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Journal of the Physical Society of Japan

Magnetic Nature of the Relaxed Excited State of F Centers and Spin Flipping Processes in the Optical Pumping Cycle

Hiroshi Ohkura, Katsushi Tara, Norio Akiyama, Kiyokazu Iwahana, Yuzo Mori

Published Nov 1, 1982• 15 citations
Publisher

Abstract

The magnetic nature of the relaxed excited state (RES) of F centers and spin-flipping processes in the optical pumping cycle have been clarified by studying the magnetic circular polarization (MCP) of emission when the pumping light is modulated between right and left circular polarization at the frequency of (ω/2π). Paramagnetic component Δ p (ω) of MCP is found to be proportional to the spin polarization P * (ω) in the RES with a proportionality constant F p . From the analysis of the dependence of Δ p (ω) at particular frequencies on the pumping photon energy E p h , F p is estimated. Thus, the E p h -dependence of the net spin-mixing parameter ε t is determined. The values of F p and ε t are found to be smaller than those determined previously. The source of discrepancy is discussed. It is suggested that the spin-mixing in the non-radiative transition process is not neglected.

DOI
10.1143/jpsj.51.3615

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The magnetic nature of the relaxed excited state (RES) of F centers and spin-flipping processes in the optical pumping cycle have been clarified by studying the magnetic circular polarization (MCP) of emission when the pumping light is modulated between right and left circular polarization at the frequency of (ω/2π). Paramagnetic component Δ p (ω) of MCP is found to be proportional to the spin polarization P * (ω) in the RES with a proportionality constant F p . From the analysis of the dependence of Δ p (ω) at particular frequencies on the pumping photon energy E p h , F p is estimated. Thus, the E p h -dependence of the net spin-mixing parameter ε t is determined. The values of F p and ε t are found to be smaller than those determined previously. The source of discrepancy is discussed. It is suggested that the spin-mixing in the non-radiative transition process is not neglected.
Magnetic circular polarization (MCP) of F centar emission has been measured for KCl, KBr, KI, RbCl, and RbBr. The optical pumping cycle is proposed to include three spin mixing parameters in absoption, radiationless decay ( ε r1 ), and emission processes. From the analysis of experimental data using formulae derived from rate equations for the cycle, para- and dia-magnetic components ( Δ p and Δ d ) of MCP, and the spin mixing parameters are determined. Pumping photon energy dependence of Δ p are observed. It shows that ε r1 for KBr depends on photon energy and predominates the net spin mixing parameter ( ε t ). Temperature dependence of Δ d are shown to be relevant to the spin orbit interaction in the relaxed excited state of F center. The source of the discrepancy found between our determined values of ε t and those by other schools is clarified.
The magnetic property of the relaxed excited state (RES) of the F center has been manifested by the experimental and theoretical study of the magnetic circular polarization (ΔMCP) of the F center emission. The para- and diamagnetic components (Δp and Δd) of ΔMCP as well as the g-shift of the RES have been experimentally determined. From the comparison of these values with those computed values on the vibronic theory, the spin-orbit interaction constant, the orbital g-factor, and the spin polarization of the RES are determined. The tuning photon energy dependence of Δp is observed. The spin-memory-loss during radiationless decay is found to be significant. The temperature dependence of Δd is mentioned.
When the pumping light is modulated between right and left circular polarization, the magnetic circular polarization of F center luminescence observed after passing through a linear polarizer has been called “the anomalous effect”. We measured this effect for the F center in KI as a function of the magnetic field H and the photon energy. These experimental data are explained by deriving a form which includes the parameter ( ε I ) for the unbalancing of circular polarization in pumping light and the spin-lattice relaxation rate of the relaxed excited state ( T 1 * ) -1 . The H -dependence of ( T 1 * ) -1 is presented.
We have solved the rate equations of the optical pumping cycle of the FFF center in the case of two spin-mixing parameters, ${\ensuremath{\epsilon}}_{+}$ and ${\ensuremath{\epsilon}}_{\ensuremath{-}}$. The solutions and the experimental results for the magnetic circular dichroism of the FFF-center emission are in complete agreement, and have allowed for the first time the measurement of the "anisotropy" of the electron-spin memory, i.e., $\frac{({\ensuremath{\epsilon}}_{\ensuremath{-}}\ensuremath{-}{\ensuremath{\epsilon}}_{+})}{({\ensuremath{\epsilon}}_{\ensuremath{-}}+{\ensuremath{\epsilon}}_{+})}$. This quantity will be very useful in order to clarify the role of the various processes responsible for the loss of the spin memory in the optical cycle. Moreover, from the rate equations we have been able to find the value of the polarization in the relaxed excited state, which is essential to calculate the spin-orbit splitting in emission.
Introduction Soon after the development of optical magnetometers based on the radio-optical double resonance method (see Chapter 4), it was realized by Bell and Bloom [1] that an alternative method for optical magnetometry was to modulate the light used for optical pumping at a frequency resonant with the Larmor precession of atomic spins. In a Bell-Bloom optical magnetometer, circularly polarized light resonant with an atomic transition propagates through an atomic vapor along a direction transverse to a magnetic field B . Atomic spins immersed in B precess at the Larmor frequency Ω L , and when the light intensity is modulated at Ω m = Ω L , a resonance in the transmitted light intensity is observed. The essential ideas of the Bell–Bloom optical magnetometer are reviewed in Chapter 1 (Section 1.2), and can be summarized in terms of what Bell and Bloom termed optically driven spin precession: in analogy with a driven harmonic oscillator, in a magnetic field B atomic spins precess at a natural frequency equal to Ω L and the light acts as a driving force oscillating at the modulation frequency Ω m . From another point of view, the Bell-Bloom optical magnetometer can be described in terms of synchronous optical pumping: when Ω m = Ω L , there is a “stroboscopic” resonance in which atoms are optically pumped into a spin state stationary in the frame rotating with Ω L . Depending on the details of the atomic structure, the spin state stationary in the rotating frame can be either a dark state that does not interact with the modulated light or a bright state for which the strength of the light–atom interaction is increased.
We have performed quantitative measurements of the variation of the on-resonance absorption coefficients ${\ensuremath{\kappa}}_{0}$ of the four hyperfine components of the Cs D1{D}_{1}D1​ transition as a function of laser power PPP, for pumping with linearly and with circularly polarized light. Sublevel populations derived from rate equations assuming isotropic population relaxation (at a rate ${\ensuremath{\gamma}}_{1}$) yield algebraic ${\ensuremath{\kappa}}_{0}(P)$ dependences that do not reproduce the experimental findings from Cs vapor in a paraffin-coated cell. However, numerical results that consider spin-exchange relaxation (at a rate ${\ensuremath{\gamma}}_{\mathrm{se}}$) and isotropic relaxation fit the experimental data perfectly well. The fit parameters, viz., the absolute value of ${\ensuremath{\kappa}}_{0}$, the optical pumping saturation power Psat{P}_{\mathrm{sat}}Psat​, and the ratio ${\ensuremath{\gamma}}_{\mathrm{se}}/{\ensuremath{\gamma}}_{1}$, are well described by the experimental conditions and yield absolute values for ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{\mathrm{se}}$. The latter is consistent with the previously published Cs-Cs spin-exchange relaxation cross section.