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The Theory of Three-level Photon Echo for Quasi-degenerated Levels

Tara Ahmadi

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

The three-level photon echo has been described in different works[1,2] by using rotating wave approximation but none of them didnt get re-sults which show the effects of detuning frequencies on frequency of ground level of system; also the effect distance between two generated levels on signal resonance is being neglected. In this work, we stud-ied a-type system theoretically and numerically. By considering the Dopplers effect in environment, we get different equation for polariza-tion of echo signal and its intensity. 1

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The Theory of Three-level Photon Echo Using of Rotating Wave Approximation

Tara Ahmadi, S. A. Pulkin, Vladimir. A Sheftsov

The three level photon echo has been described in different works by using rotating wave approximation but none of them did not get results which show the effects of field's frequencies on frequency of ground level of system. In this work, we studied a Lambda type system theoretically and numerically. By considering the Doppler effect in environment, we get different equation for polarization of echo signal and its intensity.

arXiv:1405.7674•May 29, 2014•0 citations

Three-level photon echo for quasi-degenerated Levels

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Quantum optical data storage is a key element in quantum information processing. However, most modified photon echoes protocols are still limited by lack of resonance signal to explain time scales of different systems. In this paper, we studied three-pulse photon-echo system by using density matrix in Λ-scheme.. It will be shown that the time position of three-pulse echo signals is proportional to ratio of detuning frequencies from the resonance frequencies of transitions in a non-uniform distribution. In the last part of paper, you can see the importance effect of frequency distance between two degenerate levels (d) on the delay time of signal.

International Conference Laser Optics (ICLO)•Jun 1, 2014•0 citations

Photon echoes in a resonant three-level system with arbitrary level degeneracy

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The theoretical analysis on photon echoes is reported in a resonant multi-level system with level degeneracy, by a general consideration. With respect to the system possessing more than three-fold degeneracy, the intensity of photon echoes depends not only on the areas of the exciting optical pulses, but also on their polarization characteristics. In particular, it was found that some anomalous echoes change their intensities with the polarization directions of exciting optical pulses which have different frequencies from those of the echoes because of the coherent coupling of resonant transitions with common energy level and the interference effect of transitions through the degenerate sublevels. In the first half of this paper the general formulation on the multi-level system with arbitrary degeneracy is performed, and in the second half, the application of the general theory to some typical examples is also given.

Journal of Physics A Mathematical Nuclear and General•Nov 1, 1973•10 citations

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An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.

Journal of Physics A Mathematical Nuclear and General•Nov 1, 1973•21 citations

DEGENERATE PHOTON ECHOES

Masaharu Mitsunaga, M. K. Kim, Ravinder Kachru

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.

•Jul 18, 1988•0 citations

Theory of modulated photon echoes

Axel Schenzle, S. B. Grossman, Richard G. Brewer

Photon echoes, observed recently in ruby and in ${\mathrm{NH}}_{2}$D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.

Physical Review A•May 1, 1976•23 citations
The three-level photon echo has been described in different works[1,2] by using rotating wave approximation but none of them didnt get re-sults which show the effects of detuning frequencies on frequency of ground level of system; also the effect distance between two generated levels on signal resonance is being neglected. In this work, we stud-ied a-type system theoretically and numerically. By considering the Dopplers effect in environment, we get different equation for polariza-tion of echo signal and its intensity. 1
Quantum optical data storage is a key element in quantum information processing. However, most modified photon echoes protocols are still limited by lack of resonance signal to explain time scales of different systems. In this paper, we studied three-pulse photon-echo system by using density matrix in Λ-scheme.. It will be shown that the time position of three-pulse echo signals is proportional to ratio of detuning frequencies from the resonance frequencies of transitions in a non-uniform distribution. In the last part of paper, you can see the importance effect of frequency distance between two degenerate levels (d) on the delay time of signal.
The theoretical analysis on photon echoes is reported in a resonant multi-level system with level degeneracy, by a general consideration. With respect to the system possessing more than three-fold degeneracy, the intensity of photon echoes depends not only on the areas of the exciting optical pulses, but also on their polarization characteristics. In particular, it was found that some anomalous echoes change their intensities with the polarization directions of exciting optical pulses which have different frequencies from those of the echoes because of the coherent coupling of resonant transitions with common energy level and the interference effect of transitions through the degenerate sublevels. In the first half of this paper the general formulation on the multi-level system with arbitrary degeneracy is performed, and in the second half, the application of the general theory to some typical examples is also given.
An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.
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.
Photon echoes, observed recently in ruby and in NH2{\mathrm{NH}}_{2}NH2​D gas by two-pulse laser excitation, exhibit a modulation behavior as the pulse delay time is varied. The effect, which arises in a three-level quantum system, is due to the interference of two optically coupled transitions that share a common level. In this article, the three-level echo problem is treated exactly. Wave-function solutions are incorporated that are handled conveniently by a Laplace-transform technique. We, therefore, extend the earlier theory of echo modulation by Lambert et al., by removing their restriction of on-resonance pulse excitation. This procedure allows us to examine the effect of inhomogeneous broadening on echo amplitude explicitly, and we treat the problem by numerical and also by analytical means for the case of a Doppler-broadened gas. Analytic expressions are derived either for a high or a low laser power regime corresponding to excitation of either a large or a small fraction of the Doppler linewidth. The former case is analogous to pulsed nuclear magnetic resonance and is well known, whereas the latter result is new and applies to current photon echo measurements.