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Physical Review A

Optical rotary echoes

N. C. Wong, Satoru S. Kano, Richard G. Brewer

Published Jan 1, 1980• 39 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.21.260

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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.

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Maryna D'Souza, Arvind Kumar

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.

Optica Acta International Journal of Optics•Nov 1, 1981•0 citations
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 observed the optical nutation echoes, i.e., the optical analog of rotary-spin echoes, in ruby. The experiment was carried out using a Stark switching technique. The inversion of the effective field in the rotating frame was achieved by applying a small short Stark pulse (phase-shifting pulse) whose amplitude ΔE and width Δt satisfy the condition that Δω·Δt is equal to an odd multiple of π where Δω is the frequency offset produced by ΔE. A train of nutation echoes was also observed by applying successive phase-shifting pulses. The observed nutation-echo-envelope decay time was 12 µs which is nearly equal to 2T 2 consistent with the theoretical prediction. Radiation-locking and radiation-locked echo experiments were also performed by using similar phase-shifting techniques.
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.
Optical nutation signals are found to be modified in interesting ways by a short, intense, excitation pulse. In particular, pulses of appropriate character are found to effect a time reversal of the optical nutation signal, i.e., the nutation signal after the short pulse evolves as the mirror image of the nutation signal before the pulse. In ideal cases, all dephasing effects resulting from inhomogeneous broadening are reversed, and a nutation echo occurs when all atoms rephase in the excited state. Various excitation conditions that lead to the time reversal of optical nutation signals are considered, and numerical simulations are compared with experimental results. Finally, the rephasing considered here is compared to that observed in the case of rotary echoes.
The optical analog of the nuclear magnetic resonance rotary saturation effect is demonstrated and analyzed. A 9.6-\ensuremath{\mu}m CO2{\mathrm{O}}_{2}O2​ laser resonance excitation of vibrational transitions in gaseous CH3{\mathrm{H}}_{3}H3​F creates an effective splitting in the interaction representation of the optical two-level system. A radio-frequency standing-wave Stark electric field is tuned in rotary saturation resonance with the splitting. The change in transmitted laser beam intensity, because of rotary resonance, is measured in terms of transient optical signals obtained by the Stark switching method of Brewer and Shoemaker. The measured single and multiphoton rotary saturation resonance signals are compared with perturbation and computer solutions of nonlinear Bloch-Maxwell macroscopic equations. Doppler-free rotary saturation spectra are obtained in the presence of inhomogeneous Doppler broadening by a special scheme of Fourier analysis. A discussion is presented of the coupling of energy between two traveling waves that are in double resonance with the optical two-level system. The concept of spin temperature is discussed in relation to a coherently excited optical level system with a long fluorescence lifetime. The possibility of a cross-relaxation double resonance experiment between an optical system and a spin system is outlined.
Two-quantum rotary echoes predicted by Bloch like equations for two-quantum transition have been observed in a multi-level NMR system of 27 Al nuclei in Al 2 O 3 . An rf field exactly at resonance to the two-quantum transition ( Δ m =2) was turned on at t =0 and its phase was shifted by 90° at t =τ. The echo at t =2τ was observed by using the technique of transfer of coherence reported previously. Characteristic dependence of the echo width upon inhomogeneity of rf field amplitude was confirmed experimentally.
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.