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arXiv:2212.01491 · Physical Review A

Intensity correlations in the forward four-wave mixing driven by a single pump

A. A. C. de Almeida, M. R. L. da Motta, S. S. Vianna

Published Feb 21, 2023• 9 citations
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Abstract

We study the field-intensity fluctuations of two independent four-wave-mixing signals generated in a cold rubidium sample as well as the transmission signals. We employ an experimental setup using a single cw laser to induce the nonlinear process in a forward geometry using either parallel and circular or orthogonal and linear polarizations of the input fields. Even though the spectra of each experimental configuration are significantly different due to the distinct level structures of each scenario, both cases present intensity-intensity cross correlations of the four-wave-mixing signals. We also calculate the cross correlation between the input fields and draft a theoretical model that indicates that resonant phase-noise to amplitude-noise conversion allows the observation of Rabi oscillations in the cross-correlation curves.

DOI
10.1103/physreva.107.023515

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Physical Review A•Feb 1, 1983•39 citations
We study the field-intensity fluctuations of two independent four-wave-mixing signals generated in a cold rubidium sample as well as the transmission signals. We employ an experimental setup using a single cw laser to induce the nonlinear process in a forward geometry using either parallel and circular or orthogonal and linear polarizations of the input fields. Even though the spectra of each experimental configuration are significantly different due to the distinct level structures of each scenario, both cases present intensity-intensity cross correlations of the four-wave-mixing signals. We also calculate the cross correlation between the input fields and draft a theoretical model that indicates that resonant phase-noise to amplitude-noise conversion allows the observation of Rabi oscillations in the cross-correlation curves.
We investigate the influence of the distribution of atom velocities in a hot rubidium sample on the correlation between field-intensity fluctuations of two independently generated four-wave mixing signals and between the transmission signals. The nonlinear process is driven by a single continuous-wave (cw) laser in a pure two-level system due to the forward geometry with circular and parallel polarization of the input fields. The intensity cross correlations of the four-wave mixing signals and the transmission signals present an oscillatory behavior with a clear dependence on the power of the incident fields, which indicates a connection with Rabi oscillations. A two-level theoretical model using stochastic differential equations to account for the mechanism of conversion of phase noise into amplitude noise shows good agreement with our experimental results. Moreover, we show how the response of the system is affected by the different atomic velocity groups.
In this work, we present a set of experiments involving four-wave mixing processes in rubidium atoms. We employ several experimental configurations exploring two- and three-level systems in cascade or Λ configurations, all of which are in a copropagating geometry, to investigate different physical phenomena present in each scenario. In the first experiment, we combine a cw diode laser and a 1 GHz femtosecond pulse train to generate coherent blue light through the four-wave mixing process in hot rubidium vapor. The generated coherent signal is analyzed by scanning either the diode frequency or the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler- Townes splitting with a wide separation in the doublet structure due to the configuration of copropagating fields. To model these results, we employ the density matrix formalism to write the Bloch equations and solve them numerically. The solutions allow us to explore other cases beyond those involving our experimental setup, comparing the response of the upper-level population and the generated signal coherence for homogeneously and non-homogeneously broadened systems. Moreover, in this same experiment, we also observed an unexpected interference effect between excitation routes of the four-wave mixing process when the repetition rate of the pulse train is scanned. The theoretical model demonstrates that the interfering effect appears only when the repetition rate is carefully chosen to produce a pair of modes of the frequency comb resonant with both one- and two-photon transitions for the same atomic velocity group. In the second experiment, still with a hot rubidium vapor, we explore two symmetrical degenerate four- wave mixing signals induced by two almost copropagating laser beams, with~ka and~kb wave-vectors, and detected simultaneously in the 2~ka −~kb and 2~kb −~ka directions. Each spectrum has a single peak with a short frequency separation between them, which our model indicates is due to the nonlinear behavior of the refractive indexes, a consequence of the high intensity of both input fields. Finally, we use the same experimental setup for the two symmetrical signals to study the field intensity fluctuations of the degenerate four-wave mixing signals and the transmission signals. In this case, the sample is an ensemble of cold rubidium atoms in a magneto-optical trap. There is an intensity- intensity cross-correlation between the signals due to the resonant phase-noise to amplitude-noise conversion. In this type of cold system, we can neglect the Doppler- broadening, allowing a straightforward study of the dependency of the correlations on the laser detuning. In these measurements, we observe a type of oscillation in the correlation curves that the theoretical model indicates to be connected with Rabi oscillations, revealed by the fluctuations long after the transient period.
A unified approach is presented for the treatment of stochastic fluctuations in four-wave-mixing processes, including uncorrelated and fully or partially cross-correlated input laser fields. The theory allows for phase as well as amplitude fluctuations and covers Markovian and non-Markovian (non-Lorentzian) input line shapes. The analogy between laser field fluctuations and molecular dephasing processes is discussed, and several types of fluctuation-induced resonances are considered. Uncorrelated input fields give rise to resonances similar to those described previously by Agarwal, while correlated input fields cause extra resonances of the type presented by us in earlier publications. Partial cross-correlations are treated here for the first time, with predictions for new effects: Oscillations in the intensity of the generated four-wave-mixing signal as a function of the degree of cross-correlation. The conditions for the experimental observation of these effects are discussed.
We describe an experimental and theoretical study of the four-wave mixing spectrum in ⁸⁷Rb atoms trapped in a magneto-optical trap. Our experimental setup uses a single cw laser to produce two copropagating beams inducing two identical four-wave mixing processes. The initial goal of the work was to analyze and compare these two signals, looking for what information they could give about the atomic system. However, since a single spectrum presents an unexpected valley around the resonance, we will focus the analyses and theoretical modeling in explaining this feature. In order to explain the nature of this valley, we performed several series of measurements, changing parameters such as laser intensity or optical depth of the sample. To interpret the experimental results our theoretical model consists of a simple four-level N-shaped system. We write the Bloch equations and solve them considering the lowest order solution. Four excitation routes arise from this solution, but only the direct excitation route to the four-wave mixing process seems to agree partially with the experimental data. To improve the agreement, we add the absorption of the input beams and of the generated light. Therefore, our model gives evidence that the valley is due to a dispersion in a high intensity regime and to absorption effects for a low intensity regime. We discuss in further details the successes and failures of this model as well as a few options to achieve better descriptions.
The effect of pump fluctuations on various coherent processes that arise in three-level systems interacting with two external fields is examined. Such coherent processes include the forward Hanle effect and various four-wave mixing effects such as the generation of phase-conjugate signals. A general formulation that enables one to calculate the influence of laser linewidth on the coherent signals produced in various directions is presented. Ensemble averages, over laser temporal fluctuations, of various physical quantities, such as atomic polarization, are calculated. The spectrum of polarization fluctuations is shown to consist of several new features which lead to coherent radiation in different directions depending on the resonant frequencies in the polarization fluctuations. The influence of pump linewidth on pressure-induced extra resonance (PIER) is treated in detail. The possibility of producing a laser-fluctuation-induced coherent signal at one of the atomic frequencies is examined. This new signal, which is produced in a direction different from that of the PIER signal, but has the same type of resonant character as PIER, is found to have significantly different pressure dependence than the PIER signal. The results of our numerical computations are qualitatively explained in terms of the convolutions of products of third-order susceptibilities and pump field-correlation functions.