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Chinese Physics Letters

Phase Dependence of Fluorescence Spectrum of a Two-Level Atom in a Trichromatic Field

LI Jing-yan, Xiangming Hu, Xiaoxia Li, Shi Wen-Xing, Qing Yang Xu, Hongju Guo

Published Nov 28, 2005• 4 citations
Publisher

Abstract

We examine the phase-dependent effects in resonance fluorescence of a two-level atom driven by a trichromatic modulated field. It is shown that the fluorescence spectrum depends crucially on the sum of relative phases of the sideband components compared to the central component, not simply on the respective phases. The appearance or disappearance of the central peak and the selective elimination of the sideband peaks are achieved simply by varying the sum phase. Once the sum phase is fixed, the spectrum keeps its features unchanged regardless of the respective relative phases.

DOI
10.1088/0256-307x/22/12/023

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We examine the phase-dependent effects in resonance fluorescence of a two-level atom driven by a trichromatic modulated field. It is shown that the fluorescence spectrum depends crucially on the sum of relative phases of the sideband components compared to the central component, not simply on the respective phases. The appearance or disappearance of the central peak and the selective elimination of the sideband peaks are achieved simply by varying the sum phase. Once the sum phase is fixed, the spectrum keeps its features unchanged regardless of the respective relative phases.
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 investigate the quantum noise in phase quadratures of resonance fluorescence from a two-level atom driven by a trichromatic exciting field. It is shown that the noise spectra are crucially dependent on the sum of relative phases of the sideband components compared to the central component although the sideband exciting components are much weaker than the central component. When we tune the exciting sidebands on two-photon resonance with the Mollow sideband transitions and set the phase sum to $\ensuremath{\pi}$, sideband squeezing in the in-phase quadrature remains almost the same as in the monochromatic case. Once the phase sum is set to zero, the squeezing is destroyed. The responsible mechanism is explained in terms of two-photon emission processes induced by the trichromatic components and the interference between these processes.
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 study the dependence of absorption and dispersion spectra on amplitudes and phases of the driving fields in multiple electromagnetically induced transparency. For this purpose we consider trichromatic excitation in a three-level Λ atomic system, in which a trichromatic control laser and a monochromatic probe laser are applied to two different transitions, respectively. We numerically calculate the absorption and dispersion spectra. Two characteristic features are found. Firstly, the central transparency can be made to appear or to disappear by utilizing the amplitudes and phases of the driving components. Secondly, so long as we fix the sum of two relative phases of two sideband excitation components to the central component, the absorption and dispersion spectra keep their own lineshapes unchanged no matter how we vary the respective relative phases.
The phase dependence and independence of the response of a trichromatically driven two-level medium to an arbitrarily intense probe field have been studied. The sum of the relative phases of the sideband components of the trichromatic field compared to the central component plays a crucial role in the response of the medium. For a weak probe field, as the sum of the relative phases changes from 0 to π, multiple switching can be achieved, in which switching from normal to anomalous dispersion occurs in multiple separate frequency regimes. The remarkable dependence on the sum phase is also shown for a strong probe field. On the other hand, when the sum of the two relative phases is fixed, the changes in the respective phases have no influence on the response of the medium.
We show that the trichromatic manipulation of the absorption spectrum leads to sub-half-wavelength atom localization. In particular, a three-level atom in the Λ configuration is considered, in which one transition is coupled by a trichromatic field with one sideband component being a standing-wave field while the other transition is probed by a weak monochromatic field. By varying the sum of relative phases of the sideband components of the trichromatic field to the central component, the atom is localized in either of the two half-wavelength regions with 50% detecting probability when the absorption spectrum is measured.