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Journal of the Optical Society of America B

Angled-beam photon echoes

Raymond John Beach, Burton Brody, Sven R. Hartmann

Published Apr 1, 1984• 4 citations
Publisher

Abstract

We have observed the effect of angled excitation beams on the photon echoes from the 22S1/2–22P1/2 transition of atomic lithium. The degradation of the echo from noncollinear excitations is not so great as had been feared. A calculation with the billiard-ball echo model is in good agreement with our experimental results. In a similar experiment in atomic-sodium vapor we have recorded a decay of echo intensity with increasing pulse separation over nearly 12 orders of magnitude, with the weakest signals coming from atoms that had been more than 23 lifetimes in their excited state.

DOI
10.1364/josab.1.000189

Related papers

Photon echoes in lithium vapor with the use of angled excitation beams

Raymond John Beach, Burton Brody, Sven R. Hartmann

Two-pulse photon echoes on the $2^{2}S_{\frac{1}{2}}\ensuremath{-}2^{2}P_{\frac{3}{2}}$ transition in lithium vapor are generated using laser excitation pulses with angular separations of 0.70 and 1.40 mrad. The observed degradation of echo intensity with angling of the excitation pulses is in agreement with theory. The largest echoes radiated by the lithium sample contained ${10}^{9}$ photons; the smallest echoes detected contained only an average of 0.04 photons. This intensity range of greater than ${10}^{10}$ represents measurements made over more than 15 natural lifetimes of the $2^{2}P_{\frac{3}{2}}$ state despite the degradation due to angling. Modulation of the echo signal due to the hyperfine structure of the $2^{2}P_{\frac{3}{2}}$ state is also observed.

Physical Review A•Jun 1, 1983•16 citations

Elliptical billiard-ball echo model

Raymond John Beach, Burton Brody, Sven R. Hartmann

The billiard-ball echo model is expanded to include the effects of using sub-Doppler-linewidth lasers in photon-echo experiments. The simple heuristic model which emerges explains such echo phenomena in gases as the echo time width and the degradation of echo intensity with angling of the excitation pulses. We derive simple results in the small-pulsearea limit and give formal expressions for excitation pulses of arbitrary area.

Physical Review A•May 1, 1983•12 citations

Intense incoherent light and photon echoes

Lindsey Van Wagenen

One of the long-standing difficulties in working with intense incoherent light has been the lack of a theory for predicting and explaining experimental results. The diagrammatic theory of Friedberg and Hartmann provides a solution to this problem by allowing one to study the interaction of intense incoherent light and matter with no restrictions on the intensity of the pulses. In the present investigation, two-pulse photon-echo experiments were performed with intense incoherent light in atomic sodium vapor and the results were compared with predictions calculated from the Friedberg-Hartmann diagrammatic theory. The dependence of the echo signal on the intensity of the constituent excitation pulses was studied. The results of this investigation indicate that the two-pulse incoherent photon-echo experimental data are consistent with the calculations obtained from the theory presented in the diagrammatic paper of Friedberg and Hartmann when the atomic relaxation times are included. The two-pulse-echo data show good agreement with the theoretical predictions for the case in which 4T2 = T1 (the atomic and transverse lifetimes, respectively), which represents more of a decay than has been theoretically predicted for the experimental parameters used.

Quantum Electronics and Laser Science Conference•May 2, 1993•0 citations

Photon Echoes Made Simple

Raymond John Beach, Burton Brody, Sven R. Hartmann

Photon Echoes in gases are analyzed via the Billiard Ball Echo Model both in the short and long pulse limit where the “atoms” are represented as spherical and elliptical billiard balls, respectively. Recent experiments demonstrating the elliptical billiard ball shape are presented using intensity data which ranges over close to eleven orders of magnitude.

Laser Chemistry•Jan 1, 1983•0 citations

Theory of optical coherent transients including collisional effects: Application to an extended-pulse photon echo

Ruwang Sung, P. R. Berman

The interaction between an intense radiation field and atoms that undergo collisions in an atomic vapor is studied. With the assumption that velocity-changing collisions are state independent and weak, we obtain an analytic expression for the time-dependent density-matrix elements by solving a quantum-mechanical transport equation using a dressed-state approach. Our analytical calculation is used to predict the form of the signal in an extended-pulse photon echo. The results show good agreement with an experiment carried out by Yodh et al. [Phys. Rev. Lett. 53, 659 (1984)]. It is found that the decay rate of the echo signal decreases rapidly with increasing duration of the second pulse in the pulse excitation sequence. A comparison between theory and experiment is presented and a physical interpretation of the results is given.

Physical Review A•Jun 1, 1989•2 citations

Conventional and collision photon echo in ytterbium vapor

Н. Н. Рубцова, Sergei A. Kochubei, В. Н. Ищенко +2 more

The polarization properties of the photon echo generated by two linearly polarized pulses of resonant radiation at the (6s6p)3 P 1 ↔ (6s 2)1 S 0 transition of 174Yb are investigated. A complicated polarization behavior of the photon echo versus an angle between the polarization vectors of the excitation pulses is revealed in a mixture of ytterbium vapor with inert gas. For the angles ranging from 0° to 75°, a conventional echo with its linear polarization coinciding with the second excitation pulse dominates and the echo amplitude decreases with an increasing angle. For the angles ranging from 75° to 89°, the photon echo is elliptically polarized. Finally, for an angle of 90°, the conventional echo disappears and the collision echo becomes linearly polarized along the first excitation pulse.

Laser Physics•Feb 1, 2009•9 citations
We have observed the effect of angled excitation beams on the photon echoes from the 22S1/2–22P1/2 transition of atomic lithium. The degradation of the echo from noncollinear excitations is not so great as had been feared. A calculation with the billiard-ball echo model is in good agreement with our experimental results. In a similar experiment in atomic-sodium vapor we have recorded a decay of echo intensity with increasing pulse separation over nearly 12 orders of magnitude, with the weakest signals coming from atoms that had been more than 23 lifetimes in their excited state.
Two-pulse photon echoes on the $2^{2}S_{\frac{1}{2}}\ensuremath{-}2^{2}P_{\frac{3}{2}}$ transition in lithium vapor are generated using laser excitation pulses with angular separations of 0.70 and 1.40 mrad. The observed degradation of echo intensity with angling of the excitation pulses is in agreement with theory. The largest echoes radiated by the lithium sample contained 109{10}^{9}109 photons; the smallest echoes detected contained only an average of 0.04 photons. This intensity range of greater than 1010{10}^{10}1010 represents measurements made over more than 15 natural lifetimes of the 22P322^{2}P_{\frac{3}{2}}22P23​​ state despite the degradation due to angling. Modulation of the echo signal due to the hyperfine structure of the 22P322^{2}P_{\frac{3}{2}}22P23​​ state is also observed.
One of the long-standing difficulties in working with intense incoherent light has been the lack of a theory for predicting and explaining experimental results. The diagrammatic theory of Friedberg and Hartmann provides a solution to this problem by allowing one to study the interaction of intense incoherent light and matter with no restrictions on the intensity of the pulses. In the present investigation, two-pulse photon-echo experiments were performed with intense incoherent light in atomic sodium vapor and the results were compared with predictions calculated from the Friedberg-Hartmann diagrammatic theory. The dependence of the echo signal on the intensity of the constituent excitation pulses was studied. The results of this investigation indicate that the two-pulse incoherent photon-echo experimental data are consistent with the calculations obtained from the theory presented in the diagrammatic paper of Friedberg and Hartmann when the atomic relaxation times are included. The two-pulse-echo data show good agreement with the theoretical predictions for the case in which 4T2 = T1 (the atomic and transverse lifetimes, respectively), which represents more of a decay than has been theoretically predicted for the experimental parameters used.
The interaction between an intense radiation field and atoms that undergo collisions in an atomic vapor is studied. With the assumption that velocity-changing collisions are state independent and weak, we obtain an analytic expression for the time-dependent density-matrix elements by solving a quantum-mechanical transport equation using a dressed-state approach. Our analytical calculation is used to predict the form of the signal in an extended-pulse photon echo. The results show good agreement with an experiment carried out by Yodh et al. [Phys. Rev. Lett. 53, 659 (1984)]. It is found that the decay rate of the echo signal decreases rapidly with increasing duration of the second pulse in the pulse excitation sequence. A comparison between theory and experiment is presented and a physical interpretation of the results is given.
The polarization properties of the photon echo generated by two linearly polarized pulses of resonant radiation at the (6s6p)3 P 1 ↔ (6s 2)1 S 0 transition of 174Yb are investigated. A complicated polarization behavior of the photon echo versus an angle between the polarization vectors of the excitation pulses is revealed in a mixture of ytterbium vapor with inert gas. For the angles ranging from 0° to 75°, a conventional echo with its linear polarization coinciding with the second excitation pulse dominates and the echo amplitude decreases with an increasing angle. For the angles ranging from 75° to 89°, the photon echo is elliptically polarized. Finally, for an angle of 90°, the conventional echo disappears and the collision echo becomes linearly polarized along the first excitation pulse.