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 Letters

Four-Wave Mixing of Optical and Microwave Fields

Alexander S. Zibrov, Andrey B. Matsko, Marlan O. Scully

Published Aug 15, 2002• 41 citations
Publisher

Abstract

We demonstrate degenerate four-wave mixing involving both optical and microwave fields. This four-wave mixing process, with fields that differ in frequency by 5 orders of magnitude, results from stimulated Raman scattering of the optical field from an atomic ground-state Zeeman coherence in warm rubidium vapor, which is induced and maintained by the microwave field.

DOI
10.1103/physrevlett.89.103601

Related papers

Enhanced third-order nonlinear processes based on Raman resonance

Li-Ya Pei

We observe experimentally huge enhanced four-wave mixing based on Raman resonance in an 85Rb atomic vapor system. With the decrease of coupling field power or the increase of experimental temperature, the signal tends to be narrowed down in linewidth, and be basically the same spectrum as the stimulated Raman spectroscopy. It is found that the macroscopic polarization interference effect plays a crucial role in determining the nonlinear spectra. Further more, in the Doppler-broadened Λ-type energy level system, there is a strong relationship among electromagnetically induced transparency, four-wave mixing and stimulated Raman spectroscopy. The sharp transparent window in electromagnetically induced transparency can be interpreted as the suppression of Raman gain on the linear absorption of the probe field. However, the four-wave mixing signal is a new field generated by the atomic vapor system, and it comes from the Raman gain which is affected and modified by the absorption and dispersion of the nonlinear optical medium. It shows that in a Λ-type Doppler-broadened system, in essence, both the electromagnetically induced transparency and enhanced four-wave mixing stem from stimulated Raman scattering based on the third-order nonlinear processes, just the spectra of which are from different ways and objects of detection.

Acta Physica Sinica•Jan 1, 2020•1 citation

Effect of optical pumping and Raman scattering on the degenerate four-wave mixingin coherently pumped rubidium atoms

Yifu Zhu, T. N. Wasserlauf, Paul Sanchez

We present an experimental study of cw degenerate four-wave mixing (DFWM) in Doppler-broadened rubidium atoms coupled by an additional coherent field. The coupling field and the DFWM fields were arranged in a \ensuremath{\Lambda}-type configuration from the rubidium ${\mathrm{D}}_{2}$ transitions. We found that the presence of the coherent coupling field modifies the DFWM emission:mfat lower intensities of the coupling field, the DFWM emission is enhanced; at higher intensities of the coupling field, the DFWM is reduced. The observed effect of the coupling laser on the DFWM emission may be explained by the direct competition between the resonance-enhanced two-photon Raman scattering and the optical-pumping-enhanced DFWM emission.

Physical Review A•Jan 1, 1997•5 citations

Coupling of four-wave mixing and Raman scattering by ground-state atomic coherence

Michal P. Parniak, Adam Leszczyński, Wojciech Wasilewski

We demonstrate coupling of light resonant to transition between two excited states of rubidium and long-lived ground-state atomic coherence. In our proof-of-principle experiment a nonlinear process of four-wave mixing is used to achieve light emission proportional to independently prepared ground-state atomic coherence. Strong correlations between stimulated Raman-scattering light heralding the generation of ground-state coherence and the four-wave mixing signal are measured and shown to survive the storage period, which is promising in terms of quantum memory applications. The process is characterized as a function of laser detunings.

arXiv:1512.00385•Physical Review A•May 16, 2016•15 citations

Engineering Atomic and Optical Quantum States using Four-Wave Mixing

Travis Brannan

This thesis presents a study of the four-wave mixing process in hot Rubidium vapor and its applicability to generating arbitrary quantum states, both in the optical domain and as atomic collective spin excitations. The four-wave mixing process involves a double Raman scattering event, where conservation of energy and momentum entangle these Raman-scattered photons. Heralding upon detection of one of these photons in a given mode projects the other photon onto a single photon Fock state in a well-defined mode, which may serve as a narrowband quantum light source that is compatible with atom-based quantum communication protocols. We integrate the existing technique of conditional measurements into our detection scheme, which allows us to engineer more complex quantum states. Experimentally we demonstrate the production of arbitrary superpositions of |0> and |1> in the optical Fock basis. We also present a theoretical model of this process which incorporates experimental complications such as losses, higher photon-number states, and a non-trivial temporal mode. This scheme can be extended to generate arbitrary quantum states with increasing photon numbers, at the expense of repetition rate. The atomic nature of this four-wave mixing process has an added benefit in that it allows access to excitations of the collective atomic ensemble. The optical results demonstrate the creation of transient collective spin excitations, and we present a proposal to extend this work to generate longer lived arbitrary collective atomic states.

•Jan 1, 2014•0 citations

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

Unifying Degenerate Four-Wave Mixing and Coherent Anti-Stokes Raman Scattering in Rare Media

Suresh Chandra

The degenerate and counterpropagating waves of the degenerate four-wave mixing process will appear nondegenerate and noncounterpropagating to a moving observer. A Lorentz-transformed degenerate four-wave mixing is seen to be indistinguishable from coherent anti-Stokes Raman scattering. Inverse transformations which render any given coherent anti-Stokes Raman scattering the appearance of a degenerate four-wave mixing are also presented.

Physical Review Letters•Mar 22, 1982•3 citations
We demonstrate degenerate four-wave mixing involving both optical and microwave fields. This four-wave mixing process, with fields that differ in frequency by 5 orders of magnitude, results from stimulated Raman scattering of the optical field from an atomic ground-state Zeeman coherence in warm rubidium vapor, which is induced and maintained by the microwave field.
We observe experimentally huge enhanced four-wave mixing based on Raman resonance in an 85Rb atomic vapor system. With the decrease of coupling field power or the increase of experimental temperature, the signal tends to be narrowed down in linewidth, and be basically the same spectrum as the stimulated Raman spectroscopy. It is found that the macroscopic polarization interference effect plays a crucial role in determining the nonlinear spectra. Further more, in the Doppler-broadened Λ-type energy level system, there is a strong relationship among electromagnetically induced transparency, four-wave mixing and stimulated Raman spectroscopy. The sharp transparent window in electromagnetically induced transparency can be interpreted as the suppression of Raman gain on the linear absorption of the probe field. However, the four-wave mixing signal is a new field generated by the atomic vapor system, and it comes from the Raman gain which is affected and modified by the absorption and dispersion of the nonlinear optical medium. It shows that in a Λ-type Doppler-broadened system, in essence, both the electromagnetically induced transparency and enhanced four-wave mixing stem from stimulated Raman scattering based on the third-order nonlinear processes, just the spectra of which are from different ways and objects of detection.
We present an experimental study of cw degenerate four-wave mixing (DFWM) in Doppler-broadened rubidium atoms coupled by an additional coherent field. The coupling field and the DFWM fields were arranged in a \ensuremath{\Lambda}-type configuration from the rubidium D2{\mathrm{D}}_{2}D2​ transitions. We found that the presence of the coherent coupling field modifies the DFWM emission:mfat lower intensities of the coupling field, the DFWM emission is enhanced; at higher intensities of the coupling field, the DFWM is reduced. The observed effect of the coupling laser on the DFWM emission may be explained by the direct competition between the resonance-enhanced two-photon Raman scattering and the optical-pumping-enhanced DFWM emission.
We demonstrate coupling of light resonant to transition between two excited states of rubidium and long-lived ground-state atomic coherence. In our proof-of-principle experiment a nonlinear process of four-wave mixing is used to achieve light emission proportional to independently prepared ground-state atomic coherence. Strong correlations between stimulated Raman-scattering light heralding the generation of ground-state coherence and the four-wave mixing signal are measured and shown to survive the storage period, which is promising in terms of quantum memory applications. The process is characterized as a function of laser detunings.
This thesis presents a study of the four-wave mixing process in hot Rubidium vapor and its applicability to generating arbitrary quantum states, both in the optical domain and as atomic collective spin excitations. The four-wave mixing process involves a double Raman scattering event, where conservation of energy and momentum entangle these Raman-scattered photons. Heralding upon detection of one of these photons in a given mode projects the other photon onto a single photon Fock state in a well-defined mode, which may serve as a narrowband quantum light source that is compatible with atom-based quantum communication protocols. We integrate the existing technique of conditional measurements into our detection scheme, which allows us to engineer more complex quantum states. Experimentally we demonstrate the production of arbitrary superpositions of |0> and |1> in the optical Fock basis. We also present a theoretical model of this process which incorporates experimental complications such as losses, higher photon-number states, and a non-trivial temporal mode. This scheme can be extended to generate arbitrary quantum states with increasing photon numbers, at the expense of repetition rate. The atomic nature of this four-wave mixing process has an added benefit in that it allows access to excitations of the collective atomic ensemble. The optical results demonstrate the creation of transient collective spin excitations, and we present a proposal to extend this work to generate longer lived arbitrary collective atomic states.
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.