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Journal of Physics B Atomic and Molecular Physics

Influence of photon statistics on the Bloch-Siegert shift

L Armstrong, S. Feneuille

Published Jul 1, 1973• 9 citations
Publisher

Abstract

The effect on a simple two-level atom of an electromagnetic field having an arbitrary distribution of photon occupation numbers is considered. It is shown that atomic energy levels shift of the order of magnitude of the Bloch-Siegert shift can be produced by interference between different states of the field. The interference term is similar to a phase term which appears in the calculation of the classical Bloch-Siegert shift. It is predicted that in general this term will average to zero, thus permitting interference effects between states of the field to be neglected.

DOI
10.1088/0022-3700/6/7/008

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The effect on a simple two-level atom of an electromagnetic field having an arbitrary distribution of photon occupation numbers is considered. It is shown that atomic energy levels shift of the order of magnitude of the Bloch-Siegert shift can be produced by interference between different states of the field. The interference term is similar to a phase term which appears in the calculation of the classical Bloch-Siegert shift. It is predicted that in general this term will average to zero, thus permitting interference effects between states of the field to be neglected.
The two-level rotating wave approximation for two-photon excitations in dipolar molecules is modified to include the effects of the Bloch-Siegert shift in the two-photon resonance energy. The resulting analytical results are used to establish a criterion for when Bloch-Siegert effects are important and the relevance of these effects are compared for fixed laser-molecule configurations versus orientationally averaged results. Two-level model molecules, with parallel permanent and transition dipoles, are used in this work and the effects of Bloch-Siegert shifts are discussed for resonance profiles, time-dependent populations of the excited state, and time-averaged excitation rates. Bloch-Siegert shifts can have pronounced effects on resonance energies and the shape of resonance profiles and, for example, on the magnitudes and the temporal locations of the maxima in the temporal evolution of the time-dependent properties of the system.
Interference effects produced by independent quantum sources are investigated, when the state of the field is not describable as a simple mixture of coherent states. The results of classical and quantum-mechanical calculations are compared. Whereas correlation effects are predicted both classically and quantum mechanically when the sources have random phases, there are important differences when the number of atoms is small. In particular, when each source consists of just one atom, the joint probability of detecting two photons at two different points in the receiving plane is found to vanish when the distance between them is an odd number of half fringes. Finally it is shown that when the number of atoms of each source is subject to Poisson fluctuations, one recovers the solution given by classical optics for thermal light, no matter how weak the sources may be on the average.
We consider resonance properties of an assembly of N two-level atoms interacting with an intense photon beam. The atoms are assumed to be noninteracting with each other except via the action of the electromagnetic field. Using the phase representation of the radiation field and the boson description of the atom system we calculate the one-photon resonance frequency for two kinds of the system: a beam of atoms moving with uniform velocity and a Boltzmann atom gas. The resonance frequency shift is found to be dependent on the total number of atoms and the initial preparation of the atom system. Numerical results show that the collective shift is of the same magnitude as the Bloch-Siegert one.
The time evolution of the atomic dipole moment of a two-level atom damped by an off-resonance squeezed vacuum is studied. Our results are valid for arbitrary detuning between the carrier frequency of the squeezed vacuum and the atomic transition frequency and show that the atomic dipole moment can oscillate with two dominant frequencies. These frequencies are shifted from their central values by an amount which is proportional to the degree of squeezing. We show that this shift of the frequencies is the exact equivalent of the optical Bloch-Siegert shift in the case of the ordinary vacuum damping without the rotating-wave approximation.