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Journal of Physics B Atomic Molecular and Optical Physics

Subharmonic structure under strong modulation and multicoloured coherence in three-level atoms

Harshawardhan Wanare

Published Jun 9, 2008• 2 citations
Publisher

Abstract

We demonstrate new subharmonic features that arise in the strong modulation regime when a three-level Λ system is driven by two independent phase-modulated fields. In the strong modulation regime the system exhibits subharmonic spectral features even under weak-field excitation conditions, and the peaks occur precisely at integer combinations of the modulation frequencies. The spectral technique we use, apart from being nonperturbative, systematically accounts for the hierarchy of Fourier components underlying the wave-mixing phenomena. We also identify the dominant Fourier components responsible for individual peaks of the subharmonic signal. Under symmetric excitation one obtains multicoloured coherent population trapping with the associated atomic coherence. The magnitude of the multicoloured atomic coherence is invariably lower than the usual monochromatic case, and it is shared across a series of detunings as well as across (response) frequencies.

DOI
10.1088/0953-4075/41/12/125502

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Journal of the Arkansas Academy of Science•Jan 1, 2012•0 citations
We demonstrate new subharmonic features that arise in the strong modulation regime when a three-level Λ system is driven by two independent phase-modulated fields. In the strong modulation regime the system exhibits subharmonic spectral features even under weak-field excitation conditions, and the peaks occur precisely at integer combinations of the modulation frequencies. The spectral technique we use, apart from being nonperturbative, systematically accounts for the hierarchy of Fourier components underlying the wave-mixing phenomena. We also identify the dominant Fourier components responsible for individual peaks of the subharmonic signal. Under symmetric excitation one obtains multicoloured coherent population trapping with the associated atomic coherence. The magnitude of the multicoloured atomic coherence is invariably lower than the usual monochromatic case, and it is shared across a series of detunings as well as across (response) frequencies.
We demonstrate the simultaneous occurrence of coherent population trapping at a series of frequencies separated by modulation frequency of phase-modulated fields. The two arms of the system are coupled to two phase-modulated fields and the response of the atomic system to such fields is calculated nonperturbatively. A judicious choice of modulation characteristics allows one to selectively switch on or off the occurrence of coherent population trapping at specific frequencies. A new technique is developed to compute two-dimensional tridiagonal matrix equations. This generalized technique provides the vital methodology needed to calculate the response of such systems in the strong modulation regime and for arbitrary field strengths.
We present a theoretical study of quantum coherent effects in a Λ-three-level system with a strong bichromatic coupling field and a weak probe field. When one component of the strong bichromatic coupling field is resonant with a corresponding transition and the other is detuning with an integer fraction of the Rabi frequency of the resonant field, the absorption spectrum exhibits a series of symmetrical doublets. While two frequencies of the strong bichromatic coupling field are symmetrically detuned from the transition, the position and the relative intensity of the absorption peak are both affected by the coupling field intensity and detuning. An explanation of the spectrum is given in term of the dressed-state formalism.
A subharmonic resonance occurs on irradiation of a three-level (\ensuremath{\Lambda}) system by two bichromatic fields when an integer multiple of the common frequency difference matches the Raman detuning between the two lower levels. The occurrence of these multiphoton resonances requires saturation of the Raman transition. The three-level model is applied in order to understand recent experimental studies of subharmonic Raman resonances between vibrational states of optically trapped atoms. I explain the difference between these resonances and the well-known velocity-tuned (Doppleron) resonances in two-level atoms by considering a two-state model with the excited state eliminated. I finally point out a Sisyphus cooling mechanism that is entirely dependent on an additional relaxation of the Raman coherence, comparable to collision-induced resonances.
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.
In this thesis, atomic coherence is used to enhance nonlinear optical processes in multi-level atoms. The multi-photon transitions are driven resonantly, and at the same time without absorptive losses, by using electromagnetically induced transparency (EIT), thereby allowing the study of χ(3) and χ(5) nonlinearities using weak driving fields. The coherently modified probe beam(s) and the atom-radiated signal fields arising from four- and six- wave- mixing (FWM and SWM) processes are measured in the spectral, temporal and spatial domains. In a three-level ladder-type atomic system, multiple peaks having spectral asymmetries are observed in the EIT window as well as in the FWM signal waveforms due to the diverse multiplicities of the participating atomic states. Using phase control tailored in the frequency domain, we demonstrate all-optical methods to control these spectral waveforms and discuss applications involving waveform-shaping and metrology. For the EIT study we demonstrate a switching of multiple dark peaks into bright peaks via phase-control of interferences in the underlying dark-states. In the FWM study we demonstrate all-optical spectral line shape symmetrization, linewidth narrowing and bandwidth switching. In a four-level inverted-Y-type atomic system, we drive and measure coexisting and phase-matched FWM and SWM signals. By using precision control of the relative phase and amplitude between these two processes of different nonlinear orders, we demonstrate phase coherence between them. First, a single-phase measurement is performed in the temporal and spatial domains, and the interferogram is used to measure the resonant frequency of the 5D5/2-5P3/2 atomic transition in 85Rb. Second, the method is extended to realize a capacity for two-phase measurement. In this case, the spectral bandwidth of the signal is modified in order to measure the phase-shift occurring in one Mach-Zehnder interferometer, while the intensity of the total signal waveform measures the phase-shift occurring in a second interferometer. Finally, we demonstrate phase-dependent spatial fusion between two ultra-weak optical fields by using a strong coupling field to first convert the weak fields into bosonic dark-state polaritons, which are then steered into a common all-optical waveguide mode arising due to the coupling field's intensity distribution and the resulting cross-Kerr refractive index gradient.