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Spectral analysis of the four-wave mixing in a cold atomic sample using a single CW laser

A. A. C. de Almeida

Published Feb 20, 2019• 0 citations
OpenAlex

Abstract

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.

Related papers

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

Alexandre Mendes de [UNESP] Almeida Junior

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.

•Feb 28, 2023•0 citations

Limits on the atomic description of four-wave mixing

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The limits of the well-established single-atom model for describing photon-pair generation via four-wave mixing in a diamond configuration in atomic ensembles are experimentally tested. Using a cold-atom source, biphotons are generated and detected through polarization analyzers that resolve the emitted light into horizontal and vertical components in the laboratory frame. The pump lasers driving the first and second excitation transitions are horizontally and vertically polarized, respectively. To predict single-photon counts and coincidence rates in all polarization channels, the first- and second-order correlation functions are calculated directly using a comprehensive model that accounts for all Zeeman sublevels of the relevant hyperfine states. Furthermore, the population dynamics with and without the re-pump laser of the magneto-optical trap are compared, revealing substantial differences in the populations of the Zeeman sublevels. This motivates the inclusion of two additional hyperfine levels and their corresponding Zeeman sublevels in the final model. The resulting density matrix is used to calculate expectation values of the far-field electric-field operators and compare them with experimental measurements over a range of pump-laser powers. Excellent agreement with the measured photon counts is obtained over most of this range. For the coincidence measurements, good agreement is found when the polarization of the photon generated by the first (second) decay is parallel to that of the first (second) pump beam. In contrast, the model consistently underestimates the experimental coincidence rates for the opposite polarization configuration. These findings indicate that effects beyond the internal level dynamics of individual atoms, most notably collective phenomena, are required to fully account for photon coincidences generated by four-wave mixing in atomic ensembles.

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Abstract In this paper, we suggest a theoretical model for the exchange of the orbital angular momentum (OAM) state of laser fields in a real cold atomic system for realization in an experimental setup. By using four-wave mixing (FWM) processes, we study the spatial dependence of the new weak generated signal light under electromagnetically induced transparency conditions when one of the laser lights becomes an optical vortex. We discuss the spatial dependence of FWM processes via experimental parameters for different conditions of the OAM of vortex light. We have found that the intensity and phase distributions of the new generated light depends strongly on the OAM number of the optical vortex light. Moreover, we investigate the absorption spectrum of the new generated signal light for different OAM of the optical vortex light. Our obtained results may have potential applications in quantum information science.

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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.

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Manipulation of a Large Magneto-Optical Trap: application to Four-Wave Mixing

G. L. Gattobigio

In this thesis we present a detailed experimental investigation of size- and densityscaling laws for large Magneto-Optical Traps (MOT) with up to 10^10 atoms. It is well known that laser-induced interactions, produced by multiple scattering, is the main limitation to spatial densities in a MOT. We therefore realized a ?Dark MOT? combined with a Dipole-Trap. Thus, the repulsions were considerably lower and an increase by two factor of magnitude (up to 10^12 atm/cm^3) has been observed. We also propose a qualitative model for the density (and thus for the size), which introduces the mechanical interactions induced by the repumper photons when its optical thickness becomes important. This work is part of the research project to observe Anderson localization of light in cold atoms, where densities of the order of (10^13 - 10^14 atm/cm^3) are required. For densities lower than this critical value gain mechanisms could be useful to amplify prelocalized modes. We thus implemented a pump-probe technique suitable for gain production in the atomic sample. In our case, we have been naturally lead to a Four-Wave Mixing (FWM) configuration. A detailed analysis of the properties and characteristics of FWM-signal has been presented, with, in particularly, a clear red-blue asymmetry of FWM-spectrum for high intensities of the pump beams. We explained this asymmetry by the spatial bunching of the atoms in the nodes or antinodes of the strong standing wave of the pump beams.

•Feb 29, 2008•1 citation

Interference effect and Autler-Townes splitting in coherent blue light generated by four-wave mixing

Marco Polo Moreno de Souza, A. A. C. de Almeida, S. S. Vianna

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.

arXiv:1902.10761•Physical Review A•Apr 8, 2019•14 citations
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.
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.
The limits of the well-established single-atom model for describing photon-pair generation via four-wave mixing in a diamond configuration in atomic ensembles are experimentally tested. Using a cold-atom source, biphotons are generated and detected through polarization analyzers that resolve the emitted light into horizontal and vertical components in the laboratory frame. The pump lasers driving the first and second excitation transitions are horizontally and vertically polarized, respectively. To predict single-photon counts and coincidence rates in all polarization channels, the first- and second-order correlation functions are calculated directly using a comprehensive model that accounts for all Zeeman sublevels of the relevant hyperfine states. Furthermore, the population dynamics with and without the re-pump laser of the magneto-optical trap are compared, revealing substantial differences in the populations of the Zeeman sublevels. This motivates the inclusion of two additional hyperfine levels and their corresponding Zeeman sublevels in the final model. The resulting density matrix is used to calculate expectation values of the far-field electric-field operators and compare them with experimental measurements over a range of pump-laser powers. Excellent agreement with the measured photon counts is obtained over most of this range. For the coincidence measurements, good agreement is found when the polarization of the photon generated by the first (second) decay is parallel to that of the first (second) pump beam. In contrast, the model consistently underestimates the experimental coincidence rates for the opposite polarization configuration. These findings indicate that effects beyond the internal level dynamics of individual atoms, most notably collective phenomena, are required to fully account for photon coincidences generated by four-wave mixing in atomic ensembles.
Abstract In this paper, we suggest a theoretical model for the exchange of the orbital angular momentum (OAM) state of laser fields in a real cold atomic system for realization in an experimental setup. By using four-wave mixing (FWM) processes, we study the spatial dependence of the new weak generated signal light under electromagnetically induced transparency conditions when one of the laser lights becomes an optical vortex. We discuss the spatial dependence of FWM processes via experimental parameters for different conditions of the OAM of vortex light. We have found that the intensity and phase distributions of the new generated light depends strongly on the OAM number of the optical vortex light. Moreover, we investigate the absorption spectrum of the new generated signal light for different OAM of the optical vortex light. Our obtained results may have potential applications in quantum information science.
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.
In this thesis we present a detailed experimental investigation of size- and densityscaling laws for large Magneto-Optical Traps (MOT) with up to 10^10 atoms. It is well known that laser-induced interactions, produced by multiple scattering, is the main limitation to spatial densities in a MOT. We therefore realized a ?Dark MOT? combined with a Dipole-Trap. Thus, the repulsions were considerably lower and an increase by two factor of magnitude (up to 10^12 atm/cm^3) has been observed. We also propose a qualitative model for the density (and thus for the size), which introduces the mechanical interactions induced by the repumper photons when its optical thickness becomes important. This work is part of the research project to observe Anderson localization of light in cold atoms, where densities of the order of (10^13 - 10^14 atm/cm^3) are required. For densities lower than this critical value gain mechanisms could be useful to amplify prelocalized modes. We thus implemented a pump-probe technique suitable for gain production in the atomic sample. In our case, we have been naturally lead to a Four-Wave Mixing (FWM) configuration. A detailed analysis of the properties and characteristics of FWM-signal has been presented, with, in particularly, a clear red-blue asymmetry of FWM-spectrum for high intensities of the pump beams. We explained this asymmetry by the spatial bunching of the atoms in the nodes or antinodes of the strong standing wave of the pump beams.
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.