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

Polarization-sensitive correlation spectroscopy of atomic medium

V. V. Batygin, Dmitriy V. Kupriyanov, Igor M. Sokolov

Published May 6, 1996• 0 citations
Publisher

Abstract

We have considered general polarization-sensitive correlation measurement of light intensity fluctuations based on a Hanbury Brown and Twiss interference detection scheme for probe radiation passed through angular momentum polarized atomic ensemble put into external magnetic field. The general theory is applied to the correlation spectroscopy of the atomic medium with spin ground state characterized by large relaxation times. We show and discuss the possibility of squeezing effect in transmitted light that can be caused by polarization- dependent interaction of the probe radiation with oriented atoms.

DOI
10.1117/12.239846

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We have considered general polarization-sensitive correlation measurement of light intensity fluctuations based on a Hanbury Brown and Twiss interference detection scheme for probe radiation passed through angular momentum polarized atomic ensemble put into external magnetic field. The general theory is applied to the correlation spectroscopy of the atomic medium with spin ground state characterized by large relaxation times. We show and discuss the possibility of squeezing effect in transmitted light that can be caused by polarization- dependent interaction of the probe radiation with oriented atoms.
We discuss the possibilities for using the correlation spectroscopy technique to study an atomic medium polarized in angular momentum. The general results of our previous paper are applied here to the analysis of the density matrix fluctuations of an atomic medium with a spin ground state. Such systems are characterized by a long ground state relaxation time in comparison with the excited state natural lifetime, so that any fluctuation of the atomic density matrix polarization is slowly dependent on the time process. We show how the quantum behaviour of low-frequency fluctuations can be observed via quantum features of scattered light statistics. In particular, we discuss the squeezing of transmitted light caused by the spin angular momentum orientation in the direction of an external magnetic field. This squeezing effect is explained by quantum non-commutation of angular momentum projections which are transverse to the magnetic field. Other applications of the polarization-sensitive correlation spectroscopy technique, such as the possible observation of the average atomic density matrix components and the measurement of different spectroscopic characteristics of the atomic ensemble, are also discussed.
We discuss general polarization-sensitive correlation measurements of light fluctuations based on the Hanbury Brown and Twiss interference detection scheme. Such measurements are considered as a basis for correlation spectroscopy, which allows us to observe the correlations of the fluctuations of all polarization components (Stokes parameters) of the probe light. The interferometer scheme is discussed in application to the study of the polarization-dependent interaction of light with an atomic ensemble with polarized angular momentum and put into an external magnetic field. We describe the general procedure for evaluating the photocurrent correlation function in the case of an optically thin atomic medium. Our calculations are based on the Keldysh diagram technique which is usually used for the study of non-equilibrium systems by means of the second quantized formalism. It allows us to express the Raman field-correlation functions and parametric scattering processes describing the output light fluctuations in terms of a different type of time-ordered electric field and atomic Green functions. We show that with definite conditions the photocurrent correlation function can be written as the sum of two terms proportional to the correlation functions of atomic density matrix fluctuations in symmetric and antisymmetric forms. This expression of the photocurrent correlation function can be used in various different applications.
The sensitivity of measurements in the different schemes of optical detection of magnetic resonance in an ensemble of optically orientated paramagnetic atoms has been studied. The authors have considered the standard schemes of transmission monitoring of the atomic angular momenta precession assuming a classical resonant and off-resonant probing light beam as well as interference probing scheme by squeezed radiation. The main attention has been given to the limit accuracy of Zeeman transition frequency determination in these experiments. The circumstances limiting the radiation intensity increase in these experiments have been discussed.
We investigate the properties of angular-momentum states which yield high sensitivity to rotation. We discuss the application of these ``squeezed-spin'' or correlated-particle states to spectroscopy. Transitions in an ensemble of N two-level (or, equivalently, spin-1/2) particles are assumed to be detected by observing changes in the state populations of the particles (population spectroscopy). When the particles' states are detected with 100% efficiency, the fundamental limiting noise is projection noise, the noise associated with the quantum fluctuations in the measured populations. If the particles are first prepared in particular quantum-mechanically correlated states, we find that the signal-to-noise ratio can be improved over the case of initially uncorrelated particles. We have investigated spectroscopy for a particular case of Ramsey's separated oscillatory method where the radiation pulse lengths are short compared to the time between pulses. We introduce a squeezing parameter ${\ensuremath{\xi}}_{\mathit{R}}$ which is the ratio of the statistical uncertainty in the determination of the resonance frequency when using correlated states vs that when using uncorrelated states. More generally, this squeezing parameter quantifies the sensitivity of an angular-momentum state to rotation. Other squeezing parameters which are relevant for use in other contexts can be defined. We discuss certain states which exhibit squeezing parameters ${\ensuremath{\xi}}_{\mathit{R}}$\ensuremath{\simeq}${\mathit{N}}^{\mathrm{\ensuremath{-}}1/2}$. We investigate possible experimental schemes for generation of squeezed-spin states which might be applied to the spectroscopy of trapped atomic ions. We find that applying a Jaynes-Cummings--type coupling between the ensemble of two-level systems and a suitably prepared harmonic oscillator results in correlated states with ${\ensuremath{\xi}}_{\mathit{R}}$1.
We have discussed the possibilities of correlation spectroscopy (light beating spectroscopy) technique if squeezed light is used as a probe radiation for medium monitoring. The dispersion of the fluctuation of photocurrent spectrum measured in this method is expressed in terms of fourth order photocurrent correlation function. This correlation function is considered and evaluated in assumptions of photodetection theory developed by Glauber in first nonvanishing orders in interaction of probe light with the atoms of a photodetector. We show that fourth order correlation function is determined by all field TN-ordered amplitude correlation functions up to the fourth order. In case of heterodyne detection, when the light incident on photodetector surface is the mix of strong coherent modes of local oscillator wave and weak non-coherent (squeezed) modes, the observable (photocurrent spectrum) as well as its fluctuation (noise of photocurrent spectrum) is expressed in terms of spectrum-dependent Mandel parameter. We have discussed possible improvement of sensitivity limit for correlation spectroscopy in this case.
At the beginning of the 20th century measurement precision was related exclusively to the capabilities of the experimenter and the apparatus. Any imprecision was attributed to imperfect devices for the measurement. Later on, when the quantumness of objects like photons, electrons, or atoms, was recognized, it became clear that the measurement and the object to be measured could no longer be separated. Both follow the laws of quantum physics which impose limits on the accuracy of any measurement. In the last three decades, a lot of research has been dedicated to find strategies to overcome these limitations. This new field of quantum metrology is where this work is placed. This thesis describes the generation of interparticle entanglement in form of a squeezed spin state in a cloud of cold 87Rb atoms by performing nondestructive spin measurements. Towards this goal, we have implemented a shot-noise limited polarization probing and detection system, atom counting by means of absorption imaging, spin state preparation via optical pumping and nondestructive spin state detection. The quantum noise limited spin readout with polarized light is characterized in two complementary ways in terms of sensitivity and all possible quantum and classical noise sources are measured. To address the rich opportunities provided in the multilevel structure of 87Rb with dispersive probing, we have developed and implemented a frequency offsetlock which allows a large tuning range of several GHz for the dispersive probing. Working with a magnetically sensitive atomic system triggered the development of a magnetic field imaging technique. This applies the elongated atomic sample and internal atomic states as a way of measuring magnetic fields over several millimeters with micrometer resolution and sensitivities down to a few tens of pT/ Hz. We developed a new method for tomographic measurements of the atomic density matrix. Based on our ability of shot noise limited detection of polarization rotations we can in principle, characterize the whole atomic spin state. First, measurements are shown and possible improvements are discussed. An in depth characterization of the light-atom interaction between polarized pulses of light and collective atomic states are the basis for measurements at the quantum level. On one side, we apply classical measurements of spin polarized atoms to measure the strength of the lightatom interaction. On the other side, we use quantum measurements of unpolarized atomic states to characterize all noise sources both technical and quantum. One of the major results of this thesis is the realization of quantum nondemolition measurements in a largespin system. We realized limitations to the performance of the QND measurement implied by higher order light shifts in multilevel atoms, which are often neglected for these kind of systems. We develop a technique which suppresses the detrimental effects of higher order light shifts and recovers an ideal QND measurement. The thesis culminates in the demonstration of spin squeezing in the magnetically sensitive ground state of 87Rb. We achieve a quantum noise reduction by 3 dB, where metrological sensitivity is improved by 2 dB beyond the standard quantum limit of a coherent spin state with the same spin polarization. We address the question how spatial and temporal inhomogeneities both in light and atoms influence the preparation of nonclassical states. An existing covariance matrix approach is extended and we apply it to study effects of detector time resolution, spatial inhomogeneities and atomic motion.