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Journal of the Optical Society of America B

Dynamics of triple quantum beats retrieved from coupled four-wave mixing signals

Changjun Zhu, Bei Xu, Qing Chu, Junfang He, Xiang-an Yan

Published Feb 25, 2016• 0 citations
Publisher

Abstract

A theoretical model of coupled four-wave mixing (FWM) processes comprising five atomic energy levels was proposed to investigate the coherent characteristics of atomic wave packets using perturbation theory. As several states in atoms are coherently excited by a two-photon transition, triple coupled FWM can be produced, and triple quantum beats associated with the atomic energy levels are embedded in the FWM signals. Triple coupled FWM processes were achieved experimentally in Rb vapor by two-photon excitation using broadband optical pulses. A pump–probe scheme was utilized to record the time-varying FWM signals, and Fourier transform was applied to retrieve the quantum beats. Furthermore, short-time Fourier transform was implemented to investigate the dynamics of quantum beats. The results show that the coherent characteristics of atomic wave packets, which are intimately related to the dynamics of quantum beats, can be probed by coupled nonlinear optical wave mixing.

DOI
10.1364/josab.33.000485

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A theoretical model of coupled four-wave mixing (FWM) processes comprising five atomic energy levels was proposed to investigate the coherent characteristics of atomic wave packets using perturbation theory. As several states in atoms are coherently excited by a two-photon transition, triple coupled FWM can be produced, and triple quantum beats associated with the atomic energy levels are embedded in the FWM signals. Triple coupled FWM processes were achieved experimentally in Rb vapor by two-photon excitation using broadband optical pulses. A pump–probe scheme was utilized to record the time-varying FWM signals, and Fourier transform was applied to retrieve the quantum beats. Furthermore, short-time Fourier transform was implemented to investigate the dynamics of quantum beats. The results show that the coherent characteristics of atomic wave packets, which are intimately related to the dynamics of quantum beats, can be probed by coupled nonlinear optical wave mixing.
A theoretical model consisting of 5 energy levels, with the three upper states coherently excited, was proposed to analyze the coherent characteristics of atomic wave packets using perturbative theory. Pump-probe technique was implemented to detect coupled difference frequency four-wave mixing processes for studying the coherent characteristics of Rb atomic wave packets. Quantum beats were extracted the time domain signal by Fourier transform. Moreover, the variation of quantum beats was gained by time-dependent Fourier transform. The results show that the coherent characteristics of alkali metal atomic wave packets are closely related to quantum beats embedded in the time delayed four-wave mixing signal. Theoretical results are consistent with experimental observations, possessing potential applications in multi-channel information encoding and decoding.
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.
A theoretical model consisting of 5 energy levels in coupled four-wave mixing processes was proposed to analyze the coherent characteristics of atomic wavepackets using perturbative theory. The equations of motions of the density matrix were derived and the third-order density matrix elements were presented. Under the condition that the duration of laser pulses is sufficiently short, the system response was treated as impulse response. Moreover, in the lowest order perturbation theory, the third-order nonlinear polarization was obtained using rotating-wave approximation. The results show that multiple quantum beats are embedded in the coupled four-wave mixing signals, and coherent dynamics of wavepackets can be retrieved from the quantum beat dynamics.
Wavepackets are excited in rubidium vapor by intense ultrashort (∼100 fs) pulses centered at a wavelength of 620 nm or 770 nm. The generated atomic wavepackets are optically detected via a pump-probe experiment based on axially phase-matched parametric four-wave mixing (FWM). This nonlinear process results in coherent ultraviolet (UV) or violet emission that carries information about the relative number densities of the excited states. The frequency spectrum of the UV/violet signal intensity, recorded while varying the pump-probe time delay, shows the presence of quantum beats between energy levels involved in the FWM process. The time-frequency analysis of that temporal UV/violet data is done by means of the short-time Fourier transform that leads to retrieval of the temporal evolution of amplitude and phase of the quantum beats. The observed dynamics suggest that not only atomic but also molecular ( Rb*2 ) wavepackets are generated, and that the temporal history of the amplitude of the quantum beats reflects the production of the excited atomic fragments of Rb*2 dissociation. More precisely, changes in the Rb excited state number densities alter the third-order nonlinear susceptibility chi(3) of the Rb vapor, which affects generation of the output signal wave by FWM. Dissociation into several product states is detected, and their branching ratios are estimated. Thus, atomic wavepackets, combined with FWM, appear to be a sensitive new multichannel spectroscopic means to study the fundamental process of molecular dissociation.
Two coupled parametric four-wave-mixing processes in Rb atoms are studied using perturbation theory, which reveals clear evidence of the appearance of quantum beat at 608 cm −1 , corresponding to the energy difference of the 7 s −5 d states of Rb atoms, in the parametric four-wave-mixing signals. A pump–probe technique is utilized to observe the quantum beat. Time-varying characteristics of the quantum beat are investigated using time-dependent Fourier transform. The results show that the time-varying characteristics of the quantum beat not only offers a sensitive detecting method for observing the decay of atomic wave packets, but also provides a potential tool for monitoring the dissociation of molecules.
The observation of an atomic wave packet by use of a coherent, nonlinear-optical process is reported. Wave packets formed in K or Rb vapor by two-photon excitation of ns and (n-2)dstates (n=8 for K; n=11 , 12 for Rb) with red (~620-nm) , 80-100-fs pulses were detected by four-wave mixing in pump-probe experiments. The temporal behavior of the wave packet is observed by monitoring the coherent UV radiation generated near the alkali mp(2)P? (2)S(1/2) (7</=m</=12 for Rb; 5</=m</=7 for K) resonance transitions when a probe pulse is scattered by the wave packet established by the earlier (identical) pump pulse. The spatial and spectral characteristics of the UV emission are well described by axially phase-matched four-wave mixing, and all the prominent frequency components of the wave packets are associated with energy differences between pairs of excited states for which Diota=0 or Diota=2 . These results demonstrate that the wave packet modulates chi((3))of the medium, thus rendering the wave packet detectable.