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Soviet Journal of Quantum Electronics

Excitation of the coherence of an optically orientable atomic ensemble by a pulsed magnetic field

G. V. Skrotskiǐ, G. I. Solomakho

Published Mar 31, 1974• 0 citations
Publisher

Abstract

It is shown that a perturbation of an optically oriented ensemble of atoms by a nonadiabatically applied external magnetic field makes the density matrix of the ground state generally nondiagonal. The appearance of nonzero nondiagonal elements of the density matrix (i.e., the appearance of coherence) between different Zeeman states is manifested not only by the appearance of transverse components of the magnetization but also by the excitation of nonequilibrium higher-order multipole moments. In particular, if the initial state is oriented, a transverse magnetic field pulse produces an oriented nonequilibrium state. A discussion is given of the possibility of optical detection of nonequilibrium states produced in this way and of their relaxation.

DOI
10.1070/qe1974v004n03abeh006763

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New Journal of Physics•Mar 8, 2011•11 citations
It is shown that a perturbation of an optically oriented ensemble of atoms by a nonadiabatically applied external magnetic field makes the density matrix of the ground state generally nondiagonal. The appearance of nonzero nondiagonal elements of the density matrix (i.e., the appearance of coherence) between different Zeeman states is manifested not only by the appearance of transverse components of the magnetization but also by the excitation of nonequilibrium higher-order multipole moments. In particular, if the initial state is oriented, a transverse magnetic field pulse produces an oriented nonequilibrium state. A discussion is given of the possibility of optical detection of nonequilibrium states produced in this way and of their relaxation.
The relaxation and generation of multipole orientations in a heavy-alkali-metal vapor in the presence of a weak static magnetic field are theoretically studied both for populations and for Zeeman coherences by taking into account the effects on the evolution of the atomic density matrix of the relaxation processes (by alkali-atom--buffer-gas, alkali-atom--alkali-atom with spin exchange and alkali-atom--cell-wall collisions) and of the optical pumping with any light polarization and spectral distribution. The dependence of the stationary-state multipole orientations on the pumping characteristic parameters is numerically analyzed. The detection process of these orientations is also studied.
In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.
A density-matrix approach has been developed for the angular distribution and polarization of radiative emission during single-photon atomic transitions for a general set of steady-state excitation processes in an arbitrary arrangement of static (or quasistatic) electric and magnetic fields. Particular attention has been directed at spectroscopic observations in the intense fields of the high-power ion diodes on the Particle Beam Fusion Accelerator II (PBFA II) and SABRE devices at Sandia National Laboratories and at magnetic-field measurements in tokamak plasmas. The field-dependent atomic eigenstates are represented as expansions in a complete basis set of field-free bound and continuum eigenstates. Particular emphasis has been given to directed-electron collisional excitations, which may be produced by an anisotropic incident-electron velocity distribution. We have allowed for the possibility of the coherent excitation of the nearly degenerate field-dependent atomic substates, which can give rise to a complex spectral pattern of overlapping Stark-Zeeman components. Coherent excitations may be produced by a beam of electrons that are spin-polarized at an angle with respect to the propagation direction or by nonparallel electric and magnetic fields. Our main result is a general expression for the matrix elements of the photon-polarization density operator representing the total intensity, angular distribution, and polarization of the atomic radiative emission. For the observation of radiative emission in the direction of the magnetic field, the detection of linearly polarized emission, in addition to the usual circularly polarized radiation, can reveal the presence of a perpendicular electric field or a coherent excitation mechanism.
We report an investigation to establish the physical mechanisms responsible for decoherence in the generation of photon pairs from atomic ensembles, via the protocol of Duan et al. for long-distance quantum communication [Nature (London) 414, 413 (2001)] and present the experimental techniques necessary to properly control the process. We develop a theory to model in detail the decoherence process in experiments with magneto-optical traps. The inhomogeneous broadening of the ground state by the trap magnetic field is identified as the principal mechanism for decoherence. The theory includes the Zeeman structure of the atomic hyperfine levels used in the experiment, and the polarization of both excitation fields and detected photons. In conjunction with our theoretical analysis, we report a series of measurements to characterize and control the coherence time in our experimental setup. We use copropagating stimulated Raman spectroscopy to access directly the ground-state energy distribution of the ensemble. These spectroscopic measurements allow us to switch off the trap magnetic field in a controlled way, optimizing the repetition rate for single-photon measurements. With the magnetic field off, we then measure nonclassical correlations for pairs of photons generated by the ensemble as a function of the storage time of the single collective atomic excitation. We report coherence times longer than $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, corresponding to an increase of two orders of magnitude compared to previous results in cold ensembles. The coherence time is now two orders of magnitude longer than the duration of the excitation pulses. The comparison between these experimental results and the theory shows good agreement. Finally, we employ our theory to devise ways to improve the experiment by optical pumping to specific initial states.
A perturbation method was used to solve optical Bloch equations (OBEs) for the transition F g =1→ F e =2, in order to describe the role of ground-level Zeeman coherences in the formation of electromagnetically induced absorption (EIA). A narrow Lorentzian peak, centered at zero value of the scanning magnetic field, appears in the analytical expression of the second-order correction of a density-matrix element for ground-level Zeeman coherences, (ρ g −1 , g +1 ) x 2 . Through analytical expressions for lower-order corrections of density-matrix elements, we were able to establish clear relations between the narrow Lorentzian in (ρ g − 1 , g +1 ) x 2 and higher-order corrections of optical coherences, i.e. EIA. We see from analytical expressions that these two resonances have opposite signs and that EIA becomes electromagnetically induced transparency (EIT) in the limit of low efficiency of spontaneous transfer of coherences from excited-level to ground-level Zeeman sublevels. The transient behavior of EIA follows the time evolution of (ρ g − 1 , g +1 ) x 2 . After the coupling laser is turned on, both the Lorentzian peak in (ρ g − 1 , g +1 ) x 2 and EIA reach steady state via over-damped oscillations.