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arXiv:1810.13120 · Journal of Physics B Atomic Molecular and Optical Physics

Geometry-dependent spectra and coherent-transient measurement of nearly degenerate four-wave mixing using two-photon resonance

Hideaki Hara, Yuki Miyamoto, Takahiro Hiraki, Kei Imamura, Takahiko Masuda, N. Sasao, Satoshi Uetake, A. Yoshimi, K. Yoshimura, M. Yoshimura

Published Oct 2, 2019• 0 citations
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Abstract

Abstract We study nearly degenerate four-wave mixing using a two-photon-allowed vibrational transition of parahydrogen. A signal photon is generated by a trigger photon and coherence among parahydrogen, which is prepared by two counterpropagating pump pulses, and we investigate the dependence of the signal pulse energy on the trigger frequency. The measured spectra depend on the geometry, shifting depending on the direction of the signal pulse and on the small angle formed by the counterpropagating pump pulses. Furthermore, we investigate the dependence of signal pulse energy on the incident time of the trigger pulse. The measured signal pulse energy is high if the trigger pulse is delayed slightly with respect to the pump pulses. We demonstrate that these geometry-dependent spectra and coherent-transient response can be explained by using simple models.

DOI
10.1088/1361-6455/ab4a6e

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Abstract We study nearly degenerate four-wave mixing using a two-photon-allowed vibrational transition of parahydrogen. A signal photon is generated by a trigger photon and coherence among parahydrogen, which is prepared by two counterpropagating pump pulses, and we investigate the dependence of the signal pulse energy on the trigger frequency. The measured spectra depend on the geometry, shifting depending on the direction of the signal pulse and on the small angle formed by the counterpropagating pump pulses. Furthermore, we investigate the dependence of signal pulse energy on the incident time of the trigger pulse. The measured signal pulse energy is high if the trigger pulse is delayed slightly with respect to the pump pulses. We demonstrate that these geometry-dependent spectra and coherent-transient response can be explained by using simple models.
A two-pulse degenerate four-wave mixing experiment is analyzed in the case where the medium under investigation can be modeled by two-level systems having unequal permanent dipole moments. By modeling the light pulses by double exponentials [exp(-Gamma/t/)], we give an analytical expression of the third-order nonlinear polarization of the medium. We apply this result to simulate the measured signal in such experiment. We show that in the case of a two-photon transition, a signal can be detected if the pump pulse interacts with the medium before the probe pulse contrary to what is observed for excitations in the resonance region. An attempt to explain this behavior is made and the detected signal is analyzed in terms of pure coherent processes. This effect appears as a signature of the presence of permanent dipole moments. To test this property on a more realistic system, we then have considered a one-dimensional frequency-selected infrared degenerate four-wave mixing experiment on a molecular anharmonic vibrational mode modeled by a Morse potential and coupled to a dissipative bath of harmonic oscillators. We show that the two-photon transitions allowed by the presence of permanent dipole moments enable to analyze the multilevel system dynamics as if they were the one of a two-level system. Our results can also be extended to the case of inhomogeneous broadening and are of interest to study the infrared photon-echo response of anharmonic vibrational modes.
We show theoretically that a quantum system in a nonequilibrium state interacting with a set of laser pulses in a four-wave-mixing setup leads to signal emission in directions opposite to the ones usually considered. When combined with a pump mechanism which sets a time origin for the nonequilibrium state creation, this particular optical response can be utilized to directly follow decoherence processes in real time. By varying the time delays within the probe sequence, signals in these unconventional directions can also be used to detect two-dimensional spectra determined by the dynamics of up to three-quantum coherences, revealing energetical anharmonicities and environmental influences. As a numerical example, these findings are demonstrated by considering a model of vibrational decoherence of carbon monoxide after photolysis from a hemeprotein.
A set of coupled equations is derived and used to analyze transient coherent degenerate four-wave mixing (DFWM) in a two-level system. The numerical results show that in the case of near-resonance, intense pumping, and short pulses, the properties of degenerate four-wave mixing have interesting coherent interaction characteristics, such as quasi-periodicity in the pump pulse area, probe pulse areas, and energy reflectivity, oscillatory behavior of the DFWM pulse, and generation of a DFWM signal in the case of delayed incidence, where the three incident pulses do not overlap in the medium.>
We report the observation of two-photon emission from a coherently excited vibrational state of solid parahydrogen, which is also a known quantum solid. Coherence between the ground and the excited states is prepared by stimulated Raman scattering using two visible laser pulses. The two-photon emission is triggered by another mid-infrared laser pulse. It was observed that the two-photon emission persists even when the trigger pulse is injected long after the excitation. This is due to the long decoherence time of the vibrational states of solid parahydrogen. It is found that the emission intensity increases even after the excitation pulses pass through the target completely. This coherence development is highly suppressed at high target temperatures and high residual orthohydrogen concentrations. Effects of target annealing and laser-induced damage on the target are also observed.
Measurements of the relaxation times T1 and T2 of a two-level system by nonlinear transient spectroscopic methods are discussed, where delayed incident pulses are assumed to have correlation times much shorter than T1 or T2 but varied widths. In particular, a delayed degenerate four-wave mixing (photon echoe) and apump-and-probe type transmission measurement with incoherent long pulses are considered in detail, and a principle of their use for ultrafast spectroscopy is clarified. If the field is steady and T1>>T2, the time resolutionof T2measurement by the delayed four-wave mixlng is determined by the field correlation, therefore by the spectral width of the incident light irrespective of the pulse width. The time resoution of the T1 measurement by the pump-and-probe method is determined by the intensity correlation of the incident light, whereasthe one by the delayed four-wave mixing by a higher order correlation.
We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the 3s2S1∕23s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}3s2S1∕2​, F=2F=2F=2, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, F=3F=3F=3, mF=3{m}_{F}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.