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arXiv:0709.1958

Bloch-Siegert shift for multiphoton resonances

Peter L. Hagelstein, Irfan U. Chaudhary

Published Sep 12, 2007• 1 citation
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Abstract

Recently there has been theoretical and experimental interest in Bloch-Siegert shifts in an intense photon field. A perturbative treatment becomes difficult in this multiphoton regime. We present a unitary transform and rotated model, which allows us to get accurate results away from the level anticrossings. A simple variational energy estimate leads to a new expression for the dressed two-level system energy which is accurate, and useful over a wide range of the dimensionless coupling constant.

DOI
10.48550/arxiv.0709.1958

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Recently there has been theoretical and experimental interest in Bloch-Siegert shifts in an intense photon field. A perturbative treatment becomes difficult in this multiphoton regime. We present a unitary transform and rotated model, which allows us to get accurate results away from the level anticrossings. A simple variational energy estimate leads to a new expression for the dressed two-level system energy which is accurate, and useful over a wide range of the dimensionless coupling constant.
In previous work we studied the spin-boson model in the multiphoton regime, using a rotation that provides a separation between terms that contribute most of the level energies away from resonance, and terms responsible for the level splittings at the anticrossing. Here, we consider a generalization of the spin-boson model consisting of a three-level system coupled to an oscillator. We construct a similar rotation and apply it to the more complicated model. We find that the rotation provides a useful approximation to the energy levels in the multiphoton region of the new problem. We find that good results can be obtained for the level splittings at the anticrossings for resonances involving the lower two levels in regions away from accidental or low-order resonances of the upper two levels.
Abstract. We consider a spin-boson model in which a spin 1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch-Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch-Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed. PACS numbers: 32.80.Bx,32.60.+i,32.80.Rm,32.80.WrMultiphoton Bloch-Siegert shifts and level-splittings in spin-one systems 2 1.
We consider a spin-boson model in which a spin-1 system is coupled to an oscillator. A unitary transformation is applied which allows a separation of terms responsible for the Bloch–Siegert shift, and terms responsible for the level splittings at anticrossings associated with Bloch–Siegert resonances. When the oscillator is highly excited, the system can maintain resonance for sequential multiphoton transitions. At lower levels of excitation, resonance cannot be maintained because energy exchange with the oscillator changes the level shift. An estimate for the critical excitation level of the oscillator is developed.
Bloch-Siegert shifts and widths of resonances in two-level systems are evaluated within an adiabatic approximation applicable in the multiphoton regime. The level splitting is controlled by a static field. Most attention is paid to the case of a circular driving field with the static field in the plane of rotation. This nonconventional setup was used in a recent experiment on intrashell resonances in Rydberg atoms where shifts and widths for NNN-photon resonance with NNN as large as 23 were observed [D. Fregenal et al., Phys. Rev. A 69, 031401(R) (2004)]. For this in-plane configuration the resonance widths are drastically enhanced compared to their values in the conventional configuration (linearly polarized driving field perpendicular to static field), whereas the shifts are only weakly affected.
In a recent publication [ J. Opt. Soc. Am. B5, 2015 ( 1988)], Chakmakjian et al. gave an empirical expression for the positions of subharmonic resonances of a two-level system driven by a fully amplitude modulated laser. Here we calculate exact positions of the resonances and adapt a dressed-atom analysis from the corresponding magnetic resonance problem. Thus subharmonic resonances are explained as the limiting behavior of multiphoton resonances, and, in the limit of vanishing damping, the positions of the resonances are given by analytical expressions for the generalized Bloch–Siegert shifts.