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Physical Review A

Multiphoton ac Stark effect in a bichromatically driven two-level atom

Terry Rudolph, Helen S. Freedhoff, Z. Ficek

Published Aug 1, 1998• 26 citations
Publisher

Abstract

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 $n$-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.

DOI
10.1103/physreva.58.1296

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We study the interaction of a two-level atom with two lasers of different frequencies and amplitudes: a strong laser of Rabi frequency 2\ensuremathΩ12{\ensuremath{\Omega}}_{1}2\ensuremathΩ1​ on resonance with the atomic transition, and a weaker laser detuned by subharmonics (2\ensuremathΩ1/n)(2{\ensuremath{\Omega}}_{1}/n)(2\ensuremathΩ1​/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 study the behavior of a two-level atom that is driven by a bichromatic field consisting of a strong resonant component and a weaker tunable component. In addition to the splitting of the energy levels (the multiphoton AC Stark effect), we find that the weaker component also shifts the subharmonic resonances, an effect we attribute to a dynamic Stark shift. When the weaker component is tuned to a shifted resonance, no fluorescence occurs at either the frequency of the strong component or the three-photon mixing frequency. Results are obtained with numerical techniques and explained in terms of the dressed-atom model of the system.
We have deduced analytical solutions of an energy level diagram of the doubly driven/dressed atom for a two-level atom exposed to a strong near-resonant bichromatic laser field in a special case, i.e., the bichromatic field with frequencies ω 1 and ω 2 , and Rabi frequencies Ω 1 and Ω 2 , in which the first coupling field of Ω 1 acts on the bare atomic levels, and then the resulting singly dressed states are driven by the second coupling field of Ω 2 , thus resulting in the doubly dressed atom. We have measured the probe absorption spectra of a doubly driven two-level atom. The system consists of 5 2 S 1 / 2 , F = 2 and 5 2 P 3 / 2 , F ′ = 3 states of 87 Rb atoms in a magneto-optical trap (MOT) as well as the cooling/trapping beams and an additional coupling field. As for the spectroscopic properties of the doubly driven two-level atom, theoretical analytical solutions are in general agreement with the experimental spectrum as a whole.
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.
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.
We focus on the influence of multiphoton effect on the fluorescence spectrum and photon statistics of the bichromatically driven two-level atomic system. The influence of the multiphoton effect of the weaker driving field on the system and spontaneous emission are revealed by Schrieffer-Wolff perturbation theory, respectively. The physical origin of the multiphoton process affecting the fluorescence spectral asymmetry characteristics is fully investigated by studying the population distribution and the dressed atomic transition weight. Further, the suppression condition of the central peak of the central band is investigated. The photon statistical properties of the system are revealed by studying the frequency-resolved correlations between different sidepeaks and the central peak and sidepeak, respectively. In particular, the physical picture of the asymmetry of the two-photon correlation signal that is affected by the multiphoton process of the weaker driving field affecting the timing detection is fully revealed by the two methods of correlation moment and conditional quantum state, respectively. These results of ours provide a theoretical approach for studying multiphoton processes in multichromatically driven quantum systems, as well as for developing quantum simulation techniques such as spin locking.
We study the effects of driving a two-level atom by two intense field modes that have equal frequencies but are otherwise distinguishable; the intensity of one mode is also assumed to be greater than that of the other. We calculate first the dressed states of the system, and then its resonance fluorescence and Autler-Townes absorption spectra. We find that the energy spectrum of the doubly dressed atom consists of a ladder of doublet continua. These continua manifest themselves in the fluorescence spectrum, where they produce continua at the positions of the Mollow sideband frequencies ${\mathrm{\ensuremath{\omega}}}_{\mathrm{L}}$ \ifmmode\pm\else\textpm\fi{}2\ensuremath{\Omega} of the strong field, and in the Autler-Townes absorption spectrum, which becomes a two-continuum doublet.