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Journal of Physics B Atomic and Molecular Physics

'Rotary' photon echoes

François Rohart, P. Glorieux, B. Macke

Published Dec 21, 1977• 18 citations
Publisher

Abstract

By setting on resonance a polar gas at low pressure with an inhomogeneously saturating coherent wave, an oscillating transient nutation is observed, the fast damping of which may be principally related to the electromagnetic field inhomogeneity. The authors report the first experimental evidence of 'rotary' photon echoes allowing a partial restoration of the macroscopic polarisation. These 'rotary' echoes are the electric analogues of Solomon's 'rotary spin echoes' in NMR (1959) and must be carefully distinguished from the usual photon echoes related to the free induction decay (FID). The experiments have been performed in the microwave domain and show a dramatic reduction of the expected echo amplitude due to the molecular motion. Eventual applications, alternative methods of detection and the extension to the optical domain of these 'rotary' echoes are discussed.

DOI
10.1088/0022-3700/10/18/035

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The first observation of optical rotary echoes, the optical analog of rotary spin echoes, is reported. Rotary echoes are produced in a quantum-mechanical two-level system which is driven resonantly (nutation effect) by a coherent field that suffers a sudden phase retardation. The initial nutation transient dephases, because of an inhomogeneity in either the driving field or the transition frequency of the sample, and then rephases to form an echo following the phase-shifting pulse. Hence, optical rotary and photon echoes are similar processes---the former being an interference in nutation and the latter an interference in free precession. Perturbative solutions of the Bloch equations are derived for the case where inhomogeneous dephasing arises from Doppler broadening and the Rabi frequency exceeds the homogeneous damping rate. Observations of the optical rotary echo in ${\mathrm{I}}_{2}$ vapor are facilitated by the technique of laser frequency switching, which generates precise phase shifts in the optical field. The measurements corroborate detailed theoretical predictions.

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A theoretical investigation is made of the coherent optical transient phenomena produced by the phase switching method in degenerate gaseous systems in the case of arbitrary detuning. The effect of the light wave polarisation on optical nutation and free induction is studied. Echo manifestations in the form of edge echoes, nutation echoes and induction echoes that accompany light wave phase switching are established to differ from the previously studied ones. Spectroscopic applications of the results obtained are discussed.

Journal of Physics B Atomic and Molecular Physics•Nov 28, 1982•5 citations
By setting on resonance a polar gas at low pressure with an inhomogeneously saturating coherent wave, an oscillating transient nutation is observed, the fast damping of which may be principally related to the electromagnetic field inhomogeneity. The authors report the first experimental evidence of 'rotary' photon echoes allowing a partial restoration of the macroscopic polarisation. These 'rotary' echoes are the electric analogues of Solomon's 'rotary spin echoes' in NMR (1959) and must be carefully distinguished from the usual photon echoes related to the free induction decay (FID). The experiments have been performed in the microwave domain and show a dramatic reduction of the expected echo amplitude due to the molecular motion. Eventual applications, alternative methods of detection and the extension to the optical domain of these 'rotary' echoes are discussed.
The first observation of optical rotary echoes, the optical analog of rotary spin echoes, is reported. Rotary echoes are produced in a quantum-mechanical two-level system which is driven resonantly (nutation effect) by a coherent field that suffers a sudden phase retardation. The initial nutation transient dephases, because of an inhomogeneity in either the driving field or the transition frequency of the sample, and then rephases to form an echo following the phase-shifting pulse. Hence, optical rotary and photon echoes are similar processes---the former being an interference in nutation and the latter an interference in free precession. Perturbative solutions of the Bloch equations are derived for the case where inhomogeneous dephasing arises from Doppler broadening and the Rabi frequency exceeds the homogeneous damping rate. Observations of the optical rotary echo in I2{\mathrm{I}}_{2}I2​ vapor are facilitated by the technique of laser frequency switching, which generates precise phase shifts in the optical field. The measurements corroborate detailed theoretical predictions.
We present a theory of optical two-photon rotary echo for the case when the direct couplings between the three levels due to spontaneous decay to and from the intermediate state dominate the indirect couplings (collisional, etc.) to the passive levels and the phase-interrupting (P.I.) collisions cannot be ignored. For this situation which generally obtains in the visible/U.V. region which is relevant for many two-photon transient experiments, the ‘two-photon Bloch equations’ with non-resonant intermediate state are non-trivially different from the familiar (two-level) Bloch equations with or without direct coupling. An explicit analytical calculation demonstrates two-photon rotary echo with the usual dependence on the total phase shift. The dependence of the echo peak on pulse delay time is governed by a damping constant in which ‘intensity modification’ involves only the P.I. collision constant and not the spontaneous decay constant in sharp contrast to the one-photon case. For the case of counter-propagating beams, the intensity modified echo damping constant turns out to be especially simple. We suggest that the features unique to the two-photon rotary echo can be usefully exploited for the empirical determination of the polarization decay constant.
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.
Each of three basic coherent transient phenomena (optical nutation, free polarization decay photon echo) can be generated by sufficiently abrupt modulation of the interaction between the matter and radiation. This can be performed by rapid commutation of either radiation parameters, or the parameters of the matter. I present here comparative analysis of these two approaches (the first one, using electro-optical switching of the resonant laser power to create the pulses for the gas excitation and the second one, based on the Stark switching of vibro-rotational levels in a gas, excited by CW laser radiation), used in our experiments in molecular gases, from the point of view of both their capability to generate various coherent transients and their sensitivity to the intensity of laser radiation.
Free polarization decay and photon echo were studied experimentally in polar gas 13CH3F at the transition R(4,3) of vibrational mode 0 yields 1 (nu) 3 by Stark switching of molecular levels under irradiation by CW CO2 laser at 9P(32) line. Application of 4.5 mcs pulse to the Stark electrodes inside the gas cell allows to detect the free polarization decay signal, combined with the optical nutation. The sign of the signal corresponds to the increase of absorption in the limit of low intensity (not over 0.01 W/cm2) saturating radiation. Exciting intensity growth till the level of 6.0 W/cm2 implies decrease of signal absolute value, till the change of its sign, while the oscillation of the free polarization decay signal reveals remarkable frequency shift. Such behavior is attributed to the combined action of the dynamic Stark effect of CW radiation field and the levels splitting by the Stark voltage. Two shorter (of about 0.1 and 0.2 mcs) Stark pulses, applied to the gas, generate the photon echo signals detected by the same heterodyne technique. The study of the variations of photon echo parameters versus exciting radiation intensity is in progress.
A theoretical investigation is made of the coherent optical transient phenomena produced by the phase switching method in degenerate gaseous systems in the case of arbitrary detuning. The effect of the light wave polarisation on optical nutation and free induction is studied. Echo manifestations in the form of edge echoes, nutation echoes and induction echoes that accompany light wave phase switching are established to differ from the previously studied ones. Spectroscopic applications of the results obtained are discussed.