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DEGENERATE PHOTON ECHOES

Masaharu Mitsunaga, M. K. Kim, Ravinder Kachru

Published Jul 18, 1988• 0 citations
OpenAlex

Abstract

The three-pulse stimulated photon echo has been considered as one of the most fundamental transient four wave mixing processes1, where each of the three excitation pulses induces a single elementary interaction process between a laser field and an inhomogeneously broadened two-level system., resulting in a burst of the fourth wave, i.e., echo. Now if four or more optical pulses are applied to a medium, a number of photon echoes should be expected, in general. At low excitation intensities where the perturbation theory is applicable, however, the dominant nonlinear process is still the three-pulse stimulated echo and consequently each echo signal is generated only by three of the preceding pulses. It is rather a remarkable result that the echo intensity is unaffected by the presence of all the rest of the pulses other than its three generators. With this in mind, it is theoretically and experimentally shown that by applying a single optical pulse (#1) propagating along k1 followed by N pairs of counter-propagating pulses (#2j (k2j) and #3j− (k3j = −k2j); j=1,…N) in various directions, it is possible to obtain N photon echoes along the direction -k1 opposite to the first pulse #1. We will call this degenerate photon echoes, degenerate in. the sense that the echoes are spatially overlapping and temporally simultaneous. When N=l, this scheme is reduced to the ordinary backward photon echo2,3. The doubly degenerate case (N=2) is illustrated in Fig. 1. The j-th echo will be generated by the set of pulses (#1, #2j, #3j) and appear at t = t3j + t2j − t1 where t1, i2j and t3j are the arrival times of the pulses #1, #2j and #3j, respectively.

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Masaharu Mitsunaga, M. K. Kim, Ravinder Kachru

It is shown that simultaneous and spatially overlapping multiple photon echoes can occur following application of a single optical pulse followed by multiple pairs of counterpropagating pulses in various directions-degenerate photon echoes. This scheme has been experimentally verified in Pr(3+):LaF(3) for the doubly degenerate case. In the small-pulse-area regime, the two echoes are observed to be independent with no cross talk between them. From the viewpoint of transient optical memory, this enables us to store multiple independent optical data in one sample spot and to retrieve any one of them, thereby multiplying the memory capacity of the crystal.

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Peixian Ye, Panming Fu, 中国科学院物理研究所

The stimulated photon echo in degenerate two-level system has been studied. The stimulated photon echo signal for different polarization arrangement of incident lights was obtained basing on the third-order perturbation theory, where, the density matrix was expanded in an irreducible spherical-tensor operator. The characteristics of stimulated photon echo were discussed. Taking ja = jb = 1/2 system as example, we have also studied the relaxation induced stimulated photon echo, where, the polarization arrangement of the three incident pulses is σ+→σ+→σ-.

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Optical properties of photon echoes stimulated by three frequencies

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A gaseous atomic or molecular system with four energy levels ${E}_{a}<{E}_{b}<{E}_{c}<{E}_{d}$ which is stimulated by resonant laser pulses at frequencies ${\ensuremath{\omega}}_{1}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{ba}}$, ${\ensuremath{\omega}}_{2}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{cb}}$, ${\ensuremath{\omega}}_{3}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{dc}}$ is considered. The six photon echoes which are stimulated by first and second pulses at frequencies ${\ensuremath{\omega}}_{1}$, ${\ensuremath{\omega}}_{2}$, ${\ensuremath{\omega}}_{3}$ are discussed. For wave fronts which are described by ${e}^{i(\ensuremath{\phi}\ensuremath{-}\ensuremath{\omega}t)}$ the echo phase is described by ${\ensuremath{\phi}}_{E}=\ensuremath{\Sigma}(2{\ensuremath{\phi}}_{m}^{\mathrm{II}}\ensuremath{-}{\ensuremath{\phi}}_{m}^{\mathrm{I}})$ at the sum frequency ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}+{\ensuremath{\omega}}_{3}$ with $m=1,2,3$, at ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$ with $m=1,2$, at ${\ensuremath{\omega}}_{1}$ with $m=1$, etc. For waves in the $z$ direction where $\ensuremath{\phi}=\ensuremath{\kappa}(x,y,z)+kz$ the gradient of the phase yields the wave-vector direction ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{E}=\ensuremath{\Sigma}(2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{m}^{\mathrm{II}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{m}^{\mathrm{I}})$ in a physically thin sample. A probe pulse at ${\ensuremath{\omega}}_{2}$ and ${\ensuremath{\omega}}_{3}$ after the second pulse can generate a probe-pulse echo at ${\ensuremath{\omega}}_{1}$ with phase ${\ensuremath{\phi}}_{1}=\ensuremath{\Sigma}(2{\ensuremath{\phi}}_{m}^{\mathrm{II}}\ensuremath{-}{\ensuremath{\phi}}_{m}^{\mathrm{I}})\ensuremath{-}{\ensuremath{\phi}}_{2}^{S}\ensuremath{-}{\ensuremath{\phi}}_{3}^{S}$, etc., for other frequency arrangements. Transverse phases ${\ensuremath{\kappa}}_{m}(\mathrm{xy})$ can be added and subtracted, but no application is suggested for this novel feature. When all ${\ensuremath{\kappa}}_{m}$ except one are zero, phase conjugation or phase-adaptive optics can occur.

Physical Review A•May 1, 1979•11 citations
The three-pulse stimulated photon echo has been considered as one of the most fundamental transient four wave mixing processes1, where each of the three excitation pulses induces a single elementary interaction process between a laser field and an inhomogeneously broadened two-level system., resulting in a burst of the fourth wave, i.e., echo. Now if four or more optical pulses are applied to a medium, a number of photon echoes should be expected, in general. At low excitation intensities where the perturbation theory is applicable, however, the dominant nonlinear process is still the three-pulse stimulated echo and consequently each echo signal is generated only by three of the preceding pulses. It is rather a remarkable result that the echo intensity is unaffected by the presence of all the rest of the pulses other than its three generators. With this in mind, it is theoretically and experimentally shown that by applying a single optical pulse (#1) propagating along k1 followed by N pairs of counter-propagating pulses (#2j (k2j) and #3j− (k3j = −k2j); j=1,…N) in various directions, it is possible to obtain N photon echoes along the direction -k1 opposite to the first pulse #1. We will call this degenerate photon echoes, degenerate in. the sense that the echoes are spatially overlapping and temporally simultaneous. When N=l, this scheme is reduced to the ordinary backward photon echo2,3. The doubly degenerate case (N=2) is illustrated in Fig. 1. The j-th echo will be generated by the set of pulses (#1, #2j, #3j) and appear at t = t3j + t2j − t1 where t1, i2j and t3j are the arrival times of the pulses #1, #2j and #3j, respectively.
It is shown that simultaneous and spatially overlapping multiple photon echoes can occur following application of a single optical pulse followed by multiple pairs of counterpropagating pulses in various directions-degenerate photon echoes. This scheme has been experimentally verified in Pr(3+):LaF(3) for the doubly degenerate case. In the small-pulse-area regime, the two echoes are observed to be independent with no cross talk between them. From the viewpoint of transient optical memory, this enables us to store multiple independent optical data in one sample spot and to retrieve any one of them, thereby multiplying the memory capacity of the crystal.
We apply for the first time a novel coherent transient, the cw photon echo. The propagation direction of the optical coherence prepared in a medium by a broadband cw laser beam is reversed by a pair of counterpropagating laser pulses, resulting in a continuous emission of the signal. The signal decays with a phase relaxation time T2{\mathrm{T}}_{2}T2​ and can have a quantum-beat-type modulation, giving the same wave form in one single shot as the plot of echo intensity versus pulse separation in a standard two-pulse echo experiment. Experimental demonstration is given in a Eu3+{\mathrm{Eu}}^{3+}Eu3+:YAlO3{\mathrm{YAlO}}_{3}YAlO3​ crystal.
A photon echo experiment has been performed using accumulated highly attenuated laser pulses. We show experimentally that the photon echo process can be performed with, on the average, less than one photon in each pair of excitation pulses. The results support an interpretation where this nonlinear process can be performed with, on the average, less than one photon shared between two of the optical fields involved in the degenerate four-wave-mixing process. Further, we argue that the experiment can be interpreted as a form of delayed self-interference for photon wave packets that do not overlap in both space and time.
Phase relaxation of optical excitations in condensed matter can be studied by coherent four—wave—mixing experiments in the time domain without requiring assumptions on the spectral properties of the material. For inhomogeneously broadened transitions, three laser pulses at times t = 0, t = t21 and t = T with wave vectors k1, k2 and k3, respectively, generate a stimulated photon echo pulse, emitted time—delayed at t = T+t21 in the momentum—matching direction according to k3+k2−k1. As a function of t21 the echo amplitude decays due to scattering events, described by the dephasing time constant T2 [1].
The stimulated photon echo in degenerate two-level system has been studied. The stimulated photon echo signal for different polarization arrangement of incident lights was obtained basing on the third-order perturbation theory, where, the density matrix was expanded in an irreducible spherical-tensor operator. The characteristics of stimulated photon echo were discussed. Taking ja = jb = 1/2 system as example, we have also studied the relaxation induced stimulated photon echo, where, the polarization arrangement of the three incident pulses is σ+→σ+→σ-.
A gaseous atomic or molecular system with four energy levels Ea<Eb<Ec<Ed{E}_{a}<{E}_{b}<{E}_{c}<{E}_{d}Ea​<Eb​<Ec​<Ed​ which is stimulated by resonant laser pulses at frequencies ${\ensuremath{\omega}}_{1}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{ba}}$, ${\ensuremath{\omega}}_{2}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{cb}}$, ${\ensuremath{\omega}}_{3}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{dc}}$ is considered. The six photon echoes which are stimulated by first and second pulses at frequencies ${\ensuremath{\omega}}_{1}$, ${\ensuremath{\omega}}_{2}$, ${\ensuremath{\omega}}_{3}$ are discussed. For wave fronts which are described by ${e}^{i(\ensuremath{\phi}\ensuremath{-}\ensuremath{\omega}t)}$ the echo phase is described by ${\ensuremath{\phi}}_{E}=\ensuremath{\Sigma}(2{\ensuremath{\phi}}_{m}^{\mathrm{II}}\ensuremath{-}{\ensuremath{\phi}}_{m}^{\mathrm{I}})$ at the sum frequency ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}+{\ensuremath{\omega}}_{3}$ with m=1,2,3m=1,2,3m=1,2,3, at ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$ with m=1,2m=1,2m=1,2, at ${\ensuremath{\omega}}_{1}$ with m=1m=1m=1, etc. For waves in the zzz direction where $\ensuremath{\phi}=\ensuremath{\kappa}(x,y,z)+kz$ the gradient of the phase yields the wave-vector direction ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{E}=\ensuremath{\Sigma}(2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{m}^{\mathrm{II}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{m}^{\mathrm{I}})$ in a physically thin sample. A probe pulse at ${\ensuremath{\omega}}_{2}$ and ${\ensuremath{\omega}}_{3}$ after the second pulse can generate a probe-pulse echo at ${\ensuremath{\omega}}_{1}$ with phase ${\ensuremath{\phi}}_{1}=\ensuremath{\Sigma}(2{\ensuremath{\phi}}_{m}^{\mathrm{II}}\ensuremath{-}{\ensuremath{\phi}}_{m}^{\mathrm{I}})\ensuremath{-}{\ensuremath{\phi}}_{2}^{S}\ensuremath{-}{\ensuremath{\phi}}_{3}^{S}$, etc., for other frequency arrangements. Transverse phases ${\ensuremath{\kappa}}_{m}(\mathrm{xy})$ can be added and subtracted, but no application is suggested for this novel feature. When all ${\ensuremath{\kappa}}_{m}$ except one are zero, phase conjugation or phase-adaptive optics can occur.