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Forward four-wave mixing experiments in hot and cold atomic systems

Alexandre Mendes de [UNESP] Almeida Junior

Published Feb 28, 2023• 0 citations
OpenAlex

Abstract

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.

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•Jul 27, 2023•0 citations
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, withka andkb wave-vectors, and detected simultaneously in the 2~ka −kb and 2kb −~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.
An unexpected interference effect between four-wave mixing excitation routes in rubidium vapor is observed using a combination of a cw diode laser and a 1-GHz femtosecond pulse train. The generated coherent blue light is analyzed by scanning the diode frequency and the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler-Townes splitting, and a large separation is observed in the doublet structure due to the configuration of copropagating fields. Remarkably, by scanning the repetition rate, a narrow peak appears as a signature of the interfering pathways. A nonperturbative treatment of the Bloch equations achieves good agreement with the experimental data and demonstrates that the interfering effect appears only when both lasers are resonant with one- and two-photon transitions for the same atomic velocity group.
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 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.
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.
We describe several novel experimental effects resulting from optical coherences in multilevel atoms driven with coherent laser fields. Four configurations were explored using Rb vapor cells: lambda dark-line resonances, single beam double-lambda oscillations, and cascade two-photon transitions in co- and counter-propagating geometries. Experiments were performed with high spectral-resolution using low-power diode lasers sources and optically thick cells. Two of the most striking effects we observed are: (1) a self-oscillation that occurs at 3.0 GHz on the 85Rb hyperfine frequency when a single laser field pumps the atoms, and (2) a coherent blue-beam emission that we observe in the co-propagating cascade two-photon case. These phenomena lead to complex lineshapes, and the effects sometimes dominate the well-known 3-level coherence effects. Additional higher-order mixing or cascaded interferences are apparent in all four experimental configurations. Many of these can be viewed as multi-wave mixing enhanced by optical coherences around closed-loop paths of atomic energy levels. The effects are particularly strong when four-photon closed-loop paths with resonant energy levels are possible, as in, the double-lambda system or as a four-wave mixing “box.”
In this work, we present an experimental study on the spatial profile of coherent light generated in a forward four-wave mixing (FWM) process. We are interested in investigating how the transverse structure of the incident beams, more specifically of the Hermite-Gauss (HG) modes, is transferred to the generated signal in this nonlinear process. For the experiment, we used a continuous wave diode laser to excite a sample of Rubidium atoms, on the ⁸⁵Rb D2 line, tuned to the frequency of the 5²S_(1/2) ( = 3) → 5²P_(3/2) transition. With a Spatial Light Modulator, we were able to split the laser beam in two and structure them in the desired modes. These two beams, A and B, with wave vectors kA and kB, and linear orthogonal polarizations, with quasi-copropagated configuration, were used to induce two FWM signals in the directions 2kA-kB and 2kB-kA. The spatial profile of incident beams and the two nonlinear signals were captured by a CMOS camera, and the regimes of a thin or extensive medium were investigated. We were able to obtain results for a combination of gaussian-HG beams, as well as HG-HG beams. The profiles obtained by computer simulation were compared with the experimental measurements. Our theoretical model relies on solving the paraxial equation of the generated field. It leads to the overlap integrals of the incident beams, which unfold into some interesting selection rules in the transversal plane, for the thin and extensive medium regimes, and in the longitudinal axis, only for the long medium regime. Although the extensive medium regime presents some additional selection rules, the experimental requirements are difficult to achieve in our system, among them, we highlight the Gouy phase matching. On the other hand, a good agreement between theory and experiment was observed in the thin medium regime.