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Optics and Spectroscopy

Manifestation of the Hanle effect in submillimeter EPR spectroscopy of thulium impurity ions in synthetic forsterite

V. F. Tarasov, N. K. Solovarov, Evgeny V. Zharikov

Published Oct 1, 2016• 2 citations
Publisher

Abstract

A signal related to the spin level crossing in a zero magnetic field—the Hanle effect—has been registered for the first time in the EPR spectrum. It has been shown that, in the general case, the shape of the signal is determined by two qualitatively different mechanisms: (i) the interference of unsteady-state contributions to the dynamics of atomic coherences (electric or magnetic quantum transition moments with certain phases) with close frequencies (“beats at a zero frequency”) and (ii) the summation of resonant signals determined by the steady-state dynamics of the same atomic coherences. The relaxation time of spin coherences has been determined for the EPR transition of Tm 3+ ions in synthetic forsterite.

DOI
10.1134/s0030400x16100234

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A microwave analog of the interference Hanle effect has been studied in sodium Rydberg atoms. Spontaneous emission of the microwave transition ${37P}_{3/2}\ensuremath{\rightarrow}{37S}_{1/2}$ at 70.166 GHz was replaced by an induced transition from a pulsed microwave source. A dependence of population of the ${37S}_{1/2}$ state on the magnetic field was recorded in various conditions. Good agreement with the theoretical calculations has been found. The widths and shapes of observed resonances were defined by the spectral widths of the pulsed microwave radiation and parameters of laser excitation of the initial ${37P}_{3/2}$ state. The quantum beats of magnetic sublevels appeared in the signals when the polarization of exciting laser emission was orthogonal to the magnetic field, and the interference occurred in the scheme of transitions similar to the Mach-Zehnder optical interferometer.

Physical Review A•Aug 13, 2001•2 citations
A signal related to the spin level crossing in a zero magnetic field—the Hanle effect—has been registered for the first time in the EPR spectrum. It has been shown that, in the general case, the shape of the signal is determined by two qualitatively different mechanisms: (i) the interference of unsteady-state contributions to the dynamics of atomic coherences (electric or magnetic quantum transition moments with certain phases) with close frequencies (“beats at a zero frequency”) and (ii) the summation of resonant signals determined by the steady-state dynamics of the same atomic coherences. The relaxation time of spin coherences has been determined for the EPR transition of Tm 3+ ions in synthetic forsterite.
The frequency-field and orientation dependences of the electron paramagnetic resonance (EPR) spectra are measured for impurity Tm 3+ ions in yttrium orthosilicate (Y 2 SiO 5 ) single crystals by stationary EPR spectroscopy in the frequency range of 50–100 GHz at 4.2 K. The position of the impurity ion in the crystal lattice and its magnetic characteristics are determined. The temperature dependences of the spin–lattice and phase relaxation times are measured by pulse EPR methods in the temperature range of 5–15 K and the high efficiency of the direct single-phonon mechanism of spin–lattice relaxation is established. This greatly shortens the spin–lattice relaxation time at low temperatures and makes impurity Tm 3+ ions in Y 2 SiO 5 a promising basis for the implementation of high-speed quantum memory based on rare-earth ions in dielectric crystals.
The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.
Parametric resonances associated with zero-field level crossings of the 23S1{2}^{3}{S}_{1}23S1​ level of He4{\mathrm{He}}^{4}He4 have been investigated using transverse optical pumping. A steady-state technique based on the n=0n=0n=0, p=0p=0p=0 resonance (Hanle effect) is used to measure spin-state lifetimes and determine the dependence of the thermal relaxation time on the state of the active helium discharge. The n=0n=0n=0, p=1p=1p=1 resonance is quite strong and suitable for measuring weak magnetic fields. A sensitivity of 1.0 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}8}$ G is demonstrated for this measurement technique.
The optical Hanle effect (light-shift-induced zero-field level crossing) has been investigated theoretically and experimentally. In the case of a $J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0$ three-level system and of a $J=0\ensuremath{\rightarrow}1$ two-level system, the resonance line shape has been obtained using a nonlinear-response-function method. Approximate expressions, valid under the conditions for the observation of light shifts, are obtained and compared with exact calculations as well as with the corresponding expression for the magnetic Hanle effect. As concerns the weak laser beam which produces the coherent excitation of atomic substates, we have calculated the linear response in the limiting case of monochromatic and of broad-band excitation. The experimental investigation has been performed for the Ba resonance line using two cw dye lasers at $\ensuremath{\lambda}=5535$ \AA{} and an atomic beam. The absorption- and dispersion-shaped level crossing resonances have been observed, for narrow- and broad-band excitation, by varying the power of the strong nonresonant laser beam. We have checked that the line shapes are only dependent upon the reduced variable $\frac{{P}_{L}}{\ensuremath{\delta}}$ (PL{P}_{L}PL​; beam power; $\ensuremath{\delta}$: frequency detuning). Using the theoretical expressions, we have tried to fit the experimental curves. Provided that the Gaussian distribution of the beams is taken into account, we have obtained a good agreement between theory and experiment for the whole set of experimental data.
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.
A microwave analog of the interference Hanle effect has been studied in sodium Rydberg atoms. Spontaneous emission of the microwave transition ${37P}_{3/2}\ensuremath{\rightarrow}{37S}_{1/2}$ at 70.166 GHz was replaced by an induced transition from a pulsed microwave source. A dependence of population of the 37S1/2{37S}_{1/2}37S1/2​ state on the magnetic field was recorded in various conditions. Good agreement with the theoretical calculations has been found. The widths and shapes of observed resonances were defined by the spectral widths of the pulsed microwave radiation and parameters of laser excitation of the initial 37P3/2{37P}_{3/2}37P3/2​ state. The quantum beats of magnetic sublevels appeared in the signals when the polarization of exciting laser emission was orthogonal to the magnetic field, and the interference occurred in the scheme of transitions similar to the Mach-Zehnder optical interferometer.