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

Constructive interference and efficient vacuum-ultraviolet generation in resonant six-wave mixing

Nandini Mukherjee

Published Apr 1, 1995• 2 citations
Publisher

Abstract

We consider four-photon resonant six-wave mixing and show that the efficiency of harmonic generation is limited due to destructive interference between different optical harmonics. Following the idea of ``induced transparency'' of Harris et al. [Phys. Rev. Lett. 64, 1107 (1990)], it is shown that in the presence of an auxiliary electromagnetic coupling between the four-photon excited level and a third level, the interference between various excitation channels can be made constructive. Depending upon the strength of the auxiliary wave, absorption and dispersion-free propagation of the generated wave lead to high conversion efficiency.

DOI
10.1103/physreva.51.3221

Related papers

Constructive interference in four-photon resonantly enhanced six-wave mixing

Nandini Mukherjee

Enhancement of third-harmonic generation near four-photon resonance showed1 new possibilities for direct upconversion of visible or infrared light into VUV light. However, the observed efficiencies of the four-photon resonant six-wave mixing were low. Our theoretical analysis2 showed that the efficiency is limited because of a destructive interference between the two-photon resonant Raman process E2E3 and the four- photon resonant excitation E 1 4 as shown in Fig. 1(a).

•May 8, 1994•0 citations

Effect of the coherent cancellation of the two-photon resonance on the generation of vacuum ultraviolet light by two-photon resonantly enhanced four-wave mixing

M. G. Payne, W. R. Garrett, J. P. Judish +1 more

Many of the most impressive demonstrations of the efficient generation of vacuum ultraviolet (VUV) light have made use of two‐photon resonantly enhanced four‐wave mixing to generate light at ωVUV =2ωL1±ωL2. The two‐photon resonance state is coupled to the ground state both by two photons from the first laser, or by a photon from the second laser and one from the generated VUV beam. We show here that these two coherent pathways destructively interfere once the second laser is made sufficiently intense, thereby leading to an important limiting effect on the achievable conversion efficiency.

AIP conference proceedings•Jan 1, 1989•0 citations

Highly efficient four-wave mixing in a coherent six-level system in ultraslow propagation regime

Hui‐jun Li, Guoxiang Huang

We propose a scheme to obtain a highly efficient four-wave mixing (FWM) in a coherent six-level tripod system by using a double-dark resonance and multiphoton destructive interference induced transparency. We show both analytically and numerically that the optical-wave mixing in such a system with a pump wave and an internally generated FWM wave mediated by electromagnetically induced transparency and hence propagating with matched ultraslow group velocities can result in a significant enhancement of FWM conversion efficiency. This interesting scheme may be used to generate coherent short-wavelength radiation in dense optical media with very low pump-wave intensity.

Physical Review A•Oct 10, 2007•39 citations

Consequences of induced transparency in a double-Λ scheme: Destructive interference in four-wave mixing

M. G. Payne, L. Deng

We investigate a four-state system interacting with long and short laser pulses in a weak probe beam approximation. We show that when all lasers are tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM) field is strongly absorbed. The part that is not absorbed has the exact intensity required to destructively interfere with the excitation pathway involved in producing the FWM state. We show that with this three-photon destructive interference, the conversion efficiency can still be as high as 25%. Contrary to common belief, our calculation shows that this process, where an ideal one-photon electromagnetically induced transparency is established, is not most suitable for high-efficiency conversion. With appropriate phase matching and propagation distance, and when the three-photon destructive interference does not occur, we show that the photon flux conversion efficiency is independent of probe intensity and can be close to 100%. In addition, we show clearly that the conversion efficiency is not determined by the maximum atomic coherence between two lower excited states, as commonly believed. It is the combination of phase matching and constructive interference involving the two terms arising in producing the mixing wave that is the key element for the optimized FWM generation. Indeed, in this scheme no appreciable excited state is produced, so that the atomic coherence between states |0〉 and |2〉 is always very small.

arXiv:quant-ph/0203076•Physical Review A•Jun 3, 2002•53 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

Strong quantum interferences in frequency up-conversion towards short vacuum-ultraviolet radiation pulses

Patric Ackermann, Alexander Scharf, Thomas Halfmann

We present experimental data on quantum interferences in resonantly enhanced frequency up-conversion towards the vacuum-ultraviolet spectral regime. The process is driven in xenon atoms by ultrashort (picosecond) laser pulses. We use two simultaneous frequency conversion pathways via an excited intermediate state, i.e., fifth harmonic generation of the fundamental wavelength and four-wave mixing of the fundamental and two photons of its second harmonic wavelength. Both conversion pathways yield radiation at 102 nm. The two pathways interfere, depending on the relative phase of the fundamental and second harmonic. By appropriate choice of the phase we get constructive interference (resulting in increased conversion efficiency) or destructive interference (resulting in reduced conversion efficiency). The total conversion yield shows very pronounced constructive and destructive quantum interference with a visibility of roughly 90%. A stable and highly accurate phase control setup enables such strong quantum interferences for more than 260 oscillation cycles. In an extension of the experiment, simultaneously to frequency conversion we also monitor laser-induced fluorescence as a measure for the excitation probability to the excited intermediate state. Also, in the excitation probability we observe strong quantum interferences. As an interesting feature, a small phase lag occurs between the quantum interference patterns of frequency conversion and population transfer. This is due to an additional atomic phase acquired during frequency conversion.

Physical Review A•Jun 10, 2014•9 citations
We consider four-photon resonant six-wave mixing and show that the efficiency of harmonic generation is limited due to destructive interference between different optical harmonics. Following the idea of ``induced transparency'' of Harris et al. [Phys. Rev. Lett. 64, 1107 (1990)], it is shown that in the presence of an auxiliary electromagnetic coupling between the four-photon excited level and a third level, the interference between various excitation channels can be made constructive. Depending upon the strength of the auxiliary wave, absorption and dispersion-free propagation of the generated wave lead to high conversion efficiency.
Many of the most impressive demonstrations of the efficient generation of vacuum ultraviolet (VUV) light have made use of two‐photon resonantly enhanced four‐wave mixing to generate light at ωVUV =2ωL1±ωL2. The two‐photon resonance state is coupled to the ground state both by two photons from the first laser, or by a photon from the second laser and one from the generated VUV beam. We show here that these two coherent pathways destructively interfere once the second laser is made sufficiently intense, thereby leading to an important limiting effect on the achievable conversion efficiency.
We propose a scheme to obtain a highly efficient four-wave mixing (FWM) in a coherent six-level tripod system by using a double-dark resonance and multiphoton destructive interference induced transparency. We show both analytically and numerically that the optical-wave mixing in such a system with a pump wave and an internally generated FWM wave mediated by electromagnetically induced transparency and hence propagating with matched ultraslow group velocities can result in a significant enhancement of FWM conversion efficiency. This interesting scheme may be used to generate coherent short-wavelength radiation in dense optical media with very low pump-wave intensity.
We investigate a four-state system interacting with long and short laser pulses in a weak probe beam approximation. We show that when all lasers are tuned to the exact unperturbed resonances, part of the four-wave mixing (FWM) field is strongly absorbed. The part that is not absorbed has the exact intensity required to destructively interfere with the excitation pathway involved in producing the FWM state. We show that with this three-photon destructive interference, the conversion efficiency can still be as high as 25%. Contrary to common belief, our calculation shows that this process, where an ideal one-photon electromagnetically induced transparency is established, is not most suitable for high-efficiency conversion. With appropriate phase matching and propagation distance, and when the three-photon destructive interference does not occur, we show that the photon flux conversion efficiency is independent of probe intensity and can be close to 100%. In addition, we show clearly that the conversion efficiency is not determined by the maximum atomic coherence between two lower excited states, as commonly believed. It is the combination of phase matching and constructive interference involving the two terms arising in producing the mixing wave that is the key element for the optimized FWM generation. Indeed, in this scheme no appreciable excited state is produced, so that the atomic coherence between states |0〉 and |2〉 is always very small.
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.
We present experimental data on quantum interferences in resonantly enhanced frequency up-conversion towards the vacuum-ultraviolet spectral regime. The process is driven in xenon atoms by ultrashort (picosecond) laser pulses. We use two simultaneous frequency conversion pathways via an excited intermediate state, i.e., fifth harmonic generation of the fundamental wavelength and four-wave mixing of the fundamental and two photons of its second harmonic wavelength. Both conversion pathways yield radiation at 102 nm. The two pathways interfere, depending on the relative phase of the fundamental and second harmonic. By appropriate choice of the phase we get constructive interference (resulting in increased conversion efficiency) or destructive interference (resulting in reduced conversion efficiency). The total conversion yield shows very pronounced constructive and destructive quantum interference with a visibility of roughly 90%. A stable and highly accurate phase control setup enables such strong quantum interferences for more than 260 oscillation cycles. In an extension of the experiment, simultaneously to frequency conversion we also monitor laser-induced fluorescence as a measure for the excitation probability to the excited intermediate state. Also, in the excitation probability we observe strong quantum interferences. As an interesting feature, a small phase lag occurs between the quantum interference patterns of frequency conversion and population transfer. This is due to an additional atomic phase acquired during frequency conversion.