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Chinese Journal of Physics

Four-wave mixing involving Ξ−V type system: In view of dressed state picture

Thi-Thuy Nguyen, Chin‐Chun Tsai

Published Feb 26, 2022• 3 citations
Publisher

Abstract

We theoretically investigate the four-wave mixing (FWM) characteristics in a Ξ−V type atomic system. The generated FWM is obtained by utilizing the density matrix formalism and solving the master equation. Interesting discrimination in the number of emerged peaks due to the chosen laser scanning schemes was pointed out. The dressed state picture is employed to elucidate the number of peaks emerged as well as the peak positions in the spectra. The dependence of the generated FWM signal accordingly to the change of parameters, such as Rabi frequencies and frequency detunings of the applied fields, are presented and well explained in the simplified dressed state picture. A prominent increase in FWM intensity is obtained when the Rabi frequencies of the coupling and driving field are approximately equal. The frequency detuning of the applied fields causes the shift in the peak positions, peak shape, and even brings about the FWM intensity enhancement.

DOI
10.1016/j.cjph.2022.02.017

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We theoretically investigate the four-wave mixing (FWM) characteristics in a Ξ−V type atomic system. The generated FWM is obtained by utilizing the density matrix formalism and solving the master equation. Interesting discrimination in the number of emerged peaks due to the chosen laser scanning schemes was pointed out. The dressed state picture is employed to elucidate the number of peaks emerged as well as the peak positions in the spectra. The dependence of the generated FWM signal accordingly to the change of parameters, such as Rabi frequencies and frequency detunings of the applied fields, are presented and well explained in the simplified dressed state picture. A prominent increase in FWM intensity is obtained when the Rabi frequencies of the coupling and driving field are approximately equal. The frequency detuning of the applied fields causes the shift in the peak positions, peak shape, and even brings about the FWM intensity enhancement.
Abstract We investigate the coherent control of dressing interaction in four-wave mixing (FWM) in a Y-type four-level atomic system based on the dressed states theory. We study the density matrix equation acted by two dressing fields simultaneously governing FWM signal intensity and the eigenvalues under the dressed state formalism. It is shown that the peak position and intensity of Autler–Townes splitting both originate from the dressing interaction as the detuning of the probe field is scanned. Moreover, it is observed that the interaction could be controlled by the dressing fields. Such flexibly controlled nonlinear signal has potential applications in optical communication and quantum information processing.
Four-wave mixing (FWM) in a cycling transition Fg =1 ↔ Fe =0 is investigated. Subject to a linearly polarized pump field with frequency ω c and a magnetic field, and simultaneously saturated and probed by the circularly polarized fields (σ ±) with frequencies ω s and ω p , three kinds of FWM fields with frequencies: 2ω s − ω p, ω c+ω s − ω p and ω c − ω s+ω p, emit. The multi-peaked structure of FWM spectra is obtained and explained as the resonant emission between the ‘virtual states’ in the dressed picture. The generated FMW signals have high quantum efficiency for a wide range of drive Rabi frequency and saturation Rabi frequency. Finally, the emitted fields ω c + ω s − ω p and ω c − ω s+ω p have about the same intensity for the well matching among the Zeeman splitting, drive Rabi frequency and saturation Rabi frequency.
Abstract We theoretically study the two- and three-photon coherence in a Ξ−Λ type four-level system for stationary as well moving atoms at the room temperature using density matrix formalism. We discuss the role of dressed states to elucidate the electromagnetically induced transparency and electromagnetically induced absorption phenomena. The presence of the third field induces absorption at the line centre. A negative dispersion slope owing to the enhanced absorption results in super-luminal light propagation and the group index variation with the coupling field is switched from sub- to super-luminal. Group index with probe detuning shows super-luminal light propagation behaviour at the dressed state positions. The three optical fields trigger four-wave mixing as a result of the third order nonlinearity. The transient evolution is also discussed for optimum strengths of the coupling and drive fields to realize the optical switching in the system.
Rydberg-dressed four-wave mixing (FWM) is theoretically and experimentally demonstrated with two electromagnetically induced transparency (EIT) windows generated in a Y-type Rb85 atomic configuration. Such dressing effect related to Rydberg states can lead to enhancement and suppression in the FWM process, which can be manipulated by the frequency detuning, Rabi frequency, and polarization of laser fields. Particularly, with the enhancement condition satisfied, coexisting FWM and Rydberg six-wave mixing (SWM) peaks with ultranarrow linewidth (much less than 30 MHz) are simultaneously observed. The controllable enhancement and suppression in a Rydberg-EIT medium can provide a novel nondestructive nonlinear method to investigate the spectrum involving Rydberg excitation in the atomic ensemble above room temperature.
Polarization properties of pure four-wave mixing (FWM) and dressed-FWM processes in a two-level system and a cascade three-level atomic system are theoretically and experimentally investigated. The relative intensities and polarization characteristics of the FWM signals in different laser polarization configurations and different level systems are experimentally investigated and compared. Also, the results are theoretically explained by different transition paths combinations. In the dressed-FWM processes, we study the dependence of dressing effect on the incident field's polarization. The FWM signal generated by a linearly polarized pumping field is suppressed more by the dressing field than the one generated by a circularly polarized pumping field. However, an opposite effect was observed when the probe field's polarization is changed. The multidressing mechanisms are used to explain these effects. In addition, the interference and polarization dependence of the coexisting FWM signals in the same atomic system are discussed.
The four-wave mixing (4WM) signal is calculated for a three-level quantum system in a $\ensuremath{\Lambda}$ configuration (upper level 2, lower levels 1 and 3) that is driven by three fields. Pump fields EEE and ${E}^{\ensuremath{'}}$ drive the 1-2 and 3-2 transitions, respectively. The probe field is detuned from field EEE by an amount $\ensuremath{\Delta}$. If the detuning of field EEE from the 1-2 transition frequency is equal to that of field ${E}^{\ensuremath{'}}$ from the 3-2 transition frequency (dark state pumping), there is a dark state in the absence of the probe field. Rather surprisingly, even though the probe field destroys the dark state for $\ensuremath{\Delta}\ensuremath{\ne}0$, the 4WM mixing vanishes for all $\ensuremath{\Delta}$ in the limit of dark-state pumping. The 4WM spectra are explained within the context of a semiclassical, dressed-state picture that involves the sequential emission of a probe and signal photon.