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AIP conference proceedings

Population trapping in the case of hyperfine components and nuclear decay

David F. Zaretsky, S. B. Sazonov

Published Jan 1, 1995• 0 citations
Publisher

Abstract

The new method of Doppler‐free nuclear spectroscopy is propsed. The method is based on the resonance interaction of bichromatic laser light with the atom having the hyperfine structure in its ground state. The population of hyperfine components in the model Λ‐case is calculated and the polarization rate dependence on the laser powers and the phase difference is established. The case of nonstable atoms is considered and the angular distribution of nuclear decay γ‐quanta is calculated. The ways of experimental realization of the method proposed are discussed.

DOI
10.1063/1.47543

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The new method of Doppler‐free nuclear spectroscopy is propsed. The method is based on the resonance interaction of bichromatic laser light with the atom having the hyperfine structure in its ground state. The population of hyperfine components in the model Λ‐case is calculated and the polarization rate dependence on the laser powers and the phase difference is established. The case of nonstable atoms is considered and the angular distribution of nuclear decay γ‐quanta is calculated. The ways of experimental realization of the method proposed are discussed.
We propose a Doppler-free spectroscopic method named bichromatic crossover spectroscopy (BCS), which we then use for the frequency stabilization of an off-resonant frequency that does not correspond to an atomic transition. The observed BCS in the 5S1/2 → 5P1/2 transition of 87Rb is related to the hyperfine structure of the conventional saturated absorption spectrum of this transition. Furthermore, the Doppler-free BCS is numerically calculated by considering all of the degenerate magnetic sublevels of the 5S1/2 → 5P1/2 transition in an atomic vapor cell, and is found to be in good agreement with the experimental results. Finally, we successfully achieve modulation-free off-resonant locking at the center frequency between the two 5S1/2(F = 1 and 2) → 5P1/2(F′ = 1) transitions using a polarization rotation of the BCS. The laser frequency stability was estimated to be the Allan variance of 2.1 × 10−10 at 1 s.
A method is proposed for fast and deep polarization of the system of hyperfine sublevels of the ground state of an atom having an optical excited state by means of two-component microwave pulses. The pulse of the bichromatic optical field that induces the transitions between the ground state and excited state of the atom is supposed to provide coherence among the hyperfine sublevels of the atomic ground state via the effect of coherent population trapping. The subsequent resonance microwave pulses create the polarization of equally populated ground state sublevels of the atom. The proposed polarization technique may be used for designing the new schemes of quantum computers, for the pulse transformation in optical experiments when light passes through a resonant medium containing rear-earth ions, as well as for producing polarized nuclear targets.
We consider the resonant interaction between atoms with hyperfine energy levels and a bichromatic radio-frequency field. Nuclear Zeeman levels of an impurity center in a magnetic host form a structure of this kind. Using the spin-density-matrix formalism, we solve the problem of coherent repopulation of a system of three of these levels under the action of a bichromatic resonant radio-frequency wave, taking into account transverse relaxation, and note the connection between this effect and the well-known phenomenon of coherent population capture when a laser bichromatic field interacts resonantly with a three-level system. We discuss various possibilities for observation of this effect experimentally.
A new source of the bichromatic laser field with a stable mean value of the difference frequency is used to study coherent population trapping (CPT). A high stability of the difference phase of the fields of the radiation source is achieved by phase locking the radiation frequency of two semiconductor lasers to longitudinal modes of a femtosecond laser. The first experimental results on the spectroscopy of CPT resonances in rubidium are presented. The possibility of using the new method for spectroscopy of CPT resonances in rare-earth atom vapours is discussed.
We have developed and tested an efficient mathematical model for calculating a coherent population trapping (CPT) resonance in a periodically modulated laser field when the modulation frequency fff is close to the fractional part of the hyperfine splitting frequency (HFS) in the ground state ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{HFS}}/N$ (where N=1,2,3,…N=1,2,3,\dots{}N=1,2,3,…). In such a polychromatic light, only two frequency components that are most resonant with the working optical transitions in the atom are taken into account exactly, while all other off-resonant frequency components are taken into account by using the second-order perturbation theory in the field magnitude. Within the framework of our concept, an equation for the atomic density matrix is obtained, in which all off-resonant frequency components are described by two operators (which are nondiagonal in the general case): a shift operator and a relaxation operator. This model has been verified by numerical calculations for various dependencies, in which we have not found visual differences from the results of exact calculations. Thus, in our bichromatic model, the infinite variety of periodically modulated fields in CPT spectroscopy can be uniformly described by only five parameters. In addition to a significant mathematical simplification, our model provides a clear physical picture of the various features of CPT spectroscopy in a periodically modulated laser field, including some effects that have not yet been discussed in the scientific literature. In particular, we show a widespread viewpoint that the CPT resonance shift is determined by standard ac Stark shifts of the lower levels is, in general, fundamentally incorrect, since the contribution to the light shift due to beats at the frequency ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{HFS}}$ between different off-resonant frequency components can be comparable to the value of standard ac Stark shift (or even dominate it). Therefore, even if we have detailed information on the spectral composition of the modulated field (e.g., using a spectrum analyzer), this is, in general, absolutely insufficient for determining the light shift of the CPT resonance.
We report measurements of the degree of linear polarization of scattered light as a function of excitation frequency near the Doppler-broadened NaD2\mathrm{Na} D2NaD2 resonance line. For resonant excitation of the D2D2D2 line, the hyperfine interaction strongly depolarizes the emitted light due to precession of the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ prior to spontaneous emission. However, as the laser frequency is tuned away from resonance, the polarization degree sharply rises to the level predicted using a simple JMJJ{M}_{J}JMJ​ basis, i.e., neglecting any coupling of the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ with the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$. Roughly speaking, there is a transition from FFF selection rules ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}+\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$) for resonant excitation to JJJ selection rules for off-resonant excitation. We present a rigorous calculation of the polarization degree with the use of multipole moments of the density matrix which agrees quantitatively with our data and also predicts complicated interference structure when Doppler broadening is negligible. We show that this structure may shift peaks observed in precision laser-spectroscopy experiments. For Doppler-broadened transitions we discuss a simplified approach (based on an approximation to the Voigt profile) which treats separately the contributions of resonant and off-resonant scattering.