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Journal of Experimental and Theoretical Physics Letters

Effect of the Excitation Radiation Coherence on Oscillations of the Photon Echo Intensity

V. N. Lisin, Шегеда Анатолий Михайлович, В. В. Самарцев, E. P. Chukalina

Published Mar 1, 2018• 7 citations
Publisher

Abstract

The physical reasons for observing the splitting of optical lines several orders of magnitude smaller than the spectral width of a laser pulse are investigated. A theory of coherent and incoherent photon echo (PE) in an external static magnetic field and in the presence of a pulsed magnetic field, which causes oscillations of the PE intensity, is elaborated. It is shown that the periods of oscillations in the echo intensity, the echo duration, and the dimensions of the regions in the inhomogeneous line, where the excited ions are coherent, do not depend on the degree of coherence of the laser pulse and on the external static magnetic field. As follows from the theory, in the case of the coherent excitation of the echo, the amplitude of the intensity oscillations is independent of the external static magnetic field if the inhomogeneous line is symmetric. It is shown that the amplitude of the oscillations at the incoherent excitation of the echo is equal to the autocorrelation function of the distribution function of the transition frequency along the inhomogeneous line with the argument equal to the Zeeman splitting of the optical line in the external magnetic field. In this case, the experimental values of the oscillation amplitude are in good agreement with the calculated values of the autocorrelation function for the total inhomogeneous line in LuLiF 4 :Er 3+ ( 4 I 15/2 ⇒F 9/2 transition). In the same way, the autocorrelation function has been obtained for YLiF 4 :Er 3+ on the same transition.

DOI
10.1134/s0021364018060073

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A spectroscopy method has been proposed involving a change in the time shape of the echo signal in the presence of a perturbation, which splits the frequencies of the transitions of two or more ion subgroups of the echo-active ions. This method has been applied to optical systems in which the Zeeman effect is manifested. The ion transition frequencies of ions are switched by a weak pulsed magnetic field acting during the time of the radiation of the photon echo pulse. The modulation of the photon echo signal shape was observed in LuLiF4:Er3+ and YLiF4:Er3+. The time interval between the two nearest minima corresponds to the accumulated phase of the electric dipole moment π and makes it possible to determine the difference of the g factors of the ground and excited 4 F 9/2(I) states of the Er3+ ion in the LuLiF4 the YLiF4 matrices for the known amplitude of the pulsed magnetic field. It has been shown that the echo response of the system can be programmed by the weak magnetic field pulses.

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Low magnetic fields behavior of photon echo in LuLiF4:Er3+

V. N. Lisin, В. В. Самарцев, Шегеда Анатолий Михайлович +2 more

It is reported about the first observation and studying of the photon echo in LuLiF4:Er3+. The energy transition is 4I15/2→4F9/2 (λ=6536 Å). The density of ErF3 is 0.025 wt%. The operation temperature is 1.9 K. Measurements were spent at low (up to 1200 Oe) and even zero external magnetic fields. It was studied a behavior of the photon echo intensity versus the magnetic field magnitude and direction about the crystal axis C and versus the laser pulse separation t 12. It was observed an exponential growth and then, after some plateau, an exponential decreasing of the photon echo intensity as a function of magnetic field with increasing of the magnetic field from zero value. The parameters describing the exponential growth and decreasing are not depended on direction of magnetic field. Value of a magnetic field at which the echo intensity accepts the maximum, and quantity of this maximum decrease with increased the pulse separation t 12 and the angle θ between the magnetic field and crystal axis. The echo intensity exponentially decreases with increased θ. The parameter describing the exponential decreasing is not depended on the magnitude of the field. The echo intensity as a function of pulse separation shows exponential decay. The phase relaxation time is depended on the magnitude and direction of the magnetic field. T 2 is equal to 202±16 ns at zero magnetic field. Phenomenological formula is suggested, which qualitatively presents the mentioned dependencies. Polarization properties of the backward photon echo in this crystal are studied also.

Laser Physics Letters•Apr 26, 2006•8 citations
The physical reasons for observing the splitting of optical lines several orders of magnitude smaller than the spectral width of a laser pulse are investigated. A theory of coherent and incoherent photon echo (PE) in an external static magnetic field and in the presence of a pulsed magnetic field, which causes oscillations of the PE intensity, is elaborated. It is shown that the periods of oscillations in the echo intensity, the echo duration, and the dimensions of the regions in the inhomogeneous line, where the excited ions are coherent, do not depend on the degree of coherence of the laser pulse and on the external static magnetic field. As follows from the theory, in the case of the coherent excitation of the echo, the amplitude of the intensity oscillations is independent of the external static magnetic field if the inhomogeneous line is symmetric. It is shown that the amplitude of the oscillations at the incoherent excitation of the echo is equal to the autocorrelation function of the distribution function of the transition frequency along the inhomogeneous line with the argument equal to the Zeeman splitting of the optical line in the external magnetic field. In this case, the experimental values of the oscillation amplitude are in good agreement with the calculated values of the autocorrelation function for the total inhomogeneous line in LuLiF 4 :Er 3+ ( 4 I 15/2 ⇒F 9/2 transition). In the same way, the autocorrelation function has been obtained for YLiF 4 :Er 3+ on the same transition.
A method of high-resolution time-resolved optical spectroscopy using oscillations of the photon echo intensity in the presence of a perturbation, which splits the optical frequencies of the transitions of two or more ion subgroups, has been proposed and demonstrated. This method has been applied to systems in which the Zee-man effect is manifested. The transition frequencies of ions are switched by a pulsed magnetic field. Oscillations of the photon echo intensity were observed in LiLuF4:Er3+ and LiYF4:Er3+. The first minimum corresponding to the accumulated phase of the electric dipole moment π/2 is reached in the pulsed magnetic field with an amplitude of ∼2 G at a duration of 30 ns. The Zeeman splitting in this field is ∼10 MHz, which is much less than the laser spectral width (0.15 Å ∼ 9 GHz). The g factor of the 4 F 9/2(I) excited state of the Er3+ ion in the LiLuF4 matrix has been determined in zero magnetic field. The comparison with the g-factor value found from the measurement of the absorption spectrum in a magnetic field of 8 kG has been performed.
Abstract The effect of an incoherent photon echo is studied experimentally and theoretically in 7 LiYF Er 3+ crystal ( transition). This is considered as a promising material for Raman optical quantum memory due to the extremely narrow optical transitions. Oscillations of the photon echo intensity versus the external static magnetic field are observed. The theory shows that the oscillation period is very sensitive to one of the parameters of the spin Hamiltonian in the excited state, thereby making the incoherent photon echo convenient for spectroscopic measurements.
A spectroscopy method has been proposed involving a change in the time shape of the echo signal in the presence of a perturbation, which splits the frequencies of the transitions of two or more ion subgroups of the echo-active ions. This method has been applied to optical systems in which the Zeeman effect is manifested. The ion transition frequencies of ions are switched by a weak pulsed magnetic field acting during the time of the radiation of the photon echo pulse. The modulation of the photon echo signal shape was observed in LuLiF4:Er3+ and YLiF4:Er3+. The time interval between the two nearest minima corresponds to the accumulated phase of the electric dipole moment π and makes it possible to determine the difference of the g factors of the ground and excited 4 F 9/2(I) states of the Er3+ ion in the LuLiF4 the YLiF4 matrices for the known amplitude of the pulsed magnetic field. It has been shown that the echo response of the system can be programmed by the weak magnetic field pulses.
A new scheme of the definition of g-factors as ground and excited optical states of a paramagnetic ion in zero external constant magnetic field has been proposed and experimentally realized in optical systems in which the Zeeman effect is manifested. A pulse of a weak magnetic field leads to the occurrence of relative phase shifts of the excited dipoles and, as a consequence, to modulation of a photon echo wave form if the magnetic pulse overlaps in time with the echo pulse. The modulation periods of the wave form depend on polarization of the laser light which excites the photon echo. The values of these periods for σ - and π -laser light polarization have been measured and then the g-factors of the ground 4 I 15/2 and excited 4 F 9/2 states of the Er 3+ ion in the LuLiF 4 and the YLiF 4 matrices have been determined. The g-factor values have been compared with the known literary data.
It is reported about the first observation and studying of the photon echo in LuLiF4:Er3+. The energy transition is 4I15/2→4F9/2 (λ=6536 Å). The density of ErF3 is 0.025 wt%. The operation temperature is 1.9 K. Measurements were spent at low (up to 1200 Oe) and even zero external magnetic fields. It was studied a behavior of the photon echo intensity versus the magnetic field magnitude and direction about the crystal axis C and versus the laser pulse separation t 12. It was observed an exponential growth and then, after some plateau, an exponential decreasing of the photon echo intensity as a function of magnetic field with increasing of the magnetic field from zero value. The parameters describing the exponential growth and decreasing are not depended on direction of magnetic field. Value of a magnetic field at which the echo intensity accepts the maximum, and quantity of this maximum decrease with increased the pulse separation t 12 and the angle θ between the magnetic field and crystal axis. The echo intensity exponentially decreases with increased θ. The parameter describing the exponential decreasing is not depended on the magnitude of the field. The echo intensity as a function of pulse separation shows exponential decay. The phase relaxation time is depended on the magnitude and direction of the magnetic field. T 2 is equal to 202±16 ns at zero magnetic field. Phenomenological formula is suggested, which qualitatively presents the mentioned dependencies. Polarization properties of the backward photon echo in this crystal are studied also.