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Acta Physica Sinica

STUDY OF STIMULATED PHOTON ECHO IN DEGENERATE TWO-LEVEL SYSTEM GENERAL THEARY AND RELAXATION INDUCED STIMULATED PHOTON ECHO

Peixian Ye, Panming Fu, 中国科学院物理研究所

Published Jan 1, 1985• 0 citations
Publisher

Abstract

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-.

DOI
10.7498/aps.34.725

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Physical Review Letters•Jun 4, 1984•32 citations
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-.
The polarization properties of the long-lived stimulated photon echo formed on the transition ja → jb with the atomic levels degenerate in the projections of the angular momenta are studied theoretically. The two particular transitions ja = 1 → jb = 0 and ja = 1 → jb = 1 with degenerate ground state ja = 1 are discussed. For the transitions ja = 1 → jb = 1 the polarizations and areas of the first ('write') and the third ('read') excitation pulses are found when the echo polarization faithfully reproduces the arbitrary polarization of the weak (single-photon) second ('information') pulse, so that this echo scheme may implement the quantum memory for a single-photon polarization qubit, while for the transitions ja = 1 → jb = 0 it is shown, that the echo polarization differs from that of the second pulse at any conditions.
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.
The stimulated photon echo formed by the sequence of three laser excitation pulses in gaseous medium on the transition with the angular momentum change 0-1 is considered with an account of elastic depolarizing collisions. The polarization properties of this echo may be potentially interesting for the purposes of data processing. It is shown, that with the polarization of the first pulse orthogonal to that of the second and third pulses the appearance of the echo signal will be entirely determined by the action of collisions. The existence of this echo is determined by the difference in the alignment and the orientation relaxation rates of the excited level.
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.
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.
With a three-level configuration in ytterbium vapor, we have performed the first quantitative investigation of single excited-level scattering using a stimulated photon echo (three-pulse echo). We have studied the collisional relaxation of the echo signal by rare-gas perturbers and have derived a theoretical expression for the relaxation rate. Total elastic cross sections for collisions between Yb(6s6p3P1\mathrm{Yb}(6s6p^{3}P_{1}Yb(6s6p3P1​) and Ne or Xe have been obtained.