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Optics Letters

Nutational stimulated photon echoes

Ming Tian, Randy R. Reibel, Zeb W. Barber, William Randall Babbitt

Published Jul 1, 2002• 3 citations
Publisher

Abstract

Stimulated photon echoes (SPEs) with time duration comparable to the coherent lifetime and Rabi period have been investigated theoretically and experimentally with an angled beam configuration. The Rabi oscillation effects on both the transmitted field (optical nutation) and the SPE fields are explained by analytic solutions of Maxwell-Bloch equations. The theory also predicts that an echo can exist in the noncausal direction, and this was confirmed by experiments with Tm:YAG crystal.

DOI
10.1364/ol.27.001156

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Physical Review A•Feb 1, 1997•7 citations
Stimulated photon echoes (SPEs) with time duration comparable to the coherent lifetime and Rabi period have been investigated theoretically and experimentally with an angled beam configuration. The Rabi oscillation effects on both the transmitted field (optical nutation) and the SPE fields are explained by analytic solutions of Maxwell-Bloch equations. The theory also predicts that an echo can exist in the noncausal direction, and this was confirmed by experiments with Tm:YAG crystal.
Shape correlation and magnetic field control of stimulated photon echo (SPE) are investigated as basic properties useful for optical data storage and treatment. The SPE polarization was investigated in ytterbium vapour at the intercombination transition (6s6p) 3P1 → (6s2) 1S0 for the first time in a wide range of longitudinal magnetic field strength. SPE was generated by three resonant laser pulses of identical linear polarization and wave vectors directed symmetrically at small angles to the axis of cylindric vapour cell. SPE polarization is close to linear one in zero magnetic field. As magnetic field increases, the SPE polarization acquires ellipticity with the ellipse axis rotated around magnetic field vector. Components of SPE polarization show oscillations versus magnetic field with higher contrast of the oscillations in the weak field.
The effect of random laser phase fluctuations on stimulated photon echoes (SPEs) and on coherently added SPEs was studied and evaluated both experimentally and analytically with statistical methods. The general concept of describing laser frequency fluctuations as a stationary stochastic process is presented and applied to three specific SPE configurations. The effect of phase fluctuations on erasing an SPE by coherently adding another SPE, phase-shifted by 180 degrees relative to the first, is presented.
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.
Polarization of the stimulated photon echo (SPE) at the 0 ↔ 1 transition in ytterbium vapors in the presence of a longitudinal magnetic field of 0–40 G is experimentally and theoretically studied. The SPE is generated using three light pulses with identical linear polarizations, so that the SPE polarization is the same at zero magnetic field. In the presence of a weak magnetic field, the SPE polarization vector rotates around the magnetic field vector and the depolarization of the SPE signal takes place. Each of the SPE polarization components exhibits biharmonic oscillations depending on the magnetic field. In the presence of a strong magnetic field, these oscillations vanish and the SPE becomes depolarized. The experimental data are in qualitative agreement with the results of the numerical calculations performed with the method of the evolution operator for the finite-duration excitation pulses. The application of the results for the processing of optical data is discussed.
Summary form only given. There are several conflicting descriptions of the stimulated photon echo (SPE) process. The SPE is often described as a phased array of classical dipole radiators in which the atoms' spontaneous emission during the time of the echo radiates constructively in the direction of the echo and destructively in all other directions. A second description is that the SPE arises as a linear scattering event. In this paper we numerically and experimentally show that the SPE arises from a macroscopic polarization of the medium at a time /spl tau//sub 21/ after the third pulse and its energy is extracted from the atomic excited-state population. The energy extracted from the system manifests itself as a permanent drop in the population of excited-state atoms at the time of the echo. Such a permanent drop is not consistent with first two descriptions of the SPE process.
Observation of the optical analog of the delayed nutation echo [V. S. Kuz'min et al., Zh. \'Eksp. Teor. Fiz. 99, 215 (1991) [Sov. Phys. JETP 72, 121 (1991)] recently shown in nuclear magnetic resonance is reported. We call this echo a stimulatednnutationnecho (SNE) in analogy to the three-pulse-stimulated echo that is produced from a hole pattern burnt into an inhomogeneous line. In a SNE two-pulse sequence, the first pulse burns a train of holes into the inhomogeneous absorption spectrum and its duration tp{\mathrm{t}}_{\mathrm{p}}tp​ is stored. After a long delay time the second pulse burns its own train of holes. When coincidence of these holes takes place, the SNE occurs at a time t=tp{\mathrm{t}}_{\mathrm{p}}tp​ following the start of the second pulse. Thus the second pulse reads exactly the duration of the first pulse. It is shown that for a Gaussian-shaped beam, the echo becomes sharper and well recognizable. This echo may be used for Rabi frequency measurement and spectral diffusion studies.