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Physical Review A

Polarization rotation of photon echoes in cesium vapor in a magnetic field

Thomas M. Baer, Isaac D. Abella

Published Nov 1, 1977• 42 citations
Publisher

Abstract

We report observations of the rotation of the plane of polarization of photon echoes by a weak axial magnetic field. The echoes are generated on the $6{S}_{\frac{1}{2}}$ to $7{P}_{\frac{1}{2}}$ transition in cesium (4593 \AA{}) by a sequence of two collinear laser pulses polarized in the same direction. When a magnetic field is applied along the propagation axis the polarization vector of the echo is rotated from that of the exciting pulses. We measure the intensity of the photon echo signal polarized orthogonal to the excitation pulse polarization as a function of magnetic field and pulse separation. The theoretical analysis decribes cesium atoms as a nondegenerate multilevel system, consisting of ground and excited Zeeman-split hyperfine-structure levels. The theory presented predicts the observed dependence on magnetic field strength, pulse separation, and excited- and ground-state $g$ factors. A novel method of observing photon echoes is described which uses the polarization rotation effect to replace electro-optical shutters often employed in photon echo experiments.

DOI
10.1103/physreva.16.2093

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Detailed experimental analysis of photon echo polarization in a longitudinal magnetic field is performed for the first time at the simplest quantum transition J = 1 ↔ J = 0 for which the non-Faraday rotation of photon echo polarization plane was predicted. The echo was generated at the intercombination transition (6s6p) 3P1 → (6s2) 1S0 of 174Yb by two resonant laser pulses of linear (parallel or mutually orthogonal) polarization, and the angled echo optical scheme was applied for the detection. At the magnetic field strength ℬ ⩽ 5 G the photon echo has polarization very close to linear one; its polarization plane rotates around magnetic field vector, and photon echo polarization components and integral echo power oscillate versus ℬ from its maximum value to zero, in agreement with theory. At a stronger magnetic field ℬ ∼ 40 G photon echo power oscillations disappear, no preferable orientation of polarization vector is observed; the fluctuations of exciting radiation spectrum are supposed to be responsible for this "non-polarized" echo.

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Non-Faraday rotation of photon-echo polarization was investigated at the $J=1\ensuremath{\leftrightarrow}J=0$ transition in a wide range of longitudinal magnetic field strength. The echo was generated at the intercombination transition $(6s6p)^{3}P_{1}\ensuremath{\rightarrow}(6{s}^{2})^{1}S_{0}$ of $^{174}\mathrm{Yb}$ by two resonant laser pulses of linear (parallel or mutually orthogonal) polarization. A detailed analysis of the echo polarization performed by an angled echo technique has shown quite different behavior in the weak and strong magnetic field limits. The photon echo has polarization close to linear at a magnetic field strength $\mathcal{B}\ensuremath{\leqslant}5\phantom{\rule{0.3em}{0ex}}\mathrm{G}$; its polarization plane rotates around the magnetic field vector clockwise or counterclockwise depending on the magnetic field orientation relative to the wave vector. The photon-echo polarization components and echo power oscillate as functions of $\mathcal{B}$. As the magnetic field increases, the oscillations become smaller and almost disappear at a magnetic field $\mathcal{B}\ensuremath{\approx}40\phantom{\rule{0.3em}{0ex}}\mathrm{G}$; the photon echo does not disappear at this magnetic field, but its polarization vector no longer has a preferred orientation. Numerical calculations of the photon echo generated at a spectral wide line agree with the experimental behavior of the photon-echo polarization for an arbitrary magnetic field.

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Photon-echo quantum beats arising from magnetic splitting of the cesium $7{P}_{\frac{3}{2}}\ensuremath{-}6{S}_{\frac{1}{2}}$ transition were observed in a dilute atomic vapor by means of a novel polarization-rotation technique. The quantum-beat spectrum contains frequencies generated by the hyperfine structure of the $7{P}_{\frac{3}{2}}$ level as well as those due to the Zeeman splitting of both ground and excited levels. Experimental data for both $F=3$ and $F=4$ hyperfine components of the $6{S}_{\frac{1}{2}}$ ground state and for several echo delay times were fitted to calculated spectra, including corrections arising from Faraday rotation of the echo pulses.

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We report a novel method for the observation of photon echoes and other coherent transient effects. In this method, the polarization, direction, and frequency of the polarized coherent radiation emitted by a system are switched by optical pulses. We apply this method to detect photon echoes generated on the $6{P}_{\frac{1}{2}}\ensuremath{-}7{S}_{\frac{1}{2}}$ transition in atomic thallium by two collinear and vertically polarized excitation pulses which are separated by 20 nsec. At the time of the echo, two orthogonally polarized probe pulses resonant with the $6{P}_{\frac{3}{2}}\ensuremath{-}7{S}_{\frac{1}{2}}$ transition of atomic thallium are applied to the sample to switch the photon echo from its original polarization and direction. A horizontally polarized photon echo with its propagation vector turned by about 10 mrad and its axis of polarization rotated by 90\ifmmode^\circ\else\textdegree\fi{} is detected. No electro-optical shutter is used in the experiment. The echo signal disappears either when one of the probe pulses is blocked or when both probe pulses are horizontally or vertically polarized. Echo polarization switching is also demonstrated using an unpolarized probe pulse applied prior to the echo formation time.

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Effect of magnetic field on the stimulated photon echo in ytterbium vapors

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Photon echoes in strong magnetic fields

Решетов Владимир Александрович, Igor V. Yevseyev

The polarization properties of photon echoes in strong magnetic field, when the action of this field during the time of propagation of the exciting pulses and the echo signal through the resonant gaseous medium cannot be neglected, are studied theoretically. The photon echo polarization in strong magnetic field cannot be described by the polarization vector but rather by the polarization matrix. The degree of the photon echo polarization decreases with the increase of the magnetic field strength. The dependence of the photon echo intensity on the magnetic field strength was also analyzed numerically. In strong magnetic field the fast oscillations of this intensity appear to be damping and modulated by the slower ones. The spectrum of these oscillations depend also on the spectra of the exciting pulses, so that in case of small area of the first exciting pulse its temporal shape may be reconstructed from the oscillations of the echo intensity versus the magnetic field strength.

Laser Physics Letters•Sep 16, 2004•2 citations
We report observations of the rotation of the plane of polarization of photon echoes by a weak axial magnetic field. The echoes are generated on the 6S126{S}_{\frac{1}{2}}6S21​​ to 7P127{P}_{\frac{1}{2}}7P21​​ transition in cesium (4593 \AA{}) by a sequence of two collinear laser pulses polarized in the same direction. When a magnetic field is applied along the propagation axis the polarization vector of the echo is rotated from that of the exciting pulses. We measure the intensity of the photon echo signal polarized orthogonal to the excitation pulse polarization as a function of magnetic field and pulse separation. The theoretical analysis decribes cesium atoms as a nondegenerate multilevel system, consisting of ground and excited Zeeman-split hyperfine-structure levels. The theory presented predicts the observed dependence on magnetic field strength, pulse separation, and excited- and ground-state ggg factors. A novel method of observing photon echoes is described which uses the polarization rotation effect to replace electro-optical shutters often employed in photon echo experiments.
Detailed experimental analysis of photon echo polarization in a longitudinal magnetic field is performed for the first time at the simplest quantum transition J = 1 ↔ J = 0 for which the non-Faraday rotation of photon echo polarization plane was predicted. The echo was generated at the intercombination transition (6s6p) 3P1 → (6s2) 1S0 of 174Yb by two resonant laser pulses of linear (parallel or mutually orthogonal) polarization, and the angled echo optical scheme was applied for the detection. At the magnetic field strength ℬ ⩽ 5 G the photon echo has polarization very close to linear one; its polarization plane rotates around magnetic field vector, and photon echo polarization components and integral echo power oscillate versus ℬ from its maximum value to zero, in agreement with theory. At a stronger magnetic field ℬ ∼ 40 G photon echo power oscillations disappear, no preferable orientation of polarization vector is observed; the fluctuations of exciting radiation spectrum are supposed to be responsible for this "non-polarized" echo.
Non-Faraday rotation of photon-echo polarization was investigated at the $J=1\ensuremath{\leftrightarrow}J=0$ transition in a wide range of longitudinal magnetic field strength. The echo was generated at the intercombination transition $(6s6p)^{3}P_{1}\ensuremath{\rightarrow}(6{s}^{2})^{1}S_{0}$ of 174Yb^{174}\mathrm{Yb}174Yb by two resonant laser pulses of linear (parallel or mutually orthogonal) polarization. A detailed analysis of the echo polarization performed by an angled echo technique has shown quite different behavior in the weak and strong magnetic field limits. The photon echo has polarization close to linear at a magnetic field strength $\mathcal{B}\ensuremath{\leqslant}5\phantom{\rule{0.3em}{0ex}}\mathrm{G}$; its polarization plane rotates around the magnetic field vector clockwise or counterclockwise depending on the magnetic field orientation relative to the wave vector. The photon-echo polarization components and echo power oscillate as functions of B\mathcal{B}B. As the magnetic field increases, the oscillations become smaller and almost disappear at a magnetic field $\mathcal{B}\ensuremath{\approx}40\phantom{\rule{0.3em}{0ex}}\mathrm{G}$; the photon echo does not disappear at this magnetic field, but its polarization vector no longer has a preferred orientation. Numerical calculations of the photon echo generated at a spectral wide line agree with the experimental behavior of the photon-echo polarization for an arbitrary magnetic field.
Photon-echo quantum beats arising from magnetic splitting of the cesium $7{P}_{\frac{3}{2}}\ensuremath{-}6{S}_{\frac{1}{2}}$ transition were observed in a dilute atomic vapor by means of a novel polarization-rotation technique. The quantum-beat spectrum contains frequencies generated by the hyperfine structure of the 7P327{P}_{\frac{3}{2}}7P23​​ level as well as those due to the Zeeman splitting of both ground and excited levels. Experimental data for both F=3F=3F=3 and F=4F=4F=4 hyperfine components of the 6S126{S}_{\frac{1}{2}}6S21​​ ground state and for several echo delay times were fitted to calculated spectra, including corrections arising from Faraday rotation of the echo pulses.
We report a novel method for the observation of photon echoes and other coherent transient effects. In this method, the polarization, direction, and frequency of the polarized coherent radiation emitted by a system are switched by optical pulses. We apply this method to detect photon echoes generated on the $6{P}_{\frac{1}{2}}\ensuremath{-}7{S}_{\frac{1}{2}}$ transition in atomic thallium by two collinear and vertically polarized excitation pulses which are separated by 20 nsec. At the time of the echo, two orthogonally polarized probe pulses resonant with the $6{P}_{\frac{3}{2}}\ensuremath{-}7{S}_{\frac{1}{2}}$ transition of atomic thallium are applied to the sample to switch the photon echo from its original polarization and direction. A horizontally polarized photon echo with its propagation vector turned by about 10 mrad and its axis of polarization rotated by 90\ifmmode^\circ\else\textdegree\fi{} is detected. No electro-optical shutter is used in the experiment. The echo signal disappears either when one of the probe pulses is blocked or when both probe pulses are horizontally or vertically polarized. Echo polarization switching is also demonstrated using an unpolarized probe pulse applied prior to the echo formation time.
Polarization of the stimulated photon echo (SPE) at the 0 ↔ 1 transition in ytterbium vapors in the presence of a longitudinal magnetic field of 0–40 G is experimentally and theoretically studied. The SPE is generated using three light pulses with identical linear polarizations, so that the SPE polarization is the same at zero magnetic field. In the presence of a weak magnetic field, the SPE polarization vector rotates around the magnetic field vector and the depolarization of the SPE signal takes place. Each of the SPE polarization components exhibits biharmonic oscillations depending on the magnetic field. In the presence of a strong magnetic field, these oscillations vanish and the SPE becomes depolarized. The experimental data are in qualitative agreement with the results of the numerical calculations performed with the method of the evolution operator for the finite-duration excitation pulses. The application of the results for the processing of optical data is discussed.
The polarization properties of photon echoes in strong magnetic field, when the action of this field during the time of propagation of the exciting pulses and the echo signal through the resonant gaseous medium cannot be neglected, are studied theoretically. The photon echo polarization in strong magnetic field cannot be described by the polarization vector but rather by the polarization matrix. The degree of the photon echo polarization decreases with the increase of the magnetic field strength. The dependence of the photon echo intensity on the magnetic field strength was also analyzed numerically. In strong magnetic field the fast oscillations of this intensity appear to be damping and modulated by the slower ones. The spectrum of these oscillations depend also on the spectra of the exciting pulses, so that in case of small area of the first exciting pulse its temporal shape may be reconstructed from the oscillations of the echo intensity versus the magnetic field strength.