Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Bunching-induced asymmetry in degenerate four-wave mixing with cold atoms

G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, Robin Kaiser

Published Oct 12, 2006• 13 citations
Publisher

Abstract

We have investigated degenerate four-wave mixing in a sample of cold rubidium atoms. A red-blue asymmetry is observed for high intensities of the pumping beams. This asymmetry is explained by the spatial bunching of the atoms in the nodes or antinodes of the strong standing wave of the pump beams. This explanation is confirmed by different experimental configurations and by numerical simulations.

DOI
10.1103/physreva.74.043407

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

Degenerate four-wave mixing in atomic ytterbium

Tian Li, Ryan P. Baker, Jonathan D. Weinstein

We have performed degenerate four-wave mixing experiments with cryogenically cooled atomic ytterbium. We use buffer-gas cooling to prepare high optical density samples at a temperature of 5 K, cold enough to resolve the different isotopes and hyperfine transitions. We observe four-wave mixing with cross-polarized pump and probe beams. The four-wave mixing is strongly enhanced when the laser is closely detuned from the S01(F=1/2)→P11(F′=1/2) transition of the Yb171 (I=1/2) isotope.

Bulletin of the American Physical Society•Jun 17, 2011•0 citations

Two symmetric four-wave mixing signals induced by beams with nonuniform distributions

M. R. L. da Motta

We present a theoretical analysis of the spatial shape (transverse and longitudinal) of two degenerate four-wave mixing (FWM) signals induced by fields Ea and Eb, with nonuniform transverse profiles, and wave-vectors ka and kb. The two signals are generated in a cold sample of two-level atoms, in the forward directions 2ka − kb and 2kb − ka. In all cases, the transverse shapes of the generated signals (both near- and far-field) are dictated by the projection of the nonlinear coherence onto the Laguerre-Gaussian (LG) function space. Our calculations show that the longitudinal profile of each generated beam is affected by the spectral characteristics of the medium, described by the third order nonlinear susceptibility. For Gaussian incident fields with equal detunings from resonance, the FWM beam shapes are completely symmetric, with an asymmetry induced by different detunings of incident fields. By considering incident beams with LG distributions, the topological charge conservation determines the orbital angular momentum of each signal and the longitudinal profiles show similar behaviors to the case with Gaussian beams. The phase discontinuities of LG modes reveal a rotation and distortion of the phase distribution of the FWM beams caused by the detunings. We discuss for selected configurations, the relations between both generated beams and their propagation properties. We also present preliminary experimental results of the power spectra of the two FWM signals generated in our magneto-optical trap of rubidium atoms.

•Mar 23, 2021•0 citations

Degenerate four-wave mixing in atomic ytterbium

Tian Li, Ryan P. Baker, Jonathan D. Weinstein

We have performed degenerate four-wave mixing experiments with cryogenically cooled atomic ytterbium. We use buffer-gas cooling to prepare high optical density samples at a temperature of 5 K, cold enough to resolve the different isotopes and hyperfine transitions. We observe four-wave mixing with cross-polarized pump and probe beams. The four-wave mixing is strongly enhanced when the laser is closely detuned from the S01(F=1/2)→P11(F′=1/2) transition of the Yb171 (I=1/2) isotope.

Journal of the Optical Society of America B•Sep 21, 2012•2 citations

The Experimental Study of the Influence About Pump Polarization on the Degenerate Four-wave Mixing Signals

Hai Wang

The impact of the pump polarization during the Rb atom degenerate four-wave mixing process on the degenerate four-wave mixing signals is studied.In the experiment,a pump light and the probe light transmitted in the same direction into the air chamber Rb atoms,and the other pump light propagated through the atoms in the opposite direction.Then,by changing the polarization of the two pump lights,the four-wave mixing signal is observed.The result shows that when the two pump light polarization is parallel,a strong four-wave mixing signal can be observed.While the two pump light polarization is orthogonal to each other,the four-wave mixing signal disappear.The theoretical analysis indicates that the population grating induced by the pump beam interference is the physics mechanism of the degenerate four-wave mixing signal.

Acta Sinica Quantum Optica•Jan 1, 2010•0 citations

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
We have investigated degenerate four-wave mixing in a sample of cold rubidium atoms. A red-blue asymmetry is observed for high intensities of the pumping beams. This asymmetry is explained by the spatial bunching of the atoms in the nodes or antinodes of the strong standing wave of the pump beams. This explanation is confirmed by different experimental configurations and by numerical simulations.
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.
We present a theoretical analysis of the spatial shape (transverse and longitudinal) of two degenerate four-wave mixing (FWM) signals induced by fields Ea and Eb, with nonuniform transverse profiles, and wave-vectors ka and kb. The two signals are generated in a cold sample of two-level atoms, in the forward directions 2ka − kb and 2kb − ka. In all cases, the transverse shapes of the generated signals (both near- and far-field) are dictated by the projection of the nonlinear coherence onto the Laguerre-Gaussian (LG) function space. Our calculations show that the longitudinal profile of each generated beam is affected by the spectral characteristics of the medium, described by the third order nonlinear susceptibility. For Gaussian incident fields with equal detunings from resonance, the FWM beam shapes are completely symmetric, with an asymmetry induced by different detunings of incident fields. By considering incident beams with LG distributions, the topological charge conservation determines the orbital angular momentum of each signal and the longitudinal profiles show similar behaviors to the case with Gaussian beams. The phase discontinuities of LG modes reveal a rotation and distortion of the phase distribution of the FWM beams caused by the detunings. We discuss for selected configurations, the relations between both generated beams and their propagation properties. We also present preliminary experimental results of the power spectra of the two FWM signals generated in our magneto-optical trap of rubidium atoms.
The impact of the pump polarization during the Rb atom degenerate four-wave mixing process on the degenerate four-wave mixing signals is studied.In the experiment,a pump light and the probe light transmitted in the same direction into the air chamber Rb atoms,and the other pump light propagated through the atoms in the opposite direction.Then,by changing the polarization of the two pump lights,the four-wave mixing signal is observed.The result shows that when the two pump light polarization is parallel,a strong four-wave mixing signal can be observed.While the two pump light polarization is orthogonal to each other,the four-wave mixing signal disappear.The theoretical analysis indicates that the population grating induced by the pump beam interference is the physics mechanism of the degenerate four-wave mixing signal.
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.