Physical Review A

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

Raymond John Beach, Burton Brody, Sven R. Hartmann

Published Jun 1, 1983• 16 citations

Abstract

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.

DOI: 10.1103/physreva.27.2925

Related papers

Angled-beam photon echoes

Raymond John Beach, Burton Brody, Sven R. Hartmann

Journal of the Optical Society of America BApr 1, 19844 citations

Measurement of excited-state lifetime using two-pulse photon echoes in rubidium vapor

Eric Rotberg, B. Barrett, Scott Beattie +4 more

Journal of the Optical Society of America BFeb 15, 200715 citations

Photon Echoes in Gases

J. P. GORDON, C. H. WANG, C. K. N. Patel +2 more

Physical ReviewMar 10, 1969150 citations

Conventional and collision photon echo in ytterbium vapor

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

Laser PhysicsFeb 1, 20099 citations

Intense incoherent light and photon echoes

Lindsey Van Wagenen

Quantum Electronics and Laser Science ConferenceMay 2, 19930 citations

Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+ : YAlO3

Masaharu Mitsunaga, Ryuzi Yano, Naoshi Uesugi

Physical review. B, Condensed matterJun 1, 199227 citations

Physical Review A

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

Raymond John Beach, Burton Brody, Sven R. Hartmann

Published Jun 1, 1983• 16 citations

Publisher

Abstract

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.

DOI: 10.1103/physreva.27.2925

Related papers

Angled-beam photon echoes

Raymond John Beach, Burton Brody, Sven R. Hartmann

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.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.

Journal of the Optical Society of America BApr 1, 19844 citations

Measurement of excited-state lifetime using two-pulse photon echoes in rubidium vapor

Eric Rotberg, B. Barrett, Scott Beattie +4 more

We report a measurement of the 5P3/2 excited-state lifetime using two-pulse photon echoes in Rb vapor. The measurement is precise to ∼1% and agrees with the best measurement of atomic lifetime in Rb. The results suggest that a measurement precise to ∼0.25% is possible through additional data acquisition and study of systematic effects. The experiment relies on short optical pulses generated from a cw laser using acousto-optic modulators. The excitation pulses are on resonance with the F=3-->F′=4 transition in Rb85 or the F=2-->F′=3 transition in Rb87. The resulting photon echo signal is detected using a heterodyne detection technique. The excited-state lifetime is determined by measuring the exponential decay of the echo intensity as a function of the time between the excitation pulses. We also present a study of the echo intensity as a function of excitation pulse area and compare the results to simulations based on optical Bloch equations. The simulations include the effects of spontaneous emission as well as spatial and temporal variations of the intensities of excitation pulses.We report a measurement of the 5P3/2 excited-state lifetime using two-pulse photon echoes in Rb vapor. The measurement is precise to ∼1% and agrees with the best measurement of atomic lifetime in Rb. The results suggest that a measurement precise to ∼0.25% is possible through additional data acquisition and study of systematic effects. The experiment relies on short optical pulses generated from a cw laser using acousto-optic modulators. The excitation pulses are on resonance with the F=3-->F′=4 transition in Rb85 or the F=2-->F′=3 transition in Rb87. The resulting photon echo signal is detected using a heterodyne detection technique. The excited-state lifetime is determined by measuring the exponential decay of the echo intensity as a function of the time between the excitation pulses. We also present a study of the echo intensity as a function of excitation pulse area and compare the results to simulations based on optical Bloch equations. The simulations include the effects of spontaneous emission as well as spatial and temporal variations of the intensities of excitation pulses.

Journal of the Optical Society of America BFeb 15, 200715 citations

Photon Echoes in Gases

J. P. GORDON, C. H. WANG, C. K. N. Patel +2 more

The behavior of the photon echo produced by an inhomogeneously broadened spectral line is analyzed, with particular emphasis on the effect of spatial degeneracy of the molecular energy levels. The theoretical results are used to aid in the identification of the states involved in the echoes produced from gaseous S ${\mathrm{F}}_{6}$ excited by pulses of C ${\mathrm{O}}_{2}$ laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions ( $P$ and $R$ branches) the echo induced by two linearly polarized pulses propagating along the same direction, with an angle $\ensuremath{\psi}$ between their electric vectors, is polarized at an angle greater than $\ensuremath{\psi}$ with respect to the first pulse, and the echo intensity decreases to a minimum, but not zero, as $\ensuremath{\psi}$ approaches $\frac{\ensuremath{\pi}}{2}$. An exception is the $j=1\ensuremath{\leftrightarrow}j=0$ transition, for which the echo is always polarized along the second pulse and the intensity varies as ${cos}^{2}\ensuremath{\psi}$. For ${\ensuremath{\Delta}}_{j}=0$ transitions ( $Q$ branch) the echo polarization generally lies at an angle smaller than $\ensuremath{\psi}$, i.e., between the first two pulses, and its intensity also decreases as $|\ensuremath{\psi}|$ approaches $\frac{\ensuremath{\pi}}{2}$. The exceptions for the ${\ensuremath{\Delta}}_{j}=0$ transitions are the cases $j=\frac{1}{2}\ensuremath{\leftrightarrow}j=\frac{1}{2}$ and $j=1\ensuremath{\leftrightarrow}j=1$. In the former case, the echo is polarized at an angle $2\ensuremath{\psi}$ with respect to the electric field vector of the first pulse, and the echo intensity is independent of $\ensuremath{\psi}$; whereas in the latter case, the echo behaves like that for $j=1\ensuremath{\leftrightarrow}j=0$. The dependence of the echo behavior on the angular momentum of states involved in the transition can serve to identify the transitions when measurements of the echo polarization and intensity are possible.The behavior of the photon echo produced by an inhomogeneously broadened spectral line is analyzed, with particular emphasis on the effect of spatial degeneracy of the molecular energy levels. The theoretical results are used to aid in the identification of the states involved in the echoes produced from gaseous S${\mathrm{F}}_{6}$ excited by pulses of C${\mathrm{O}}_{2}$ laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions ($P$ and $R$ branches) the echo induced by two linearly polarized pulses propagating along the same direction, with an angle $\ensuremath{\psi}$ between their electric vectors, is polarized at an angle greater than $\ensuremath{\psi}$ with respect to the first pulse, and the echo intensity decreases to a minimum, but not zero, as $\ensuremath{\psi}$ approaches $\frac{\ensuremath{\pi}}{2}$. An exception is the $j=1\ensuremath{\leftrightarrow}j=0$ transition, for which the echo is always polarized along the second pulse and the intensity varies as ${cos}^{2}\ensuremath{\psi}$. For ${\ensuremath{\Delta}}_{j}=0$ transitions ($Q$ branch) the echo polarization generally lies at an angle smaller than $\ensuremath{\psi}$, i.e., between the first two pulses, and its intensity also decreases as $|\ensuremath{\psi}|$ approaches $\frac{\ensuremath{\pi}}{2}$. The exceptions for the ${\ensuremath{\Delta}}_{j}=0$ transitions are the cases $j=\frac{1}{2}\ensuremath{\leftrightarrow}j=\frac{1}{2}$ and $j=1\ensuremath{\leftrightarrow}j=1$. In the former case, the echo is polarized at an angle $2\ensuremath{\psi}$ with respect to the electric field vector of the first pulse, and the echo intensity is independent of $\ensuremath{\psi}$; whereas in the latter case, the echo behaves like that for $j=1\ensuremath{\leftrightarrow}j=0$. The dependence of the echo behavior on the angular momentum of states involved in the transition can serve to identify the transitions when measurements of the echo polarization and intensity are possible.

Physical ReviewMar 10, 1969150 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.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 PhysicsFeb 1, 20099 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.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 ConferenceMay 2, 19930 citations

Stimulated-photon-echo spectroscopy. II. Echo modulation in Pr3+ : YAlO3

Masaharu Mitsunaga, Ryuzi Yano, Naoshi Uesugi

Stimulated-photon-echo measurements as a function of both the first-to-second (\ensuremath{\tau}) and the second-to-third (T) pulse separations were conducted to study the echo-modulation behavior for the $^{3}$ ${\mathit{H}}_{4}$ ${\mathrm{\ensuremath{-}}}^{1}$ ${\mathit{D}}_{2}$ transition of a cryogenic ${\mathrm{Pr}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ sample. When T is shorter than the excited-state lifetime ${\mathit{T}}_{1}$ , deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds ${\mathit{T}}_{1}$ , the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.Stimulated-photon-echo measurements as a function of both the first-to-second (\ensuremath{\tau}) and the second-to-third (T) pulse separations were conducted to study the echo-modulation behavior for the $^{3}$${\mathit{H}}_{4}$${\mathrm{\ensuremath{-}}}^{1}$${\mathit{D}}_{2}$ transition of a cryogenic ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$ sample. When T is shorter than the excited-state lifetime ${\mathit{T}}_{1}$, deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds ${\mathit{T}}_{1}$, the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.

Physical review. B, Condensed matterJun 1, 199227 citations

Two-pulse photon echoes on the

2^{2}S_{\frac{1}{2}}\ensuremath{-}2^{2}P_{\frac{3}{2}}

{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.

{\mathrm{F}}_{6}

excited by pulses of C

{\mathrm{O}}_{2}

laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions (

P

and

R

branches) the echo induced by two linearly polarized pulses propagating along the same direction, with an angle $\ensuremath{\psi}$ between their electric vectors, is polarized at an angle greater than $\ensuremath{\psi}$ with respect to the first pulse, and the echo intensity decreases to a minimum, but not zero, as $\ensuremath{\psi}$ approaches $\frac{\ensuremath{\pi}}{2}$. An exception is the $j=1\ensuremath{\leftrightarrow}j=0$ transition, for which the echo is always polarized along the second pulse and the intensity varies as ${cos}^{2}\ensuremath{\psi}$. For ${\ensuremath{\Delta}}_{j}=0$ transitions (

Q

branch) the echo polarization generally lies at an angle smaller than $\ensuremath{\psi}$, i.e., between the first two pulses, and its intensity also decreases as $|\ensuremath{\psi}|$ approaches $\frac{\ensuremath{\pi}}{2}$. The exceptions for the ${\ensuremath{\Delta}}_{j}=0$ transitions are the cases $j=\frac{1}{2}\ensuremath{\leftrightarrow}j=\frac{1}{2}$ and $j=1\ensuremath{\leftrightarrow}j=1$. In the former case, the echo is polarized at an angle $2\ensuremath{\psi}$ with respect to the electric field vector of the first pulse, and the echo intensity is independent of $\ensuremath{\psi}$; whereas in the latter case, the echo behaves like that for $j=1\ensuremath{\leftrightarrow}j=0$. The dependence of the echo behavior on the angular momentum of states involved in the transition can serve to identify the transitions when measurements of the echo polarization and intensity are possible.

^{3}

{\mathit{H}}_{4}

${\mathrm{\ensuremath{-}}}^{1}$

{\mathit{D}}_{2}

transition of a cryogenic

{\mathrm{Pr}}^{3+}

{\mathrm{YAlO}}_{3}

sample. When T is shorter than the excited-state lifetime

{\mathit{T}}_{1}

, deep echo modulations along both the \ensuremath{\tau} and T axes are observed, the frequencies of which correspond to the excited-state sublevel splittings. When T exceeds

{\mathit{T}}_{1}

, the modulation is still observed, although only along the \ensuremath{\tau} axis. A density-matrix theory is developed in a perturbative manner to explain these coherent dynamical properties. The numerically simulated three-dimensional plots of the echo intensity versus \ensuremath{\tau} and T are presented, predicting quite satisfactorily the seemingly complicated experimental modulation patterns.