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Physical Review A

ac Stark effect in a doubly driven three-level atom

Changjiang Wei, Dieter Suter, Andrew S. M. Windsor, Neil B. Manson

Published Sep 1, 1998• 43 citations
Publisher

Abstract

In this paper we present a detailed treatment of the ac Stark effect of a three-level atom driven by two strong laser fields in a cascade scheme. We consider two situations where there is a weak laser field probing a new transition starting from one of the three levels to a fourth level. In one case the initial level of the probed transition is the ground state and in the other case the initial level is the intermediate state. For both situations we derive an analytical expression for the absorptive and dispersive responses of the weak probe field and present the spectrum obtained from numerical calculation. The general feature of the spectrum has a three-peak structure. The positions and relative intensities of the three spectral components are affected strongly by the driving field intensities and detunings. An account of the spectrum is given in terms of the dressed-state formalism.

DOI
10.1103/physreva.58.2310

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Journal of Physics B Atomic and Molecular Physics•Mar 14, 1978•22 citations
In this paper we present a detailed treatment of the ac Stark effect of a three-level atom driven by two strong laser fields in a cascade scheme. We consider two situations where there is a weak laser field probing a new transition starting from one of the three levels to a fourth level. In one case the initial level of the probed transition is the ground state and in the other case the initial level is the intermediate state. For both situations we derive an analytical expression for the absorptive and dispersive responses of the weak probe field and present the spectrum obtained from numerical calculation. The general feature of the spectrum has a three-peak structure. The positions and relative intensities of the three spectral components are affected strongly by the driving field intensities and detunings. An account of the spectrum is given in terms of the dressed-state formalism.
We investigate the steady-state spontaneous emission spectrum of a three-level atom driven by two coherent fields and the absorption spectrum of a weak probe passing through a collection of such driven atoms. We find that the fluorescence spectrum is strongly affected by the decay rates of all the levels involved in the atomic evolution and not just by the decay parameters of the specific transition whose emission spectrum is being monitored. In particular, the spectral components can acquire very different widths and peak heights relative to the case of the standard resonance fluorescence in which a two-level system is driven by a single near-resonant field. An external probe signal passing through the gas of three-level atoms may be absorbed or amplified, as in the standard two-level case, but under specific operating conditions, amplification (or absorption) occurs over the entire range where the atomic response is appreciable. In this case the existence of amplification or absorption is controlled solely by the population difference between two dressed states of the system. We provide numerical results in support of our arguments for arbitrary values of the atomic and field parameters and also develop an analytic description in the limit of strong driving fields that leads to explicit line-shape and linewidth formulas.
Summary form only given.It is well known that a strongly driven transition exhibits a doublet splitting when probed by a weak field, commonly known as AC Stark splitting. It can be observed either by probing the driven two-level itself (Mollow-type spectrum) or via a third level (Autler-Townes-type spectrum). These two type splittings can have very different characteristics, particularly when driven resonantly. The absorptive Mollow spectrum consists of two dispersion-like features, whereas for the Autler-Townes spectrum there is a simple doublet splitting. In this paper we report the observation of both Mollow and Autler-Townes spectrum simultaneously by applying two strong driving fields in a three-level configuration.
We study the interaction of a two-level atom with two lasers of different frequencies and amplitudes: a strong laser of Rabi frequency $2{\ensuremath{\Omega}}_{1}$ on resonance with the atomic transition, and a weaker laser detuned by subharmonics $(2{\ensuremath{\Omega}}_{1}/n)$ of the Rabi frequency of the first. We find that under these conditions the second laser couples the dressed states created by the first in an nnn-photon process, resulting in ``doubly dressed'' states and in a ``multiphoton ac Stark'' effect. We calculate the eigenstates of the doubly dressed atom and their energies, and illustrate the role of this multiphoton ac Stark effect in its fluorescence, absorption, and Autler-Townes spectra.
We examine the absorption of a weak probe beam by a laser driven V-type atom with a pair of closely lying excited levels, where both the driving and probe lasers interact simultaneously with the two transitions. The effects of quantum interference among decay channels on the absorption spectra are also investigated. We introduce dipole moments in the dressed-state representation and the Hamiltonian in terms of the dressed states describing the interaction between the probe and the atom. In the degenerate case, features similar to that of a driven two-level atomic system are found due to some dark transitions in the spontaneous emission and the fact that the probe beam only detects certain transitions. In the nondegenerate case, the absorption spectrum is strongly influenced by the degree of quantum interference, resulting in different line shapes for emission peaks, absorption peaks, and dispersionlike profiles. The effect of probe polarization on the absorption spectrum is also investigated.
Calculations based on a full master equation approach have been made of the absorption spectrum for a certain three-level system in which two states mod 2), mod 1) are strongly driven by a near resonant monochromatic laser field whose Rabi frequency is large compared with the natural lifetime width of mod 2). A third state mod 3) is coupled to the nearby state mod 2) by a static electric field. As the static field coupling increases the spectrum in the neighbourhood of the laser frequency changes from the partly emissive, partly absorptive Mollow form to an absorptive spectrum with two strong peaks. Also, the spectrum in the neighbourhood of the upper level transition frequency changes from an Autler-Townes doublet to a spectrum where a new emissive line appears at the Rabi frequency. In terms of the dressed atom model, this transition corresponds to an intradoublet transition previously forbidden in two-level atoms, though predicted to occur in certain two-level molecular systems. The spectrum is interpreted in terms of a dressed atom model. In general terms not only do the dressed atom transition frequencies correlate well with the spectral features, but there is also good agreement between the heights and widths of the spectral features and those obtained from the full master equation approach. The importance of using the full dipole operator in the basic definitions of the spectral quantities is also demonstrated.
Studies are made of a system consisting of a molecule interacting with both an intense electromagnetic field resonant with a molecular transition frequency and a weak RF probe field at the Rabi frequency. An earlier study of this system (Freedhoff et al., ibid., vol.8, p.L209 (1975)) is extended to include the effects of photon cascades and of laser detuning. The method of calculation is the dressed-atom description and master-equation approach of Cohen-Tannoudji and Reynaud (1977). Unlike the earlier study, the present treatment produces quantitatively correct expressions for the emission and absorption spectra both in the visible and in the RF regions. More importantly, however, the predicted absorption intensity is greatly enhanced over that in the earlier study, and, for negative detuning of the laser, amplification of the RF signal is predicted.