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arXiv:quant-ph/0312070 · Physical Review B

Phase-dependent decoherence of optical transitions in Pr3+:LaF3 in the presence of a driving field

Geoff J. Pryde, Matthew J. Sellars, N. B. Manson

Published Feb 20, 2004• 5 citations
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Abstract

The decoherence times of orthogonally phased components of the optical transition dipole moment in a two-level system have been observed to differ by an order of magnitude. This phase anisotropy is observed in coherent transient experiments where an optical driving field is present during extended periods of decoherence. The decoherence time of the component of the dipole moment in phase with the driving field is extended compared to ${T}_{2},$ obtained from two-pulse photon echoes, in analogy with the spin locking technique of NMR. This is the first phase-dependent investigation of optical decoherence in the presence of a driving field.

DOI
10.1103/physrevb.69.075107

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The decoherence times of orthogonally phased components of the optical transition dipole moment in a two-level system have been observed to differ by an order of magnitude. This phase anisotropy is observed in coherent transient experiments where an optical driving field is present during extended periods of decoherence. The decoherence time of the component of the dipole moment in phase with the driving field is extended compared to T2,{T}_{2},T2​, obtained from two-pulse photon echoes, in analogy with the spin locking technique of NMR. This is the first phase-dependent investigation of optical decoherence in the presence of a driving field.
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.
In this paper we consider the coherences that are produced in a photon (or spin) locking experiment involving a molecular \ntwo-level system. New coherences, not anticipated from the Feynman-Vernon-Hellwarth representation, are predicted if \nthe transition is inhomogeneously broadened. The influence of duration, power, and phase of the driving and probe pulses \nin the locking experiment on the shape of the simulated echo responses is discussed in detail, and a comparison with experiments \nis made.
Using on-demand coherence conversion via optical locking, a dynamic coherent control of the collective atom phase has been demonstrated for longer photon storage beyond the critical constraint of spin phase decay time, where the storage time can be extended up to hours in a rare-earth-doped solid. Coherent transient phenomena such as photon echoes have been investigated for frozen phase decay via coherent population transfer using a simple deshelving optical pulse pair. Unlike the rephasing halt applied to two-pulse photon echoes, where optical decoherence is accelerated by spin inhomogeneous broadening, a completely atom phase-locked coherence conversion has been observed in three-pulse photon echoes, resulting in spin dephasing-free coherence control. Here, the mechanism of the atom phase-locked coherence conversion via optical locking has been investigated in a solid medium whose optical transition is imperfect, where partial coherence is lost via optical depth-dependent imperfect population transfer. The relationship between coherence loss and optical depth is analyzed, where nearly perfect photon echo efficiency can be obtained for ultralong photon storage in an optically thick medium.
Regularities of the optical coherence transformation in three-level systems, resulting from instability development and superradiance, are considered. It is shown that the superradiance eliminates optical coherence on the adjacent optically allowed transitions and induces optical coherence on the optically forbidden transition. This, in turn, makes it possible to observe new effects of photon-echo type. In such a way the known cases of supperradiant emission from the LaF3:Pr3+ medium admit the described phase memory effect.
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.