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Physical Review A

Effect of local-field correction on a strongly pumped resonance

Richard M. Friedberg, Sven R. Hartmann, Jamal T. Manassah

Published Sep 1, 1989• 70 citations
Publisher

Abstract

We present a general formalism that incorporates local-field corrections into Bloch's equations and use it to calculate the strong-field susceptibility of a pressure-broadened gas consisting of two-level atoms. The major effect is to introduce a dynamic Lorentz shift that varies throughout the resonance line shape. We also calculate the susceptibility associated with a weak field (probe) in the presence of a strong field (pump) when the pump and probe are at the same frequency. Here the effect is to introduce both a variable shift and a greater distortion of the line shape.

DOI
10.1103/physreva.40.2446

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Analytic expressions for the peak positions and pump frequency shift of equal intensity weak probe Autler-Townes transitions to a third level in the presence of a linearly polarized pump field are given. It is found that the presence of the third level affects the pump field dressing of the strongly excited two levels. A comparison of the Bloch-Siegert shift estimated by this weak probe technique with earlier methods suggests this condition provides a practical method for obtaining the Bloch-Siegert shift for three level systems where the pump field does not directly excite the probe transition. If the pump field off-resonantly drives the probe transition, additional light shifts occur which may dominate the Bloch-Siegert shift.

Physical Review A•Mar 1, 1998•4 citations
We present a general formalism that incorporates local-field corrections into Bloch's equations and use it to calculate the strong-field susceptibility of a pressure-broadened gas consisting of two-level atoms. The major effect is to introduce a dynamic Lorentz shift that varies throughout the resonance line shape. We also calculate the susceptibility associated with a weak field (probe) in the presence of a strong field (pump) when the pump and probe are at the same frequency. Here the effect is to introduce both a variable shift and a greater distortion of the line shape.
We calculate the effect of the local-field correction (LFC) on the local response at ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$ and 2${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$ of a medium consisting of two-level systems when subject to a pump of arbitrary intensity at ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ and a weak probe at ${\mathrm{\ensuremath{\omega}}}_{\mathit{s}}$. The pump is considered strong if its reduced intensity I=${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}^{2}$/${\ensuremath{\gamma}}_{1}$${\ensuremath{\gamma}}_{2}$ is large compared to unity. Here ${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}$ is the Rabi frequency and ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$ are the longitudinal and transverse relaxation rates. In the weak pump case the LFC manifests itself as a fixed or static frequency shift. When the pump is strong, the response is independent of the LFC. At intermediate pump intensities the effect of LFC is dependent on the intensity of the pump. Both line-shift and line-shape distortions are present. The LFC thus gives rise to a shift in the resonance response that varies according to the intensity and frequency of the applied radiation. We call this effect the dynamic Lorentz shift.
A theory of pump-probe spectroscopy is developed in which optical fields drive two-photon Raman transitions between ground states of an ensemble of three-level atoms. Effects related to the recoil the atoms undergo as a result of their interactions with the fields are fully accounted for in this theory. The linear absorption coefficient of a weak probe field in the presence of two pump fields of arbitrary strength is calculated. For subrecoil cooled atoms, the spectrum consists of eight absorption lines and eight emission lines. In the limit that ${\ensuremath{\chi}}_{1}\ensuremath{\ll}{\ensuremath{\chi}}_{2},$ where ${\ensuremath{\chi}}_{1}$ and ${\ensuremath{\chi}}_{2}$ are the Rabi frequencies of the two pump fields, one recovers the absorption spectrum for a probe field interacting with an effective two-level atom in the presence of a single pump field. However, when ${\ensuremath{\chi}}_{1}\ensuremath{\gtrsim}{\ensuremath{\chi}}_{2},$ new interference effects arise that allow one to selectively turn on and off some of these recoil-induced resonances.
We calculate a probe response of a homogeneously broadened two-level transition in the presence of a strong pump. The derivation is carried out for a generalized interaction Hamiltonian, which gives a uniform account of both the Bloch - Siegert shift and dynamic Stark splitting. It is shown that the Bloch - Siegert shift can be viewed as an extreme situation of the dynamic Stark splitting, commonly known as light shift in the literature. Finally using a perturbative approach an analytical expression for the Bloch - Siegert shift is obtained, which is compared with the previous results.
Analytic expressions for the peak positions and pump frequency shift of equal intensity weak probe Autler-Townes transitions to a third level in the presence of a linearly polarized pump field are given. It is found that the presence of the third level affects the pump field dressing of the strongly excited two levels. A comparison of the Bloch-Siegert shift estimated by this weak probe technique with earlier methods suggests this condition provides a practical method for obtaining the Bloch-Siegert shift for three level systems where the pump field does not directly excite the probe transition. If the pump field off-resonantly drives the probe transition, additional light shifts occur which may dominate the Bloch-Siegert shift.