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arXiv:quant-ph/0307028 · Journal of Optics B Quantum and Semiclassical Optics

Characterizing the spin state of an atomic ensemble using the magneto-optical resonance method

Brian Julsgaard, Jacob Friis Sherson, Jens Lykke Sørensen, Eugene Simon Polzik

Published Sep 24, 2003• 62 citations
arXivHTMLPDF

Abstract

Quantum information protocols utilizing atomic ensembles require preparation of a coherent spin state (CSS) of the ensemble as an important starting point. We investigate the magneto-optical resonance method for characterizing a spin state of caesium atoms in a paraffin coated vapour cell. Atoms in a constant magnetic field are subject to an off-resonant laser beam and an RF magnetic field. The spectrum of the Zeeman sub-levels, in particular the weak quadratic Zeeman effect, enables us to measure the spin orientation, the number of atoms, and the transverse spin coherence time. Notably the use of 894 nm pumping light on the D1 line, ensuring the state F = 4, m F = 4 is a dark state, helps us to achieve spin orientation of better than 98%. Hence we can establish a CSS with high accuracy, which is critical for the analysis of the entangled states of atoms.

DOI
10.1088/1464-4266/6/1/002

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Quantum information protocols utilizing atomic ensembles require preparation of a coherent spin state (CSS) of the ensemble as an important starting point. We investigate the magneto-optical resonance method for characterizing a spin state of caesium atoms in a paraffin coated vapour cell. Atoms in a constant magnetic field are subject to an off-resonant laser beam and an RF magnetic field. The spectrum of the Zeeman sub-levels, in particular the weak quadratic Zeeman effect, enables us to measure the spin orientation, the number of atoms, and the transverse spin coherence time. Notably the use of 894 nm pumping light on the D1 line, ensuring the state F = 4, m F = 4 is a dark state, helps us to achieve spin orientation of better than 98%. Hence we can establish a CSS with high accuracy, which is critical for the analysis of the entangled states of atoms.
In this work we investigate the magneto-optical resonance on 87Rb D1 line. In two-level degenerated system this resonance is due to the interference between the Zeeman sub-levels, created by interaction of resonance linear polarized laser beam with the atoms. The observed signal is detected by sweeping magnetic field B around its zero value. This phenomenon is also known as a Coherent Population Trapping (CPT) in Hanle-configuration. In a coated vacuum cell the fluorescence signal has a complex form, because the anti-relaxation coating preserves the created coherence, having different relaxation rates. The ground state coherence is transmitted by the laser field to the upper level; thereby polarization moments with different rank contribute to the fluorescence. The manifestation of the different polarization moments in the observed signal depends on the geometry of the experiment – direction of observation, plane of the laser polarization, polarization of the registered light. The resonances obtained in the fluorescence having different polarization are compared in order to clear up what are the contributions to the fluorescent signal from the polarization moments with different rank. The experiment is performed on the D1 87Rb line, F=2→ F=1 transition in a paraffin-coated cell. The magneto-optical resonances, detected in two orthogonal polarizations are measured. Numerical calculations with parameters, close to the experimental ones are performed by using a program, which is based on the irreducible tensor operator formalism. The results of the modelling are compared with the measured ones at different experimental conditions.
Atomic spin polarization of alkali atoms in the ground-state can survive thousands of collisions with paraffin-coated cell walls. The resulting long spin-relaxation times achieved in evacuated, paraffin-coated cells enable precise measurement of atomic spin precession and energy shifts of ground-state Zeeman sublevels. In the present work, nonlinear magneto-optical rotation with frequency-modulated light (FM NMOR) is used to measure magnetic field-induced spin precession for rubidium atoms contained in a paraffin-coated cell. The magnetometric sensitivity of FM NMOR for the rubidium D2 line is studied as a function of light power, detuning, frequency-modulation amplitude, and rubidium vapor density. For a 5-cm-diameter cell at temperature T≈35 °C, the optimal shot-noise-projected magnetometric sensitivity is found to be 2×10−11 G/Hz (corresponding to a sensitivity to spin precession frequency of ≈10 μHz/Hz or a sensitivity to Zeeman sublevel shifts of ≈4×10−20 eV/Hz).
In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.
We demonstrate the accurate determination of the magnetic strength of a microwave field utilizing the dressed cesium atom as a sensor. A bias magnetic field is initially used to split the Zeeman levels of the ground state. Its value is carefully selected to ensure that the microwave field to be measured is closely resonant to a pair of selected hyperfine Zeeman levels ( | F = 3 , m F = 3 ⟩ and | F = 4 , m F = 4 ⟩ ), while other states are neglected. This approach significantly simplifies the interaction model. A weak radio-frequency magnetic field is utilized to drive atoms away from the specified magnetic quantum number state to its neighbor, whose population imbalance is supervised by optical readout. The long atomic transverse relaxation time due to the antirelaxation coatings of alkali-metal-vapor cells makes it possible to precisely depict the interaction between atoms and the microwave field. Consequently, the microwave field can be accurately determined with an uncertainty of less than 1% even beyond 100 nT, corresponding to a radio-frequency spectral line broadening less than 100 Hz. The features we have identified enable us to expand the possibilities of developing new metrology for measuring microwave fields in an alternative way.
A symmetric magneto-optical resonance arising from the single two-quantum RF transition $|{F}_{g}=1,{m}_{{F}_{g}}=\ensuremath{-}1\ensuremath{\rangle}\ensuremath{\leftrightarrows}|{F}_{g}=1,\phantom{\rule{4pt}{0ex}}{m}_{{F}_{g}}=1\ensuremath{\rangle}$ in an optically aligned atomic ensemble is studied in the case when the quadratic Zeeman shift exceeds the width of the resonance. It is shown that the signal-to-noise ratio of the resonance can be significantly increased by applying the phase modulation to the RF field at a frequency close to the value of quadratic Zeeman shift. This theoretical prediction is corroborated by the experimental results with 87Rb^{87}\mathrm{Rb}87Rb atoms. The proposed technique can be used in magnetometers based on atomic alignment or by utilizing multiquantum RF resonances in optically oriented atomic ensembles.
The relaxation of atomic polarization in buffer-gas-free, paraffin-coated cesium vapor cells is studied using a variation on Franzen's technique of ``relaxation in the dark'' [Franzen, Phys. Rev. 115 850 (1959)]. In the present experiment, narrow-band, circularly polarized pump light, resonant with the Cs D2 transition, orients atoms along a longitudinal magnetic field, and time-dependent optical rotation of linearly polarized probe light is measured to determine the relaxation rates of the atomic orientation of a particular hyperfine level. The change in relaxation rates during light-induced atomic desorption (LIAD) is studied. No significant change in the spin relaxation rate during LIAD is found beyond that expected from the faster rate of spin-exchange collisions due to the increase in Cs density.