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Optics Letters

Ultrahigh-frequency interference beats in transient, incoherent-light four-wave mixing

J. E. Golub, THOMAS W. MOSSBERG

Published Jul 1, 1986• 26 citations
Publisher

Abstract

An angled-beam, transient four-wave mixing experiment is described in which nanosecond-duration, broad-bandwidth excitation pulses are employed to measure picosecond collisional dephasing and subpicosecond interference beats in atomic Rb vapor. The 7.2-THz interference beat, which corresponds to a 237 cm(-1) Rb fine-structure splitting, is apparently the fastest material-specific beat yet observed. We discuss practical limitations on the time resolution attainable with this technique and propose means of circumventing them by using broad-bandwidth collinear excitation beams and an angled narrow-bandwidth probe.

DOI
10.1364/ol.11.000431

Related papers

Studies of picosecond collisional dephasing in atomic sodium vapor using broad-bandwidth transient four-wave mixing

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We have employed dye-laser pulses of 10-nsec duration and 1.5–10-nm bandwidth in a transient four-wave-mixing experiment to study high-perturber-pressure collisional dephasing in dilute atomic sodium vapor. Working at argon perturber pressures of several atmospheres, we are able clearly to resolve dephasing times over a thousand times shorter than our excitation pulse duration. Measured dephasing rates are in excellent agreement with those measured by more traditional methods. When both of the sodium D lines are excited, our signal displays quantum-beat-like oscillations at the 0.52-THz frequency difference between these two states. We provide a simple picture explaining the origin of these beats.

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High resolution quantum beat spectroscopy has been realized to study atomic wave packet dynamics. Wave packets comprising pairs of low quantum number (n = 5 - 8) electronic states were formed in Rb vapor with ultrafast laser pulses, and their dynamics was observed by an all-optical technique of parametric four wave mixing (PFWM). The experimental apparatus designed, constructed and automated for this work provided unprecedented signal intensity that enabled time-frequency-resolved analysis of wave packet dynamics with picosecond temporal resolution over the course of 1100 ps. Both time-resolved and non-time-resolved discrete Fourier methods were applied to measure the concurrent formation of multiple wave packets. Many novel effects and interactions have been measured either for the first time or with greatly improved signal-to-noise ratio. Among them were the formation of the 8S1/2 - 6D5/2 wave packet that was not directly excited by the ultrafast radiation, formation and relative dynamics of quantum beating harmonics up to 73 THz, and quantum beating revivals. The effects of vapor number density and temperature were analyzed experimentally. Interference between the 7S1/2 - 5D5/2 and 8S1/2 - 6D5/2 wave packets (frequencies of 18.225 THz and 10.73 THz, respectively) has been observed for the first time and will be described in detail.

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INTERFERENCE BETWEEN THE 5d5/2 – 5p3/2 AND 5p3/2 – 5s1/2 COHERENCES (386.4 AND 384.1 THz) IN Rb OBSERVED BY ULTRAFAST FOUR-WAVE MIXING SPECTROSCOPY

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\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.32]{Fig1.eps} \end{wrapfigure} Coherences at 386.2 THz and 384.1 THz, corresponding to the 5d$_{5/2}$ – 5p$_{3/2}$ and 5p$_{3/2}$ – 5s$_{1/2}$ difference frequencies, respectively, have been established in the Rb atom during pump-probe experiments involving pairs of identical ~150 fs pulses produced by a Ti:\chem{Al_2O_3} laser and a Michelson interferometer. The interference between the two coherences within the atom is observed through a parametric four-wave mixing process in Rb and detection of the signal wave intensity at 420 nm. Scanning the time delay between the pump and probe pulses over a 600 ps interval produces a sampling rate over 300 THz and allows for a spectral domain resolution of 0.05 cm$^{-1}$ to be achieved. The figure at right shows several spectra recorded near 2.1 THz, the (5d$_{5/2}$ – 5p$_{3/2}$) - (5p$_{3/2}$ – 5s$_{1/2}$) difference frequency, with varying angle between the pump and probe pulses (i.e., the phase matching angle) and varying Rb background density. A Fano interference window is clearly observed, and analysis of these and similar spectra demonstrates that the amplitude and phase of the coherently-coupled, three Rb state system can be controlled precisely.

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Time-delayed four-wave mixing using incoherent light for observation of ultrafast population relaxation

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Time-delayed four-wave mixing using incoherent light has been proposed as a new method to measure the ultrafast population relaxation time T1. Assuming three input beams of incoherent light with much longer duration than T1, the theoretical calculation has shown that the decay curve by T1 appears in the signal profile and that the time resolution is determined by the correlation time of the light. The decay time to be observed is twice that of the transient four-wave mixing with short pulses. We have experimentally confirmed the prediction by observing picosecond population relaxations of organic dye solutions, using nanosecond pulses from a normal broadband dye laser. An advantage of the present method over the pump-probe method using incoherent light is also discussed.

Journal of the Optical Society of America B•Aug 1, 1987•37 citations
An angled-beam, transient four-wave mixing experiment is described in which nanosecond-duration, broad-bandwidth excitation pulses are employed to measure picosecond collisional dephasing and subpicosecond interference beats in atomic Rb vapor. The 7.2-THz interference beat, which corresponds to a 237 cm(-1) Rb fine-structure splitting, is apparently the fastest material-specific beat yet observed. We discuss practical limitations on the time resolution attainable with this technique and propose means of circumventing them by using broad-bandwidth collinear excitation beams and an angled narrow-bandwidth probe.
We have employed dye-laser pulses of 10-nsec duration and 1.5–10-nm bandwidth in a transient four-wave-mixing experiment to study high-perturber-pressure collisional dephasing in dilute atomic sodium vapor. Working at argon perturber pressures of several atmospheres, we are able clearly to resolve dephasing times over a thousand times shorter than our excitation pulse duration. Measured dephasing rates are in excellent agreement with those measured by more traditional methods. When both of the sodium D lines are excited, our signal displays quantum-beat-like oscillations at the 0.52-THz frequency difference between these two states. We provide a simple picture explaining the origin of these beats.
High resolution quantum beat spectroscopy has been realized to study atomic wave packet dynamics. Wave packets comprising pairs of low quantum number (n = 5 - 8) electronic states were formed in Rb vapor with ultrafast laser pulses, and their dynamics was observed by an all-optical technique of parametric four wave mixing (PFWM). The experimental apparatus designed, constructed and automated for this work provided unprecedented signal intensity that enabled time-frequency-resolved analysis of wave packet dynamics with picosecond temporal resolution over the course of 1100 ps. Both time-resolved and non-time-resolved discrete Fourier methods were applied to measure the concurrent formation of multiple wave packets. Many novel effects and interactions have been measured either for the first time or with greatly improved signal-to-noise ratio. Among them were the formation of the 8S1/2 - 6D5/2 wave packet that was not directly excited by the ultrafast radiation, formation and relative dynamics of quantum beating harmonics up to 73 THz, and quantum beating revivals. The effects of vapor number density and temperature were analyzed experimentally. Interference between the 7S1/2 - 5D5/2 and 8S1/2 - 6D5/2 wave packets (frequencies of 18.225 THz and 10.73 THz, respectively) has been observed for the first time and will be described in detail.
\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.32]{Fig1.eps} \end{wrapfigure} Coherences at 386.2 THz and 384.1 THz, corresponding to the 5d5/2_{5/2}5/2​ – 5p3/2_{3/2}3/2​ and 5p3/2_{3/2}3/2​ – 5s1/2_{1/2}1/2​ difference frequencies, respectively, have been established in the Rb atom during pump-probe experiments involving pairs of identical ~150 fs pulses produced by a Ti:\chem{Al_2O_3} laser and a Michelson interferometer. The interference between the two coherences within the atom is observed through a parametric four-wave mixing process in Rb and detection of the signal wave intensity at 420 nm. Scanning the time delay between the pump and probe pulses over a 600 ps interval produces a sampling rate over 300 THz and allows for a spectral domain resolution of 0.05 cm−1^{-1}−1 to be achieved. The figure at right shows several spectra recorded near 2.1 THz, the (5d5/2_{5/2}5/2​ – 5p3/2_{3/2}3/2​) - (5p3/2_{3/2}3/2​ – 5s1/2_{1/2}1/2​) difference frequency, with varying angle between the pump and probe pulses (i.e., the phase matching angle) and varying Rb background density. A Fano interference window is clearly observed, and analysis of these and similar spectra demonstrates that the amplitude and phase of the coherently-coupled, three Rb state system can be controlled precisely.
Two coupled axially phase matched parametric four-wave mixings have been achieved in Rb vapor by using broad bandwidth laser pulses. Coherent radiations at 420 nm produced by difference-frequency optical wave mixing processes were detected and a pump-probe scheme was employed to record time varying characteristics of the parametric four-wave mixing signals. Quantum beatings at 608 cm-1 and 70 cm-1 were retrieved from the time varying signals by Fourier transform. Moreover, time dependent Fourier transform was utilized to analyze the dynamics of quantum beatings. The results indicate that two wave packets associated with the two quantum beating frequency components interact strongly and the quantum beating dynamics can be controlled by adjusting Rb number density.
Time-delayed four-wave mixing using incoherent light has been proposed as a new method to measure the ultrafast population relaxation time T1. Assuming three input beams of incoherent light with much longer duration than T1, the theoretical calculation has shown that the decay curve by T1 appears in the signal profile and that the time resolution is determined by the correlation time of the light. The decay time to be observed is twice that of the transient four-wave mixing with short pulses. We have experimentally confirmed the prediction by observing picosecond population relaxations of organic dye solutions, using nanosecond pulses from a normal broadband dye laser. An advantage of the present method over the pump-probe method using incoherent light is also discussed.