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Optics Letters

Atomic wave-packet dynamics and third-harmonic generation in sodium

Hrvoje Skenderović, Silvije Vdović

Published Sep 20, 2013• 4 citations
Publisher

Abstract

In femtosecond degenerate four-wave mixing experiments in sodium vapor, quantum beats are observed at the wavelength of the third harmonic when the fundamental beams are three-photon resonant. The period of beating, which corresponds to fine structure energy-level splitting, does not change with the atomic number density, buffer gas pressure, or laser intensity. Surprisingly, the third-harmonic signal is observed only at negative time delays for the transient grating pulse sequence. We relate this to the well-known interference effect between excitation pathways involving the fundamental and the third-harmonic fields, which leaves atoms virtually unexcited and prevents formation of population grating.

DOI
10.1364/ol.38.003811

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In femtosecond degenerate four-wave mixing experiments in sodium vapor, quantum beats are observed at the wavelength of the third harmonic when the fundamental beams are three-photon resonant. The period of beating, which corresponds to fine structure energy-level splitting, does not change with the atomic number density, buffer gas pressure, or laser intensity. Surprisingly, the third-harmonic signal is observed only at negative time delays for the transient grating pulse sequence. We relate this to the well-known interference effect between excitation pathways involving the fundamental and the third-harmonic fields, which leaves atoms virtually unexcited and prevents formation of population grating.
We have observed a new component in the signals produced by degenerate four-wave mixing of 5-nsec optical pulses by the DDD-line resonances of sodium vapor. This component is comparable in intensity to that previously observed from a grating pattern of excited sodium atoms, but arises rather from a grating of coherently aligned (but not optically pumped) ground-state atoms. This component exists when there are no spatial intensity beats between input waves.
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.
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.
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.
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.