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Physical Review A

Time reversal of optical nutation signals

Yu Bai, Arjun G. Yodh, THOMAS W. MOSSBERG

Published Aug 1, 1986• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.34.1222

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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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Optical Nutation Echoes in Ruby

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Stimulated Nutation Echo: Dynamic and Decay Properties

G. Bimbo, R. Boscaino, M. Cannas +2 more

We study experimentally the dynamical and decay properties of the Stimulated Nutation Echo (SNE) in a two-level spin system. This is the signal which appears in the transient response of the system to the second pulse at time tau_1 elapsed from its beginning and coinciding with the duration of the first pulse. The information about the first pulse duration is imprinted into the population difference of the inhomogeneously broadened ensemble of the two-level absorbers. The decay of the SNE signal has two contributions. One originates from the population decay during the time tau between the pulses. Another is caused by the coherence loss during the excitation by the first pulse and the reading time of the second pulse. Experimental results on the decay properties induced by these mechanisms are presented. The dependence of these decay rates on the pulse intensity is discussed, and its relationship with the anomalous (non-Bloch) decay of other coherent transients in solids is examined.

arXiv:physics/0203039•Mar 13, 2002•0 citations
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 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 study experimentally the dynamical and decay properties of the stimulated nutation echo (SNE) in a two-level spin system, the signal of which allows the observation timescale of the driven coherence relaxation to be extended. This signal appears in the transient response of the system to the second pulse at time τ 1 from its start and coinciding with the duration of the first pulse. The information about the first pulse duration is imprinted into the population difference of the inhomogeneously broadened ensemble of the two-level absorbers. The decay of the SNE signal has two contributions. One originates from the population decay during the time τ between the two pulses. Another is caused by the coherence loss during the excitation by the first pulse and the reading time of the second pulse. Experimental results on the decay properties induced by these mechanisms are presented for the first time. We investigate the dependence of these decay rates on the pulse intensity and we examine its relationship with the anomalous (non-Bloch) decay of other coherent transients in solids.
It is shown theoretically that, when two-level atoms are nonresonantly excited by a double light pulse that is a superposition of two rectangular pulses of identical frequency but different amplitude, it is possible to form multiple nutational echo signals whose amplitude is determined by the relationships between the Rabi frequencies of the double pulse, the inhomogeneous line width, and the detuning from resonance. It is established that these signals result from null beats between polarization vibrations at variable frequencies and at the generalized Rabi frequency. The optimum conditions for observing multiple echo signals in different experimental situations are considered.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
We have studied the temporal profile of photon-echo signals generated by combined gated cw and pulsed dye-laser excitation of the inhomogeneously broadened, 555.6-nm absorption line of (174)Yb vapor. We find that the echo profile is, after time reversal, essentially identical with that of the first excitation pulse. We give a new analysis of this effect. Since time-reversed pulse reproduction should also occur in inhomogeneously broadened solid samples, and since we observe time-reversed reproduced pulses up to 4% as intense as the input pulse, this effect may have important applications in optical signal-processing systems.
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.
We study experimentally the dynamical and decay properties of the Stimulated Nutation Echo (SNE) in a two-level spin system. This is the signal which appears in the transient response of the system to the second pulse at time tau_1 elapsed from its beginning and coinciding with the duration of the first pulse. The information about the first pulse duration is imprinted into the population difference of the inhomogeneously broadened ensemble of the two-level absorbers. The decay of the SNE signal has two contributions. One originates from the population decay during the time tau between the pulses. Another is caused by the coherence loss during the excitation by the first pulse and the reading time of the second pulse. Experimental results on the decay properties induced by these mechanisms are presented. The dependence of these decay rates on the pulse intensity is discussed, and its relationship with the anomalous (non-Bloch) decay of other coherent transients in solids is examined.