We have measured the emission spectrum of two-level-like Ba atoms driven by a continuous-wave bichromatic field containing a strong resonant component and a weaker component detuned from atomic resonance by the strong-field Rabi frequency. With the specified detuning, the weak field resonantly drives a transition of the atom--strong-field dressed states. Observed spectra show that each peak of the normal (single-driving-field) resonance fluorescence triplet is split into three subpeaks separated by one-half the weak-field Rabi frequency. Also seen is another triplet of peaks displaced from the atomic resonance by twice the strong-field Rabi frequency. Splitting of the normal triplet peaks can be explained through weak-field dressing of the strong-field dressed states. The origin of the additional triplet is less transparent. Comparison with theory is made.
We have measured the emission spectrum of two-level-like Ba atoms driven by a continuous-wave bichromatic field containing a strong resonant component and a weaker component detuned from atomic resonance by the strong-field Rabi frequency. With the specified detuning, the weak field resonantly drives a transition of the atom--strong-field dressed states. Observed spectra show that each peak of the normal (single-driving-field) resonance fluorescence triplet is split into three subpeaks separated by one-half the weak-field Rabi frequency. Also seen is another triplet of peaks displaced from the atomic resonance by twice the strong-field Rabi frequency. Splitting of the normal triplet peaks can be explained through weak-field dressing of the strong-field dressed states. The origin of the additional triplet is less transparent. Comparison with theory is made.
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.
We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving field is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mollow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving field. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we show that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.
We analyze the fluorescence and absorption spectra of a two-level atom driven by a bichromatic field with frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, separated by ${\mathrm{\ensuremath{\omega}}}_{2}$-${\mathrm{\ensuremath{\omega}}}_{1}$=2\ensuremath{\delta}, and Rabi frequencies (at resonance) 2${\mathrm{\ensuremath{\Omega}}}_{1}$ and 2${\mathrm{\ensuremath{\Omega}}}_{2}$ such that their ratio \ensuremath{\alpha}=${\mathrm{\ensuremath{\Omega}}}_{2}$/${\mathrm{\ensuremath{\Omega}}}_{1}$1. We focus on the case of ${\mathrm{\ensuremath{\omega}}}_{1}$ close to the atomic frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$ near the Rabi sideband frequency ${\mathrm{\ensuremath{\omega}}}_{1}$+2${\mathrm{\ensuremath{\Omega}}}_{1}$; the detunings are denoted by ${\mathrm{\ensuremath{\Delta}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$-${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{1}$+2${\mathrm{\ensuremath{\Omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$. We find that the spectra depend critically on the detuning ${\mathrm{\ensuremath{\Delta}}}_{2}$: For large ${\mathrm{\ensuremath{\Delta}}}_{2}$, the fluorescence spectrum consists of the well known Mollow triplet, centered at ${\mathrm{\ensuremath{\omega}}}_{1}$; for smaller (but nonzero) ${\mathrm{\ensuremath{\Delta}}}_{2}$, the spectrum is composed of a triplet at ${\mathrm{\ensuremath{\omega}}}_{1}$ together with doublets near the sideband frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2${\mathrm{\ensuremath{\Omega}}}_{1}$. However, when ${\mathrm{\ensuremath{\Delta}}}_{2}$=0 (and \ensuremath{\alpha}\ensuremath{\ll}1), the spectrum consists of a doublet centered at ${\mathrm{\ensuremath{\omega}}}_{1}$ and triplets at ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2${\mathrm{\ensuremath{\Omega}}}_{1}$: there is then no fluorescence at ${\mathrm{\ensuremath{\omega}}}_{1}$. As \ensuremath{\alpha} increases, additional triplet structures appear in the spectrum at frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2n${\mathrm{\ensuremath{\Omega}}}_{1}$ with intensities proportional to ${\mathrm{\ensuremath{\alpha}}}^{2(\mathit{n}\mathrm{\ensuremath{-}}1)}$, n\ensuremath{\gtrsim}1, and a line reappears at ${\mathrm{\ensuremath{\omega}}}_{1}$, with intensity proportional to ${\mathrm{\ensuremath{\alpha}}}^{4}$. The absorption by the system of a weak probe beam is also strongly dependent on the detuning, and the spectrum is composed of emission-dispersion-absorption features located near ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}2n${\mathrm{\ensuremath{\Omega}}}_{1}$. An analysis in the dressed-atom picture is presented which explains the physical origin of all these features, in both fluorescence and absorption. \textcopyright{} 1996 The American Physical Society.
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 examine spectral signatures of Rydberg atoms driven with near-resonant dual-tone radio-frequency (RF) fields in the regime of strong driving. We experimentally demonstrate and theoretically model a variety of nonlinear and multiphoton phenomena in the atomic Rydberg response that manifest in the EIT spectra. Our results echo previous studies of two-level atoms driven with bichromatic optical fields. In comparison to the optical studies, the RF-driven Rydberg system utilizes a more complex excitation pathway, and electromagnetic fields from two different spectral regimes: a two-photon optical excitation continuously creates highly excited Rydberg atoms, while RF fields drive resonant coupling between the Rydberg levels and generate strong mixing. Yet, our spectra reflect nearly identical effects of the dual-tone RF fields on the atomic Rydberg observables, showing detuning-dependent splittings and Rabi frequency dependent peak numbers and relative strengths, and avoided crossings at subharmonic resonances. We thus validate previous two-state models in this more complex physical system. In the context of Rydberg electrometry, we use these investigations to explore a technique where we tune a known RF field to observe spectra which give frequency and power of an unknown RF field using the complex dual-tone spectra.
We have measured the emission spectrum of two-level-like Ba atoms driven by two strong, equal-amplitude fields with frequency separation 2\ensuremath{\delta}. The spectrum consists of a series of peaks with an essentially constant spacing \ensuremath{\delta} and alternating linewidths. These features differ qualitatively from the characteristic triplet spectrum observed in the case of strong monochromatic excitation. Certain features of the observed spectrum such as its comblike structure can be motivated in terms of the energy spectrum of atom--bichromatic-field product states. Other features, such as the alternating linewidths, require more subtle analysis.