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

Optics Letters

Pressure-induced degenerate frequency resonance in four-wave light mixing

A. R. Bogdan, Yehiam Prior, N. Bloembergen

Published Feb 1, 1981• 80 citations
Publisher

Abstract

Phase-matched four-wave mixing in sodium vapor with a helium buffer gas is carried out in a noncoplanar geometry. The directions of the four light beams remain nondegenerate even if all frequencies are equal. A sharp zerodifference frequency resonance in the intensity of the parametrically generated fourth beam by three incident beams is observed that is proportional to the square of the pressure of the buffer gas. A theoretical interpretation of this effect caused by elimination of destructive interference between two coherent pathways is presented.

DOI
10.1364/ol.6.000082

Related papers

Quantitative characteristics of pressure-induced degenerate frequency resonance in four-wave mixing with continuous-wave laser beams

A. R. Bogdan, M. C. Downer, N. Bloembergen

The linewidth and intensity of the four-wave degenerate mixing signal in Na vapor have been observed as functions of He buffer-gas pressure with cw single-mode dye-laser beams. The width is independent of He pressure, and a quantitative comparison with theory is made. We also report the observation of a new effect, a four-wave mixing Raman-type resonance between two equally populated hyperfine levels.

Optics Letters•Jul 1, 1981•54 citations

High-resolution four-wave light-mixing studies of collision-induced coherence in Na vapor

Lewis J. Rothberg, N. Bloembergen

Near-resonant four-wave light mixing in Na vapor with inert buffer gases reveals collision-induced coherences when the difference frequency between two incident light beams equals the hyperfine splitting or the Zeeman splitting between two states of the $3^{2}S$ ground-state manifold. The Doppler broadening of the corresponding resonances decreases with increasing buffer-gas pressure. The width of the resonances becomes significantly narrower than the spontaneous linewidth of the near-resonant intermediate state and is determined by spin-exchange collisions between ground-state atoms. The dependence of the intensity of these collision-induced resonances on buffer-gas pressure and detuning from one-photon resonances is measured. Selection rules for various polarizations of the incident light fields and directions of an externally applied magnetic field are established.

Physical Review A•Aug 1, 1984•90 citations

Light-shift-induced spatial structures: Application to degenerate four-wave mixing

M. Schiffer, E. Cruse, Wulfhard K. Lange

Degenerate four-wave mixing in dense sodium vapor under conditions of strong pressure-induced Zeeman pumping is investigated. Thermal diffusion and its interplay with the Zeeman light shift are found to be responsible for the generation of a grating mechanism that is not sensitive to thermal washout. The effect can be observed experimentally after eliminating the influence of radiation trapping by the use of nitrogen as a buffer gas. Under these conditions large nonlinearities are produced which also influence the propagation of the signal wave via collision-aided circular birefringence.

Physical Review A•May 1, 1994•7 citations

Theoretical study of atom collision by two-nondegenerate four-wave mixing

孙江 Sun Jiang, Xiaoyang Chang, Su-Heng Zhang +1 more

In recent years, the collisional redistribution of radiation and collision-induced broadening of Rydberg atomic spectral lines by buffer gas perturbation have aroused the renewed interest. Rydberg atoms having a large dipole moment and long lifetime can interact with each other coherently for relatively long time, which makes them a potential candidate for quantum information processing. Besides, collisional redistribution has an important potential application in laser cooling and trapping. Based on previous experimental data, in this paper, two-nondegenerate four-wave mixing (NFWM) for studying atom collision, composed of two-photon resonant NFWM and collisional redistribution NFWM, is reported. The spectrum variation of the two-NFWM affected by the pressure, temperature, detuning and collision-broadening rate coefficient is analyzed. The principle of two-NFWM involving three incident beams is explained as follows. Consider two-NFWM in a |0-|1-|2 cascade three-level system, where states between |0 and |1 and between |1 and |2 ightangle are coupled by resonant frequencies 1 and 2 , respectively. Beam 1 with frequency 1 propagates along the direction opposite to the direction of beam 2, beams 2 and 2' have the same frequency 2, and between their directions there exists a small angle. Assuming that 1 1 and 2 2 so that 1 drives the transition from |0 to |1 while 2 drives the transition from |1 to |2, the simultaneous interactions of atoms with beams 1 and 2 will induce atomic coherence between |0 and |2 through two-photon excitation. This coherence is probed by beam 2', and as a result a two-photon resonant NFWM signal of frequency 1 is generated in the direction almost opposite to the direction of beam 2'. To avoid strong absorption at the resonant frequency of transition from |0 to |1, here the wavelength of beam1 is detuned from the exact resonance. An atom population of level |1 caused by collisional redistribution can be induced when a certain buffer gas pressure is imposed. The collisional redistribution NFWM process also exists in this case. Beam 2 drives the transition from |1 to |2 to induce an atomic coherence which is probed by beam 2' for giving rise to an atomic population grating. A collisional redistribution NFWM signal propagating along the same direction as the two-photon resonant NFWM signal is generated when beam 1 is scattered by the grating. Much information about atomic collisions can be obtained by analyzing the two NFWM signals. In a cascade three-level system composed of ground state, intermediate state and Rydberg state, and the two-NFWM can be used to investigate not only the broadening and shifting of the Rydberg level but also the collisional redistribution of the intermediate state. Unlike other experiments studying the pressure dependence of the longitudinal relaxation rate of atom states, this technique is a purely optical coherent means, and can measure the transverse relaxation rate 20 between Rydberg state and ground state as well as the pressure dependence of the transverse relaxation rate 21 between Rydberg state and intermediate state.

Acta Physica Sinica•Jan 1, 2016•0 citations

Generation of frequency degenerate twin beams in Rb85 vapor

Jun Fang Jia, Wei Du, J. F. Chen +3 more

We demonstrate a new phase-matching geometry for four-wave mixing processes in hot Rb85 vapor, in which all four fields propagate in different directions but two of them are degenerate in frequency. When used as a parametric amplifier with an injected seed, two types of quantum mechanically correlated twin-beam states, either frequency degenerate or nondegenerate, can be generated. The quantum noise reduction in the intensity difference is almost 7 dB for the nondegenerate type and nearly 5 dB for the degenerate type. The spatial nondegeneracy of the four waves allows a variety of configurations of parametric processes, leading to flexible control for both phase insensitive and sensitive parametric amplification. The spatially nondegenerate but frequency degenerate four-wave mixing process will find wide applications in quantum metrology, quantum communication, and quantum information of continuous variables.

Optics Letters•Sep 28, 2017•12 citations

Effects of four-wave mixing on four-photon resonance excitation and ionization in the presence of a three-photon intermediate state resonance enhancement

M. G. Payne, J. C. Miller, Roger C. Hart +1 more

We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and \ensuremath{\Vert}\ensuremath{\Delta}${\mathit{k}}_{\mathit{r}}$L\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}${\mathit{k}}_{\mathit{r}}$ is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when \ensuremath{\Vert}\ensuremath{\Delta}${\mathit{k}}_{\mathit{r}}$b\ensuremath{\Vert}\ensuremath{\gg}1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.

Physical Review A•Dec 1, 1991•19 citations
Phase-matched four-wave mixing in sodium vapor with a helium buffer gas is carried out in a noncoplanar geometry. The directions of the four light beams remain nondegenerate even if all frequencies are equal. A sharp zerodifference frequency resonance in the intensity of the parametrically generated fourth beam by three incident beams is observed that is proportional to the square of the pressure of the buffer gas. A theoretical interpretation of this effect caused by elimination of destructive interference between two coherent pathways is presented.
Near-resonant four-wave light mixing in Na vapor with inert buffer gases reveals collision-induced coherences when the difference frequency between two incident light beams equals the hyperfine splitting or the Zeeman splitting between two states of the 32S3^{2}S32S ground-state manifold. The Doppler broadening of the corresponding resonances decreases with increasing buffer-gas pressure. The width of the resonances becomes significantly narrower than the spontaneous linewidth of the near-resonant intermediate state and is determined by spin-exchange collisions between ground-state atoms. The dependence of the intensity of these collision-induced resonances on buffer-gas pressure and detuning from one-photon resonances is measured. Selection rules for various polarizations of the incident light fields and directions of an externally applied magnetic field are established.
Degenerate four-wave mixing in dense sodium vapor under conditions of strong pressure-induced Zeeman pumping is investigated. Thermal diffusion and its interplay with the Zeeman light shift are found to be responsible for the generation of a grating mechanism that is not sensitive to thermal washout. The effect can be observed experimentally after eliminating the influence of radiation trapping by the use of nitrogen as a buffer gas. Under these conditions large nonlinearities are produced which also influence the propagation of the signal wave via collision-aided circular birefringence.
In recent years, the collisional redistribution of radiation and collision-induced broadening of Rydberg atomic spectral lines by buffer gas perturbation have aroused the renewed interest. Rydberg atoms having a large dipole moment and long lifetime can interact with each other coherently for relatively long time, which makes them a potential candidate for quantum information processing. Besides, collisional redistribution has an important potential application in laser cooling and trapping. Based on previous experimental data, in this paper, two-nondegenerate four-wave mixing (NFWM) for studying atom collision, composed of two-photon resonant NFWM and collisional redistribution NFWM, is reported. The spectrum variation of the two-NFWM affected by the pressure, temperature, detuning and collision-broadening rate coefficient is analyzed. The principle of two-NFWM involving three incident beams is explained as follows. Consider two-NFWM in a |0-|1-|2 cascade three-level system, where states between |0 and |1 and between |1 and |2 ightangle are coupled by resonant frequencies 1 and 2 , respectively. Beam 1 with frequency 1 propagates along the direction opposite to the direction of beam 2, beams 2 and 2' have the same frequency 2, and between their directions there exists a small angle. Assuming that 1 1 and 2 2 so that 1 drives the transition from |0 to |1 while 2 drives the transition from |1 to |2, the simultaneous interactions of atoms with beams 1 and 2 will induce atomic coherence between |0 and |2 through two-photon excitation. This coherence is probed by beam 2', and as a result a two-photon resonant NFWM signal of frequency 1 is generated in the direction almost opposite to the direction of beam 2'. To avoid strong absorption at the resonant frequency of transition from |0 to |1, here the wavelength of beam1 is detuned from the exact resonance. An atom population of level |1 caused by collisional redistribution can be induced when a certain buffer gas pressure is imposed. The collisional redistribution NFWM process also exists in this case. Beam 2 drives the transition from |1 to |2 to induce an atomic coherence which is probed by beam 2' for giving rise to an atomic population grating. A collisional redistribution NFWM signal propagating along the same direction as the two-photon resonant NFWM signal is generated when beam 1 is scattered by the grating. Much information about atomic collisions can be obtained by analyzing the two NFWM signals. In a cascade three-level system composed of ground state, intermediate state and Rydberg state, and the two-NFWM can be used to investigate not only the broadening and shifting of the Rydberg level but also the collisional redistribution of the intermediate state. Unlike other experiments studying the pressure dependence of the longitudinal relaxation rate of atom states, this technique is a purely optical coherent means, and can measure the transverse relaxation rate 20 between Rydberg state and ground state as well as the pressure dependence of the transverse relaxation rate 21 between Rydberg state and intermediate state.
We demonstrate a new phase-matching geometry for four-wave mixing processes in hot Rb85 vapor, in which all four fields propagate in different directions but two of them are degenerate in frequency. When used as a parametric amplifier with an injected seed, two types of quantum mechanically correlated twin-beam states, either frequency degenerate or nondegenerate, can be generated. The quantum noise reduction in the intensity difference is almost 7 dB for the nondegenerate type and nearly 5 dB for the degenerate type. The spatial nondegeneracy of the four waves allows a variety of configurations of parametric processes, leading to flexible control for both phase insensitive and sensitive parametric amplification. The spatially nondegenerate but frequency degenerate four-wave mixing process will find wide applications in quantum metrology, quantum communication, and quantum information of continuous variables.
We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​L\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​ is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​b\ensuremath{\Vert}\ensuremath{\gg}1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.