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Bloch vector projection noise

Lijun Wang, A. M. Bacon, H. Z. Zhao, John E. Thomas

Published May 1, 1994• 0 citations
OpenAlex

Abstract

In the optical measurement of the Bloch vector components describing a system of N two-level atoms, the quantum fluctuations in these components are coupled into the measuring optical field. This paper develops the quantum theory of optical measurement of Bloch vector projection noise. The preparation and probing of coherence in an effective two-level system consisting of the two ground states in an atomic three-level lambda-scheme are analyzed.

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In the optical measurement of the Bloch vector components describing a system of N two-level atoms, the quantum fluctuations in these components are coupled into the measuring optical field. This paper develops the quantum theory of optical measurement of Bloch vector projection noise. The preparation and probing of coherence in an effective two-level system consisting of the two ground states in an atomic three-level lambda-scheme are analyzed.
I study the coherent interaction of a three-level atom in the lambda configuration with pump, Stoke, and anti-Stokes laser fields. The pump laser field drives transitions from the two non-degenerate lower levels to the excited state which is highly detuned for either transition. This excited state is also coupled to each of the lower states by Stokes or anti-Stokes transitions so that this system may represent a model of four-wave mixing. Assuming large detunings, the excited state is adiabatically eliminated from obtaining an effective two-level system with Raman coupling between the levels. Optical Bloch equations are obtained for this effective two-level system, and phenomenological damping terms are added for collisional dephasing of the Raman transitions. The equations are solved for the steady-state as well as by the method of adiabatic following. From these solutions we obtain the polarization.
Every measurement of the population in an uncorrelated ensemble of two-level systems is limited by what is known as the quantum projection noise limit. Here, we present quantum-projection-noise-limited performance of a Ramsey-type interferometer using freely propagating coherent atoms. The experimental setup is based on an electro-optic modulator in an inherently stable Sagnac interferometer, optically coupling the two interfering atomic states via a two-photon Raman transition. Going beyond the quantum projection noise limit requires the use of reduced quantum uncertainty (squeezed) states. The experiment described demonstrates atom interferometry at the fundamental noise level and allows the observation of possible squeezing effects in an atom laser, potentially leading to improved sensitivity in atom interferometers.
The noise-induced coherence created via the quantum interference of incoherent radiation in atomic three-level systems of V and \ensuremath{\Lambda} types driven by a pair of weak laser pulses is shown to result in exchange of optical vortices. In the three- level V-type atom-light coupling the system is populated in its ground level, while in the \ensuremath{\Lambda} model the system is initially prepared in an electromagnetically induced transparency state. By solving the quantum optical Maxwell-Bloch equations and with quantum interference of incoherent radiation present, we show that the orbital angular momentum (OAM) of the vortex probe beam can be transferred to a generated signal field. While the exchange efficiency in the V configuration is higher, the losses are less in the \ensuremath{\Lambda} scheme when we consider such a noise-induced coherence. We further discuss the effects of phase mismatching and inhomogeneous broadening on the energy conversion between light beams carrying OAM.
We measure phase-dependent optical noise spectra for a simple system: long-lived coherently driven two-level atoms in an atomic beam. Very different noise spectra are measured for radiation which is in phase and out of phase with the driving field. The spectra and corresponding analysis afford clear insights into the roles played by three distinct sources of atomic noise. The measured noise spectra are in good agreement in magnitude and shape with results of a quantum treatment using no free parameters.