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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Spontaneous coherent population trapping effect in atoms+field system

А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published May 10, 1996• 0 citations
Publisher

Abstract

For jg equals j yields je equals j - 1 and jg equals j yields je equals j optical transitions (where jg, je are the total angular momenta of ground (g) and excited (e) states) previously unknown exact solution of quantum self-consistent problem on resonant atom-electromagnetic field interaction is found. This solution describes arbitrary set of field modes having same uniform elliptical polarization and atoms being in noninteracting with field coherent population trapping (CPT)-state. Some peculiarities of this spontaneous CPT-effect are investigated. We define the geometrical conditions (the relative orientation of light and static fields) for the existence of spontaneous CPT-effect in atoms + quantized field system in the presence of external static magnetic and electric fields.

DOI
10.1117/12.239483

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For jg equals j yields je equals j - 1 and jg equals j yields je equals j optical transitions (where jg, je are the total angular momenta of ground (g) and excited (e) states) previously unknown exact solution of quantum self-consistent problem on resonant atom-electromagnetic field interaction is found. This solution describes arbitrary set of field modes having same uniform elliptical polarization and atoms being in noninteracting with field coherent population trapping (CPT)-state. Some peculiarities of this spontaneous CPT-effect are investigated. We define the geometrical conditions (the relative orientation of light and static fields) for the existence of spontaneous CPT-effect in atoms + quantized field system in the presence of external static magnetic and electric fields.
A full quantum treatment of coherent population trapping (CPT) is given for a system of resonantly coupled atoms and electromagnetic field. We develop a regular analytical method of the construction of generalized dark states (GDS). It turns out that GDS do exist for all optical transitions FgtoFeF_g\\to F_eFg​toFe​, including bright transitions FtoF+1F\\to F+1FtoF+1 and F′′toF′′F''\\to F''F′′toF′′ with F′′F''F′′ a half-integer, for which the CPT effect is absent in a classical field.
We consider peculiarities of coherent population trapping (CPT) effect on magnetic sublevels of fine structure levels for Thallium (TI) atoms. The system of levels taken into account consists of eight levels. By considering spontaneous decay onto the levels of thermostat we have found the solutions of Schroedinger equation in resonant approximation and so we have found the populations of magnetic sublevels. We have considered different geometries of experiment. Among them there are the cases for which the polarization vectors of both components of radiation fields are parallel to each other and parallel or perpendicular to magnetic field, polarization vectors are perpendicular to each other (one of them is parallel to magnetic field). Also the orientation of magnetic field may be parallel or perpendicular to wave vector of radiation field. Also we have considered different initial populations of magnetic sublevels. In contrary to trivial initial populations of sublevels of the ground state of an atom we have considered the initial population of another metastable fine structure level of TI atom. This situation can take place for atomic photofragments produced in the photodissotiation of diatomic molecules.
A full quantum treatment of coherent population trapping (CPT) is given for a system of resonantly coupled atoms and electromagnetic field. We develop a regular analytical method of the construction of generalized dark states (GDS). It turns out that GDS do exist for all optical transitions F g → F e , including bright transitions F → F + 1 and F '' → F '' with F '' a half-integer, for which the CPT effect is absent in a classical field. We propose an idea to use an optically thick medium with a transition F '' → F '' with F '' ⩾ 3/2 a half-integer as a "quantum filter", which transmits only a quantum light with limited number of photons. Such a quantum filter can be used as a deterministic source of Fock's state of light.
The motion of previously cooled atoms in a spatial grating formed by lin (perpendicular) lin laser field configuration and the static uniform magnetic field is considered in the case of Fg equals 1 yields Fe equals 1 transition. We show that in the case of high intensity laser fields (when Rabi frequency is greater than Zeeman splitting, Doppler shift, natural width, and detuning) atoms are captured in long-lived coherent population trapping (CPT) state while heating, incoherent photon scattering, and atom-atom photon exchange are strongly reduced. The frequency, the damping time of oscillation, and the localization size are obtained for atoms moving near the bottom of potential wells in the frame of harmonic approximation. Narrowing of vibrational spectral lines due to the CPT-effect is predicted.
In order to investigate effects of coherent population trapping (CPT) on electromagnetically induced transparency (EIT), we added an external weak magnetic field to identify a quantization axis. The laser beam whose polarization is parallel to the direction of the external magnetic field and the perpendicular laser are coupled to different transitions. CPT generated by two circular polarization components of the strong coupling beam when the polarization was perpendicular to the quantization axis, was competed with (EIT) so that absorption reduction could be larger than the case without CPT. We investigated the mechanism of steady-state light amplification without inversion using an incoherent pumping laser.
At the conditions of two-photon resonance the effect of coherent population trapping (CPT) can take place. The CPT may be observed as in absorption so in resonance fluorescence. The CPT is widely applied in high resolution spectroscopy, laser cooling, atomic optics and so on. Earlier the peculiarities of CPT resonances on fine structure levels of an atom have been considered on example of thallium atoms. It was shown that the form and number of resonances are influenced by geometry of experiment and initial conditions (initial level populations). As the investigations of CPT on fine structure levels are the object of interest last years, we have considered the numerical analysis of dependence the form of CPT resonances on fine structure levels of T1 atoms as lower levels of Λ-system on polarization of radiation fields. The cases of elliptical, linear and circular polarization have been considered.