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Physical Review A

Stability and phase-dependent dynamics of an atom driven by a strong resonant field and a tunable moderate-strength perturber field

THOMAS W. MOSSBERG, Maciej Lewenstein

Published Jan 1, 1989• 23 citations
Publisher

Abstract

We have studied the transient response of undamped two-level atoms to excitation by a classical bichromatic field consisting of a strong resonant component and a moderate-strength, tunable, ``perturber'' component. It is found that the strong field tends to stabilize the atom against the influence of the perturber field. Exceptions to this general result occur when the perturber is detuned from the strong field by the Rabi frequency of the latter or its subharmonics. We believe this stabilization phenomenon is a semiclassical analog of the effect that leads to the dynamical modification of spontaneous emission [M. Lewenstein and T. W. Mossberg, Phys. Rev. Lett. 59, 775 (1987)], and the presence of detunings at which the stabilization fails provides a simple motivation for the Rabi subharmonic resonances found in certain cw bichromatic spectra. Interestingly, when the perturber field is relatively weak, detuned from the atomic resonance by the strong-field Rabi frequency, and turned on with a specific initial phase relative to the strong field, one finds that the bichromatic field can be employed to dressed-state polarize initially ground-state atoms. In a related vein, we find that perturbations at the subharmonic detunings lead to interesting phase-dependent atomic dynamics. Results were obtained using both numerical and approximate analytical techniques entirely within the context of the rotating-wave approximation. The validity of the latter is ensured by demanding that all detunings and Rabi frequencies are vanishingly small compared to the atomic transition frequency.

DOI
10.1103/physreva.39.163

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We have studied the transient response of undamped two-level atoms to excitation by a classical bichromatic field consisting of a strong resonant component and a moderate-strength, tunable, ``perturber'' component. It is found that the strong field tends to stabilize the atom against the influence of the perturber field. Exceptions to this general result occur when the perturber is detuned from the strong field by the Rabi frequency of the latter or its subharmonics. We believe this stabilization phenomenon is a semiclassical analog of the effect that leads to the dynamical modification of spontaneous emission [M. Lewenstein and T. W. Mossberg, Phys. Rev. Lett. 59, 775 (1987)], and the presence of detunings at which the stabilization fails provides a simple motivation for the Rabi subharmonic resonances found in certain cw bichromatic spectra. Interestingly, when the perturber field is relatively weak, detuned from the atomic resonance by the strong-field Rabi frequency, and turned on with a specific initial phase relative to the strong field, one finds that the bichromatic field can be employed to dressed-state polarize initially ground-state atoms. In a related vein, we find that perturbations at the subharmonic detunings lead to interesting phase-dependent atomic dynamics. Results were obtained using both numerical and approximate analytical techniques entirely within the context of the rotating-wave approximation. The validity of the latter is ensured by demanding that all detunings and Rabi frequencies are vanishingly small compared to the atomic transition frequency.
Theoretical studies have shown that the transient dynamics of an undamped two-level atom, driven by a bichromatic laser field consisting of a strong resonant pump and a moderate strength tunable perturber, are complex. Among the interesting results, it has been found that the strong field tends to stabilize the atom against the influence of the perturber field.1 Exceptions occur when the perturber is detuned from the strong field by the Rabi frequency of the pump or its subharmonics. In addition, it has been found that the atomic response depends strongly on the initial relative phase of the two excitation-field components.1,2 We have constructed an experimental apparatus to study the transient response of two-level like Yb atoms to bichromatic field excitations. The transient bichromatic laser field is generated by sending a dye laser beam double pass through an AOM driven by a bichromatic rf field. All the optical field parameters, amplitudes, frequencies, and phases, are controlled by corresponding rf field parameters.
The quantum trajectories method is illustrated for the resonance fluorescence of a two-level atom driven by a multichromatic field. We discuss the method for the time evolution of the fluorescence intensity in the presence of bichromatic and trichromatic driving fields. We consider the special case wherein one multichromatic field component is strong and resonant with the atomic transition whereas the other components are much weaker and arbitrarily detuned from the atomic resonance. We find that the phase-dependent modulations of the Rabi oscillations, recently observed experimentally [Q. Wu, D. J. Gauthier, and T. W. Mossberg, Phys. Rev. A 49, R1519 (1994)] for the special case when the weaker component of a bichromatic driving field is detuned from the atomic resonance by the strong-field Rabi frequency, appear also for detunings close to the subharmonics of the Rabi frequency. Furthermore, we show that for the atom initially prepared in one of the dressed states of the strong field component the modulations are not sensitive to the phase. We extend the calculations to the case of a trichromatic driving field and find that apart from the modulations of the amplitude there is a modulation of the frequency of the Rabi oscillations. Moreover, the time evolution of the fluorescence intensity depends on the phase regardless of the initial conditions and a phase-dependent suppression of the Rabi oscillations can be observed when the sideband fields are tuned to the subharmonics of the strong-field Rabi frequency.
We experimentally investigate the transient dynamics of two-level atoms under bichromatic optical excitation. Novel new dynamical behavior is observed that may be interpreted classically in terms of the vector model or in a modem vein as resonant monochromatic excitation of dressed atoms. We show the first observation of dressed-atom optical mutations. We also show that the system dynamics depend critically on the initial relative phase of the two excitation-field components and that controlled bichromatic excitation may lead to complete dressed-state polarization of initially ground-state atoms.
We experimentally investigate the transient dynamics of two-level atoms driven by a bichromatic optical excitation field when the bichromatic field is configured to contain a strong resonant component and a weaker nonresonant perturber component. We concentrate on the experimental situation in which the two-level atoms are prepared in an eigenstate (dressed state) of the coupled atom-resonant field system prior to exposure to the perturber field. We experimentally demonstrate perturber-field-induced, optical nutation of the dressed-state populations. We show how nutation of the dressed-state populations manifests itself in the fluorescence signal of the transiently driven atoms. We observe that the detuning of the perturber field from transitions between the dressed states of the atom-resonant field system plays the same role in determining the character of the dressed-state optical nutation as the atom-field detuning in the case of the ordinary optical nutation of atomic populations. Our experiments demonstrate the utility of the dressed-atom picture in understanding the complex dynamics of bichromatically driven atoms in a variety of circumstances.
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 examine the radiative properties of a two-level atom driven by a strong bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\delta}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{0}$+${\mathrm{\ensuremath{\delta}}}_{2}$, which can be asymmetrically placed about the atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and can have different Rabi frequencies ${\mathrm{\ensuremath{\Omega}}}_{1}$ and ${\mathrm{\ensuremath{\Omega}}}_{2}$. Applying the optical Bloch equations for the bichromatic excitation, we derive an infinite set of equations of motion for the time evolution of the atomic variables. The equations are solved numerically by matrix inversion and Laplace transforms. Using the quantum regression theorem, we then solve for the steady-state total fluorescence intensity, and the resonance-fluorescence and absorption spectra. The spectra are found to depend on the frequency difference 2\ensuremath{\delta}=${\mathrm{\ensuremath{\delta}}}_{1}$+${\mathrm{\ensuremath{\delta}}}_{2}$, the average detuning \ensuremath{\Delta}=${\mathrm{\ensuremath{\omega}}}_{0}$-1/2(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$), and the Rabi frequencies of the driving fields. For ${\mathrm{\ensuremath{\Omega}}}_{1}$=${\mathrm{\ensuremath{\Omega}}}_{2}$=\ensuremath{\Omega}, the total fluorescent intensity displays a series of maxima for \ensuremath{\Delta}=\ifmmode\pm\else\textpm\fi{}n\ensuremath{\delta}\ensuremath{\mp}${\mathrm{\ensuremath{\Omega}}}^{2}$/4\ensuremath{\delta}, where the n are the odd integers. The intensity-dependent shift from the resonances n\ensuremath{\delta} is explained as an analog of the generalized Bloch-Siegert shift. The resonance-fluorescence spectrum for \ensuremath{\Delta}\ensuremath{\ne}0 appears to contain more peaks than that for \ensuremath{\Delta}=0.This is due to the splitting of the central peak and the even sidebands into doublets. The absorption spectrum of a weak-probe beam for \ensuremath{\Delta}=0 and equal Rabi frequencies consists of a symmetric series of dispersionlike sidebands separated from ${\mathrm{\ensuremath{\omega}}}_{0}$ by integer multiples of \ensuremath{\delta}, together with a central absorption peak at ${\mathrm{\ensuremath{\omega}}}_{0}$, whose amplitude oscillates with \ensuremath{\Omega}. For \ensuremath{\Delta}\ensuremath{\ne}0 and/or ${\mathrm{\ensuremath{\Omega}}}_{1}$\ensuremath{\ne}${\mathrm{\ensuremath{\Omega}}}_{2}$, the odd sidebands remain dispersionlike, while the central peak and the even sidebands split into absorption-emission doublets. A simple physical interpretation of the spectral features is given in terms of the dressed-atom model.