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Chinese Physics B

Spectral properties of a Ξ-configuration atom driven by a pair of bichromatic fields

Kang Jin, Xiao-Tao Xie, Zhenyi Jiang

Published Jan 1, 2013• 1 citation
Publisher

Abstract

The absorption spectrum and the incoherent fluorescence spectrum of the lower transition in an S-configuration three-level atomic system driven by a pair of bichromatic fields is investigated. The transmission of the absorption profile from a multipeaked feature to a single-peak feature is identified. Adjusting the relative phase between the two driving fields, the splitting effects of the spectral peaks occur both in the fluorescence and the absorption spectra. Furthermore, phase modulating can dramatically lead to a great suppression of the amplitudes of the whole absorption spectrum. Physically, this effect is attributed to the phase-sensitive nature of the populations and coherence between the atomic states of the system.

DOI
10.1088/1674-1056/22/1/014205

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Amplitude-modulated optical double resonance

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We have investigated the interaction between bichromatic optical fields and atomic transitions. We have considered both the interaction of a saturating bichromatic field in the form of a 100% amplitude-modulated field resonantly interacting with a single atomic transition as well as the interaction of a pair of 100% amplitude-modulated fields with two coupled atomic transitions. In our studies of a single atomic transition resonantly excited by a 100% amplitude-modulated field we have used a fully quantum-electrodynamical analysis to model the Autler-Townes effect induced by a bichromatic optical field. We find that the effect induced by a bichromatic field is markedly different from the effect produced by a monochromatic exciting field. We have derived analytic expressions for the bichromatic Autler-Townes absorption spectrum. The absorption spectrum consists of equally spaced lines spaced by the modulation frequency. The linewidths of neighboring lines alternate as functions of the field strength. Experimentally, we observed this spectrum for both resonant and detuned 100% amplitude-modulated driving fields by monitoring the absorption of a weak monochromatic field as it was tuned about the resonance frequency of the 3²P₃/₂(F = 3, mF = 3) ↔ 4²D₅/₂(F = 4, mF = 4) transition while driving the 3²S₁/₂(F = 2, mF = 2) ↔ 3²P₃/₂(F = 3, mF = 3) transition with a saturating 100% amplitude-modulated field. We found excellent agreement between our predicted and measured spectra. We then investigated the resonant interaction between a pair of 100% amplitude-modulated fields and two atomic transitions sharing a common atomic level. We considered both a three-level atomic cascade system and a three-level atomic lambda system. We examined the effect that the relative phase between the two modulations has on the rate at which the modulated fields are absorbed. We find that the saturated time-averaged field absorption exhibits parametric resonances in both the cascade and lambda systems. The time-averaged absorption is strongly dependent upon the relative phase of modulation between the two fields and for certain phase differences the time-averaged absorption can be enhanced over the maximum saturated absorption experienced by cw fields of the same time-averaged intensities. We also find that the stationary atomic response exhibits periodic oscillations and for the cascade system periodic two-photon inversions of up to 40% can be achieved. We further find dark absorption resonances as a function of phase in the lambda system. We analyze the results from the point of view of semi-classical adiabatic dressed states.

•Jan 1, 1998•0 citations
The absorption spectrum and the incoherent fluorescence spectrum of the lower transition in an S-configuration three-level atomic system driven by a pair of bichromatic fields is investigated. The transmission of the absorption profile from a multipeaked feature to a single-peak feature is identified. Adjusting the relative phase between the two driving fields, the splitting effects of the spectral peaks occur both in the fluorescence and the absorption spectra. Furthermore, phase modulating can dramatically lead to a great suppression of the amplitudes of the whole absorption spectrum. Physically, this effect is attributed to the phase-sensitive nature of the populations and coherence between the atomic states of the system.
We theoretically investigate the spectral properties of a VVV-type three-level atom driven by two bichromatic fields with a common frequency difference. By decomposing the master equation using harmonic expansions and invoking quantum regression theorem, fluorescence and probe absorption spectra of the strong atomic transition are numerically calculated under the steady state condition. We find that both fluorescence and absorption spectra exhibit two interesting features, which are equidistant comblike structures and phase-dependent line splittings. In the comblike structures, each fluorescence peak can be made subnatural by manipulating the relative intensities of the coupling fields, while for the absorption lines only the central peak can be narrowed. Line splittings are induced by the relative phase delay between the envelopes of the amplitudes of the two bichromatic fields. Interestingly, we find that the manipulation of the relative phase delay results in the emergence of sharp subnatural dips in the absorption spectra. As a natural consequence of the subnatural absorption dips, absorption spectra in atomic vapors exhibit striking subnatural burning holes for the counterpropagating probe beam geometry.
Abstract The resonance fluorescence of a four-level atom in J = 1/2 to J = 1/2 transition driven by two coherent fields is studied. We find that the incoherent fluorescence spectrum shows a direct indication of vacuum-induced coherence in the atomic system. We show that such coherence manifests itself via an enhancement or suppression of the spectral peaks in the π -polarized fluorescence. The effect of the relative phase of the driving fields on the spectral features is also investigated. We show that phase-dependent enhancement or suppression of the fluorescence peaks appears in the incoherent spectrum emitted along the σ transitions. It is found that this phase dependence occurs because of the polarization-detection scheme employed for the observation of the fluorescence light. We present an analytical explanation, based on dressed-states of the atom-field system, to interpret the numerical results.
The steady-state populations, the fluorescent intensity-intensity correlation function, and the resonance fluorescence and absorption spectra of a two-level atom bichromatically driven by a strong, coherent field and a weak, stochastic field with tunable carrier frequency and wide bandwidth are investigated analytically. Surprisingly, the population is inverted if the stochastic field is appropriately detuned from the coherent field, which is assumed resonant with the atomic transition. The resonance fluorescence spectrum still displays a three-peaked structure, but with linewidths and heights that depend upon the frequency and bandwidth of the stochastic field as well as the intensities of both fields. Asymmetric fluorescence spectra are found when the coherent field is detuned from the atomic resonance frequency. The intensity-intensity correlation function varies dramatically with the carrier frequency of the stochastic field. For appropriate choices of the parameters, the fluorescent emission of the atom is antibunched for all time. The absorption spectral features also deviate significantly from those of the monochromatically driven atom. By appropriately tuning the stochastic field, one finds that a sharp peak (absorption) or hole (gain) can occur at line center and the probe beam can be amplified at either the lower-frequency Rabi sideband or the higher-frequency sideband and the inversionless gain can be enhanced.
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 have investigated the interaction between bichromatic optical fields and atomic transitions. We have considered both the interaction of a saturating bichromatic field in the form of a 100% amplitude-modulated field resonantly interacting with a single atomic transition as well as the interaction of a pair of 100% amplitude-modulated fields with two coupled atomic transitions. In our studies of a single atomic transition resonantly excited by a 100% amplitude-modulated field we have used a fully quantum-electrodynamical analysis to model the Autler-Townes effect induced by a bichromatic optical field. We find that the effect induced by a bichromatic field is markedly different from the effect produced by a monochromatic exciting field. We have derived analytic expressions for the bichromatic Autler-Townes absorption spectrum. The absorption spectrum consists of equally spaced lines spaced by the modulation frequency. The linewidths of neighboring lines alternate as functions of the field strength. Experimentally, we observed this spectrum for both resonant and detuned 100% amplitude-modulated driving fields by monitoring the absorption of a weak monochromatic field as it was tuned about the resonance frequency of the 3²P₃/₂(F = 3, mF = 3) ↔ 4²D₅/₂(F = 4, mF = 4) transition while driving the 3²S₁/₂(F = 2, mF = 2) ↔ 3²P₃/₂(F = 3, mF = 3) transition with a saturating 100% amplitude-modulated field. We found excellent agreement between our predicted and measured spectra. We then investigated the resonant interaction between a pair of 100% amplitude-modulated fields and two atomic transitions sharing a common atomic level. We considered both a three-level atomic cascade system and a three-level atomic lambda system. We examined the effect that the relative phase between the two modulations has on the rate at which the modulated fields are absorbed. We find that the saturated time-averaged field absorption exhibits parametric resonances in both the cascade and lambda systems. The time-averaged absorption is strongly dependent upon the relative phase of modulation between the two fields and for certain phase differences the time-averaged absorption can be enhanced over the maximum saturated absorption experienced by cw fields of the same time-averaged intensities. We also find that the stationary atomic response exhibits periodic oscillations and for the cascade system periodic two-photon inversions of up to 40% can be achieved. We further find dark absorption resonances as a function of phase in the lambda system. We analyze the results from the point of view of semi-classical adiabatic dressed states.