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arXiv:physics/0004046 · Physical Review A

Nonlinear ground-state pump-probe spectroscopy

P. R. Berman, B. Dubetsky

Published Oct 19, 2000• 6 citations
arXivHTMLPDF

Abstract

A theory of pump-probe spectroscopy is developed in which optical fields drive two-quantum, Raman-like transitions between ground-state sublevels. Three fields are incident on an ensemble of atoms. Two of the fields act as the pump field for the two-quantum transitions. The absorption or gain of an additional probe field is monitored as a function of its detuning from one of the fields which constitutes the pump field. Although the probe absorption spectrum displays features common to those found in pump-probe spectroscopy of single-quantum transitions, new interference effects are found to modify the spectrum. Many of these features can be explained within the context of a dressed-atom picture.

DOI
10.1103/physreva.62.053412

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Journal of Experimental and Theoretical Physics•Dec 1, 2007•3 citations
A theory of pump-probe spectroscopy is developed in which optical fields drive two-quantum, Raman-like transitions between ground-state sublevels. Three fields are incident on an ensemble of atoms. Two of the fields act as the pump field for the two-quantum transitions. The absorption or gain of an additional probe field is monitored as a function of its detuning from one of the fields which constitutes the pump field. Although the probe absorption spectrum displays features common to those found in pump-probe spectroscopy of single-quantum transitions, new interference effects are found to modify the spectrum. Many of these features can be explained within the context of a dressed-atom picture.
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 present our experimental investigations of nonlinear ground-state pump-probe spectroscopy in ultracold rubidium 85 produced in a magneto-optical trap (MOT). Nonlinear ground-state pump-probe spectroscopy is a two-photon analog of traditional two-level pump-probe spectroscopy. When a two-level atom is driven with an intense, single frequency near-resonant laser field the absorption spectrum of a weak probe field exhibits absorption and gain features not seen without the pump field. These saturated absorption line shapes, obtained under different pump field conditions, are known as the Mollow spectra. Nonlinear ground-state pump-probe spectroscopy is a three-level process, in which an intense two-photon pump field drives transitions between two components of the ground state coupled through an intermediate excited state. When the frequencies of the pump fields are tuned far from the intermediate state resonance, spontaneous emission is significantly reduced and narrow spectral lines are possible. The absorption/gain spectrum of a weak probe field, tuned in the vicinity of the intermediate state virtual level, resembles the Mollow spectrum except that new interference processes arise due to competition between two-photon pathways involving the probe field and each of the two pump fields. This interference significantly affects the probe absorption spectrum, and new features appear that are not present in the two-level case. We describe our measurements of this process, including the MOT that produces the ultracold collection of atoms, and the system of injection-locked extended cavity diode lasers that produce the phase-coherent laser fields used in our measurements.
This thesis presents theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrarily strong pump field drives a given atomic transition and a weak probe field drives the same transition. We have carried out calculations of probe absorption in vapors for arbitrary ratios of natural width and detuning to the Doppler width associated with a given transition. New line shape features which were absent in previous theories are observed.
When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near \ensuremath{\Delta}'=0 and amplification peak centered near \ensuremath{\Delta}'=2\ensuremath{\Delta} (\ensuremath{\Delta} and \ensuremath{\Delta}' are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit \ensuremath{\Vert}\ensuremath{\Delta}\ensuremath{\Vert}\ensuremath{\gg}\ensuremath{\chi}\ensuremath{\gg}\ensuremath{\Gamma}, where \ensuremath{\chi} is the Rabi frequency associated with the pump field and 2\ensuremath{\Gamma} is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near \ensuremath{\Delta}'=\ensuremath{\Delta}; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>\ensuremath{\Gamma}. If ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$, one of the doublets can be resolved provided that ${\mathrm{\ensuremath{\omega}}}_{\mathit{k}}$>${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$, where ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.
We present results of our experimental investigations of nonlinear ground-state pump-probe spectroscopy in ultracold 85{}^{85}85Rb collected in a magneto-optical trap. These measurements represent an extension of a similar pump-probe spectroscopy in a two-level atomic system when strongly driven by a near-resonant pump beam. In the present three-level system, coherence-induced gain at the probe laser frequency can be observed at specific frequencies within the spectrum. The absorption or gain spectra that we observe resemble those of the two-level gain spectra, but different interference processes lead to features that are not present in the two-level case. We describe our measurements of this interaction in this work.
The absorption/gain spectrum of a weak probe field is theoretically analyzed for an atomic three-level Λ system driven by a strong pump field and perturbed by collisions with buffer-gas atoms. It is assumed that both pump and probe drive the same transition. When the dark state is sufficiently long lived, the probe spectrum exhibits an extremely narrow (possibly subnatural-width) resonance. It is shown that coherence-preserving collisions drastically (both qualitatively and quantitatively) change the probe absorption spectrum even at a low collision frequency, when Dicke narrowing is negligible. Strong coherence effects on the resonance structure at low gas pressures is explained by a change in refractive index due to coherence-preserving collisions for particles in the resonant velocity group.