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Journal of Physics B Atomic and Molecular Physics

Optical nutation and free induction of degenerate systems

Aleksey I. Alekseev, Ashat M. Basharov

Published Nov 28, 1982• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/15/22/026

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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.
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.
Coherent transient effects are the optical analogs of the many transient phenomena seen in pulsed nuclear magnetic resonance experiments on spin systems. For example, photon-echo and optical nutation are the respective optical equivalents of spin echo and transient nutation of nuclear magnetic resonance. In Stark-switching and frequency-switching techniques the laser field and the molecules are brought into resonance in a sequence of pulses, the rest of the time they remain well off-resonance. So far it has been assumed that the off-resonance field does not have any measureable influence on the experimental results and is utilized to implement a very efficient detection scheme. This work discusses how the off-resonance field affects the coherent transient effects. It is shown here how this field, by inducing changes in the index of refraction as small as 10⁻⁶ produces easily observable effects in photon echo and delayed optical nutation.
When an intense and short laser pulse or a fast-switching-on/off laser field interacts with a resonant absorbing medium, several optical coherent transient effects can be observed, including the self-induced transparency effect, photon echo effect, optical nutation effect, and the optical free induction decay effect. The study of these effects enables us to gain a deeper understanding of the coherent transient interaction of an intense pulsed or rapidly switched optical field with the resonant medium, and to measure the magnitude of the dipole-moment matrix elements, relaxation parameters, and spectral broadening mechanisms of the investigated materials. On the other hand, these optical coherent transient effects can also be applied for developing special techniques of optical pulse delay, pulse reshaping, and optical pulse manipulation.
Abstract Chapter 4 treats the three most important coherent optical transient phenomena using primarily the Bloch vector model. One section is devoted to each effect: nutation, free induction decay, and the photon echo. Through this, the idea that steady-state response to light develops slowly, on a timescale set by inertia in the atom–field interaction, is introduced. Nutation is considered both with and without damping. In the last section, three possible approaches to describing the photon echo are briefly compared to gain perspective on the advantages and disadvantages of algebraic echo analysis, rotation matrix multiplication, or density matrix methodology. By the end of this chapter the reader is prepared for the remaining chapters in which the density matrix approach is used exclusively to calculate the effects of light on a wide variety of systems.
The general formalism of transient four-wave mixing is developed using the diagrammatic technique of Yee and Gustafson, and applied systematically to two-, three-, and four-level systems. The results predict all possible photon-echo phenomena including free-induction decay in the low-intensity limit. Connections to transient saturation spectroscopy and other coherent transient effects can also be made. The treatment can be readily extended to the more general problem of coherent transient optical effects with nnn waves.