We show that the description of light in terms of Stokes operators in combination with the assumption of Gaussian statistics results in a dramatic simplification of the experimental study of fluctuations in the light transmitted through an atomic vap
or: no local oscillator is required, the detected quadrature is easily selected by a wave-plate angle and the complete noise ellipsis reconstruction is obtained via matrix diagonalization. We provide empirical support for the assumption of Gaussian statistics in quasi-resonant light transmitted through an $^{87}$Rb vapor cell and we illustrate the suggested approach by studying the evolution of the fluctuation ellipsis as a function of laser detuning. Applying the method to two light beams obtained by parting squeezed light in a beamsplitter, we have measured entanglement and quantum discord.
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.
We describe the development of a simple atomic magnetometer using $^{87}$Rb vapor suitable for Earth magnetic field monitoring. The magnetometer is based on time-domain determination of the transient precession frequency of the atomic alignment aroun
d the measured field. A sensitivity of 1.5 nT/$sqrt{Hz}$ is demonstrated on the measurement of the Earth magnetic field in the laboratory. We discuss the different parameters determining the magnetometer precision and accuracy and predict a sensitivity of 30 pT/$sqrt{Hz}$
We have studied relative-intensity fluctuations for a variable set of orthogonal elliptic polarization components of a linearly polarized laser beam traversing a resonant $^{87}$Rb vapor cell. Significant polarization squeezing at the threshold level
(-3dB) required for the implementation of several continuous variables quantum protocols was observed. The extreme simplicity of the setup, based on standard polarization components, makes it particularly convenient for quantum information applications.
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 sublev
el 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 of (Zeeman) multi-level configurations are identified.
