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arXiv:1502.07868 · Physical Review A

Fluctuation properties of laser light after interaction with an atomic system: Comparison between two-level and multilevel atomic transitions

A. Lezama, Riadh Rebhi, Anders Kastberg, Sébastien Tanzilli, Robin Kaiser

Published Sep 28, 2015• 6 citations
arXivHTMLPDF

Abstract

The complex internal atomic structure involved in radiative transitions has an effect on the spectrum of fluctuations (noise) of the transmitted light. A degenerate transition has different properties in this respect than a pure two-level transition. We investigate these variations by studying a certain transition between two degenerate atomic levels for different choices of the polarization state of the driving laser. For circular polarization, corresponding to the textbook two-level-atom case, the optical spectrum shows the characteristic Mollow triplet for strong laser drive, while the corresponding noise spectrum exhibits squeezing in some frequency ranges. For a linearly polarized drive, corresponding to the case of a multilevel system, additional features appear in both optical and noise spectra. These differences are more pronounced in the regime of a weakly driven transition: whereas the two-level case essentially exhibits elastic scattering, the multilevel case has extra noise terms related to spontaneous Raman transitions. We also discuss the possibility to experimentally observe these predicted differences for the commonly encountered case where the laser drive has excess noise in its phase quadrature.

DOI
10.1103/physreva.92.033853

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The complex internal atomic structure involved in radiative transitions has an effect on the spectrum of fluctuations (noise) of the transmitted light. A degenerate transition has different properties in this respect than a pure two-level transition. We investigate these variations by studying a certain transition between two degenerate atomic levels for different choices of the polarization state of the driving laser. For circular polarization, corresponding to the textbook two-level-atom case, the optical spectrum shows the characteristic Mollow triplet for strong laser drive, while the corresponding noise spectrum exhibits squeezing in some frequency ranges. For a linearly polarized drive, corresponding to the case of a multilevel system, additional features appear in both optical and noise spectra. These differences are more pronounced in the regime of a weakly driven transition: whereas the two-level case essentially exhibits elastic scattering, the multilevel case has extra noise terms related to spontaneous Raman transitions. We also discuss the possibility to experimentally observe these predicted differences for the commonly encountered case where the laser drive has excess noise in its phase quadrature.
By means of quantum stochastic calculus we construct a model for an atom with two degenerate levels which is stimulated by a circularly polarized laser and we compute its fluorescence spectrum. Let us stress that, once the model for the unitary atom–field dynamics has been given, then the spectrum is computed without further approximations. If only the absorption/emission term is included in the interaction, we reobtain the Mollow spectrum in the case of a monochromatic laser and the Kimble–Mandel spectrum in the case of a ‘phase diffusion model’ for a non-monochromatic laser. However, our model can also describe another type of light scattering, a ‘direct scattering’ due to the response of the atom as a whole, which we expect to be small but which interferes with the scattering due to the absorption/emission channel. When both the scattering channels are introduced we obtain a modification of the Mollow–Kimble–Mandel spectrum, which shares its main features with the usual case, but which presents some asymmetries even in the case of no detuning.
We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field, and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving-field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific to (Zeeman) multilevel configurations are identified.
We have investigated theoretically the possibility of employing noisy laser fields for spectroscopic purposes. The basis for this spectroscopy is a modification of the statistic of the fluctuations caused by the nonlinear interaction. All atomic resonances within the range of several bandwidths can be observed in the power spectrum, even in case of large inhomogeneous broadening. We have derived analytical, nonperturbative results for a real Gaussian, a complex Gaussian, and a phase-diffusing field. The mean transmitted intensity and its variance as well as the power spectrum have been evaluated in the limit of weak absorption for two-level systems. Without modification, we can apply our results also to other transition schemes. As an example, the power spectrum of the D2{\mathit{D}}_{2}D2​ transition of 133Cs^{133}\mathrm{Cs}133Cs driven by a phase-diffusing field is calculated. For this four-level system we find qualitative agreement with experimental results by Yabuzaki et al. [Phys. Rev. Lett. 67, 2453 (1991)].
Summary form only given. The problem of an atom driven by a strong laser was first investigated theoretically in 1969 by B.R. Mollow. He discovered that the resonance fluorescence spectrum has a three-peaked structure with the central peak being more pronounced than the two side peaks. The common Mollow triplet fluorescence pattern can be altered in many ways, by making adjustments to the system. The system can be placed in a squeezed vacuum, the atom can be placed in a cavity, or a bichromatic field can be used instead of a monochromatic laser. These alterations all have an effect on the resulting resonance fluorescence and probe absorption spectra. Other interesting modifications occur when the atom interacts with a stochastic field as well as a laser. The previous approaches were numerical. Here we also obtain analytic solutions (in certain limits) which provide additional insight.
We investigate different kinds of polarization-correlated-emission schemes, including a maser and a laser concept. In these systems, coherently prepared atoms drive the electromagnetic field. We demonstrate that the atomic coherence can lead to a reduction of noise fluctuations within a linear theory. In the homogeneously broadened case the amplitude noise is strongly affected by the atomic coherence, leading to noise quenching in the laser and even squeezing in the maser. On the other hand, the phase fluctuations are unaffected by the coherence between the lasing levels. We then study the effect of inhomogeneous broadening of the atomic transition frequency. We find the interesting result that the noise reduction due to the atomic coherence is not destroyed but redistributed between the phase and amplitude of the electromagnetic field.
The absorption properties of degenerate two-level atomic systems tested by a weak probe field in the presence of an intense pump field have been analyzed. The theoretical model previously presented in Phys. Rev. A 61, 013801 (1999) that appears to be suitable for arbitrary choices of the pump intensity, level angular momenta, and pump and probe polarizations, was used for the calculation of the spectra for several basic configurations. Experimental absorption spectra obtained on a Rb atomic beam for different pump and probe field polarizations show good agreement with the calculation. The spectra are in general essentially different from and more complex than the classical Mollow absorption triplet.