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Journal of Experimental and Theoretical Physics Letters

New possibilities for producing photon echoes from a homogeneous ensemble of atoms and with the use of a single light pulse

G. N. Nikolaev

Published May 1, 1997• 0 citations
Publisher

Abstract

In investigations of predicted new types of photon echoes — an echo from a homogeneous ensemble of atoms and an echo of a single light pulse — have established that the magnitude and form of these new types of photon echoes are completely determined by the type of optical transition and by the “area” and polarization of the exciting light pulses (and the form can be controlled by varying the magnetic field). It is also established that the echo amplitude decreases for both small (compared to 1) and large light-pulse areas, and the optimal areas for which the maximum echo is obtained have been found. Investigations show that such photon echoes can also appear under conditions when an ordinary photon echo is absent (in atomic or molecular gases at high pressure, in the far-IR region of the spectrum, from cooled trapped atoms or ions, and so on).

DOI
10.1134/1.567425

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The active use of resonators in quantum technologies increases the interest of their application in the creation of optical and microwave quantum memory. The use of photon and spin echoes opens up the possibility of storing a large number of light pulses in one such memory cell. High efficiency of such quantum memory is achieved in an optically dense resonant media, in which the formation of a photon (spin) echo can be accompanied by an increase in the nonlinear interaction of light with atoms causing the appearance of multiple echo signals. In this paper, we develop the pulse area approach to study general nonlinear properties of the primary and multi-pulse echo signals excited in a two-level atomic ensemble located in ring cavities with volumetric and surface modes. Conditions under which one or more echo pulses can be generated are analyzed. The solutions obtained are compared with recent experimental results. We show that the area theorem is one of the simplest and most powerful analytical tools for studying a highly nonlinear and dynamical process of the formation of the sequence of photon/spin echo signals in resonant media inside the resonator.

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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.

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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
In investigations of predicted new types of photon echoes — an echo from a homogeneous ensemble of atoms and an echo of a single light pulse — have established that the magnitude and form of these new types of photon echoes are completely determined by the type of optical transition and by the “area” and polarization of the exciting light pulses (and the form can be controlled by varying the magnetic field). It is also established that the echo amplitude decreases for both small (compared to 1) and large light-pulse areas, and the optimal areas for which the maximum echo is obtained have been found. Investigations show that such photon echoes can also appear under conditions when an ordinary photon echo is absent (in atomic or molecular gases at high pressure, in the far-IR region of the spectrum, from cooled trapped atoms or ions, and so on).
In the limit of small exciting light-pulse areas the amplitude and polarization of the tri-level photon echo in gases formed by the exciting pulses with arbitrary shapes are obtained. It is shown that the dependence of the tri-level photon echo signal on the mutual orientation of the exciting pulse polarization vectors may be used to determine the optical coherence-matrix relaxation characteristics for an optically forbidden transition. The conditions under which a tri-level photon echo pulse repeats the shape of each of the exciting pulses are defined. It is proved that the tri-level photon-echo polarization properties do not depend on the shapes of the exciting pulses, either for small light-pulse areas or for the tri-level echo formation on narrow spectral lines.
Pulse area approach has been established as a versatile analytical tool for studying the resonant interaction between the light and the resonant atomic ensemble. In recent years photon and spin echoes in cavity assisted schemes become increasingly interesting. In this article we develop the photon echo pulse area approach to describe primary and multi-pulse echo generation in the atomic ensemble placed in the ring cavity. We show that the pulse area approach predicts relative echo magnitudes and whether the system is operating in a single- or a multi-pulse generation regime. We also analyze the conditions needed for the realization of these generation regimes. This work develops the pulse area theorem approach for analytical study of photon/spin echoes in optical and microwave cavities and echo based protocols of quantum memory.
A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the 3 P 0-3 H 6 transition in impurity praseodymium ions in the LaF3 matrix upon ultrashort coherent excitation of the adjacent optically allowed 3 H 4-3 P 0 transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the 3 P 0-3 H 6 generation transition and completely eliminates polarization at the 3 H 4-3 P 0 excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden 3 H 6-3 H 4 transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.
The active use of resonators in quantum technologies increases the interest of their application in the creation of optical and microwave quantum memory. The use of photon and spin echoes opens up the possibility of storing a large number of light pulses in one such memory cell. High efficiency of such quantum memory is achieved in an optically dense resonant media, in which the formation of a photon (spin) echo can be accompanied by an increase in the nonlinear interaction of light with atoms causing the appearance of multiple echo signals. In this paper, we develop the pulse area approach to study general nonlinear properties of the primary and multi-pulse echo signals excited in a two-level atomic ensemble located in ring cavities with volumetric and surface modes. Conditions under which one or more echo pulses can be generated are analyzed. The solutions obtained are compared with recent experimental results. We show that the area theorem is one of the simplest and most powerful analytical tools for studying a highly nonlinear and dynamical process of the formation of the sequence of photon/spin echo signals in resonant media inside the resonator.
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 SF6{\mathrm{F}}_{6}F6​ excited by pulses of CO2{\mathrm{O}}_{2}O2​ laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions (PPP and RRR 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 (QQQ 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 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.