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International Conference on Ultrafast Phenomena

Ultrafast Two-Photon Free Induction Decay

Dorine Keusters, Peifang Tian, Warren S. Warren

Published Jan 1, 2002• 1 citation
Publisher

Abstract

Direct optical analogs of (two-dimensional) NMR experiments require detection of the phase of a coherence induced by a (series of) laser pulses, which is difficult [1]. Recently it was demonstrated that by using a phase coherent pulse pair created by an acousto optic pulse shaper (AOPS), this phase information can be detected conveniently and fast. [2, 3] This technique was demonstrated on the one-photon transitions in Rubidium [3]. The same technique can be used to detect a coherence that is induced by two photons simultaneously [4], as we demonstrate experimentally by detecting the two-photon free induction decay (TPFID) of Rb and coumarin. Since the two-photon transition in Rb is resonance enhanced, several types of coherences are induced in the two-photon process. An AOPS allows a separation of these types of coherences, and has potential advantages for suppressing scattered light.

DOI
10.1364/up.2002.fb5

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Direct optical analogs of (two-dimensional) NMR experiments require detection of the phase of a coherence induced by a (series of) laser pulses, which is difficult [1]. Recently it was demonstrated that by using a phase coherent pulse pair created by an acousto optic pulse shaper (AOPS), this phase information can be detected conveniently and fast. [2, 3] This technique was demonstrated on the one-photon transitions in Rubidium [3]. The same technique can be used to detect a coherence that is induced by two photons simultaneously [4], as we demonstrate experimentally by detecting the two-photon free induction decay (TPFID) of Rb and coumarin. Since the two-photon transition in Rb is resonance enhanced, several types of coherences are induced in the two-photon process. An AOPS allows a separation of these types of coherences, and has potential advantages for suppressing scattered light.
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We demonstrate a method for femtosecond, phase sensitive detection of optical polarization, using an acousto-optic pulse shaper to create a sequence of up to several hundred phase coherent pulses. Essential to this method is the ability of the acousto-optic pulse shaper to update the phase relation of the pulses in the sequence on a nanosecond timescale. The method is demonstrated by measuring the optical free induction decay’ of rubidium vapor, and can be particularly useful for experiments involving very low or very high optical densities. It can easily be extended to multidimensional spectroscopy.
A simple application of the Stark-pulse technique, developed by Brewer and Shoemaker, demonstrates optical free induction decay-the optical analog of free induction decay in NMR. A molecular sample which is coherently prepared by a cw laser beam exhibits such a decay when it is suddenly switched out of resonance by a Stark field. Observations are presented for a nondegenerate Doppler-broadened infrared transition of NH2{\mathrm{H}}_{2}H2​D, where the sample is optically thin, and the decay behavior can be compared quantitatively with a solution of the Bloch equations. When the molecular sample is prepared under steady-state conditions, the solutions are analytic; for pulse excitation, a numerical solution is required. The treatment invokes a hard-collision relaxation model. Such characteristics as the abrupt termination of the decay and the related edge echo, which result from Doppler dephasing, can be examined for Stark pulses of finite extent.
Large-amplitude oscillations are predicted in the free-induction decay (FID) of atomic or spin two-level quantum systems that are coherently prepared by a resonant electromagnetic field in the form of a square amplitude pulse of duration TTT. The effect should be detectable in nuclear magnetic resonance (NMR) or in optical resonance experiments when the transition line shape is inhomogeneously broadened (${T}_{2}^{*}\ensuremath{\ll}{T}_{2}$) and the applied field is intense enough that the pulse area $\ensuremath{\chi}T\ensuremath{\ge}2\ensuremath{\pi}$, where $\ensuremath{\chi}$ is the Rabi frequency. Physically, the effect is due to Rabi oscillations which are generated in the preparative stage and are then reproduced because of atomic memory in the radiative period which follows. The atomic polarization derived from the Bloch equations assumes the form of an integral over the inhomogeneous line shape, and can be evaluated numerically for arbitrary linewidth $\ensuremath{\sigma}$ or analytically when $\ensuremath{\sigma}\ensuremath{\rightarrow}\ensuremath{\infty}$. The characteristics of the oscillation are unusual since the oscillation frequency, which is of order $\ensuremath{\chi}$, increases with time while the oscillation envelope vanishes identically for times $t\ensuremath{\ge}2T$. Coherent emission is therefore confined to one pulse width TTT immediately following the pulse. Previous NMR and infrared FID experiments with small-area pulses ($\ensuremath{\chi}T\ensuremath{\le}4\ensuremath{\pi}$), interpreted erroneously in terms of an edge echo effect, support the oscillatory FID behavior described here. For the case $\ensuremath{\chi}T>4\ensuremath{\pi}$, an experimental test would be even more decisive, as the oscillations are more pronounced.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy.In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels.It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid.Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180" pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes.The role of pulse phase is extensively analyzed.Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters.The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem.Phys.Lett.48, 256 (1977); Orlowski et al., ibid.54, 197 (1978)).The relative merits offluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences.Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions.In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy. In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels. It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid. Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180° pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes. The role of pulse phase is extensively analyzed. Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters. The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem. Phys. Lett. 48, 256 (1977); Orlowski et al., ibid. 54, 197 (1978)]. The relative merits of fluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences. Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions. In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.