit case of the perturbative Hamiltonian.
The Bloch-Siegert shift displayed by a spin 1/2 particle system is measured in a double resonance experiment on the ground state of an optically oriented 199 Hg vapour. The displacement of the nuclear magnetic resonance peaks corresponding to the one and three quantum transitions are studied as a function of the radiofrequency field intensity. Similarly, the displacement of the component of the vapour polarization which is modulated at twice the RF field frequency is observed. The experimental results are compared with the existing theoretical approaches to the Bloch-Siegert effect, and a good agreement is found with the semiclassical theory leading to the continued fraction solution.
We demonstrate that a highly excited quantum electromagnetic mode strongly interacting with a single qubit exhibits several distinct resonances in addition to the Bloch-Siegert resonance condition that arises in the interaction with classical radiation. The resonance phenomena are associated with non-classical effects: Collapse of Rabi oscillations, splitting of the photon wave packet, and field-qubit entanglement. The analysis is based on a semiclassical phase-space flow of 2-by-2 matrices and becomes exact when the photon number tends to infinity. The flow equations are solved perturbatively and numerically, showing that the resonant detuning of the field and qubit frequencies lie on two branches in the leading order, that further split into distinct curves in higher orders.