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Physical Review A

Spin noise measurement with diamagnetic atoms

Makoto Takeuchi, S. Ichihara, T. Takano, M. Kumakura, Yoshiro Takahashi

Published Jun 27, 2007• 6 citations
Publisher

Abstract

We report the measurement of the atomic spin noise of the diamagnetic atom ytterbium (Yb). Yb has various merits for utilizing the quantum nature of the atomic spin ensemble compared with the paramagnetic atoms used in all previous experiments. From the magnitude of the noise level and dependence on the detuning, we concluded that we succeeded in the measurement of $^{171}\mathrm{Yb}$ atomic spin noise in an atomic beam.

DOI
10.1103/physreva.75.063827

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We report the measurement of the atomic spin noise of the diamagnetic atom ytterbium (Yb). Yb has various merits for utilizing the quantum nature of the atomic spin ensemble compared with the paramagnetic atoms used in all previous experiments. From the magnitude of the noise level and dependence on the detuning, we concluded that we succeeded in the measurement of 171Yb^{171}\mathrm{Yb}171Yb atomic spin noise in an atomic beam.
We report observation of the paramagnetic Faraday rotation of spin-polarized ytterbium (Yb) atoms. As the sample of the atoms, we used atomic beam, released atom from magneto-optical trap (MOT), and trapped atoms in far-off-resonant trap (FORT). Since Yb is diamagnetic and has spin-1/2 isotope, it is an ideal sample for the spin physics, such as quantum non-demolition measurement of spin (spin QND), for example. From the results of the rotation angle, we confirmed that the atoms were almost perfectly polarized.
We explore the applications of spin noise spectroscopy (SNS) for detection of the spin properties of atomic ensembles in and out of equilibrium. In SNS, a linearly polarized far-detuned probe beam on passing through an ensemble of atomic spins acquires the information of the spin correlations of the system which is extracted using its time-resolved Faraday-rotation noise. We measure various atomic, magnetic and sub-atomic properties as well as perform precision magnetometry using SNS in rubidium atomic vapor in thermal equilibrium. Thereafter, we manipulate the relative spin populations between different ground state hyperfine levels of rubidium by controlled optical pumping which drives the system out of equilibrium. We then apply SNS to probe such spin imbalance non-perturbatively. We further use this driven atomic vapor to demonstrate that SNS can have better resolution than typical absorption spectroscopy in detecting spectral lines in the presence of various spectral broadening mechanisms.
The spin-noise mechanisms in a spin-1 system are theoretically and experimentally investigated in detail. Eight different independent spin degrees of freedom are isolated, leading to spin-noise signals at the Larmor frequency or its second harmonic in the presence of a magnetic field. The signatures of these different modes of the detuned probe light beam polarization fluctuations, observed either as Faraday rotation noise or as ellipticity noise, are shown to depend dramatically on the probed transition. In particular, depending on the Zeeman structure of the upper level of the transitions, the different noise modes can be visible or not, and their dependence on the probe polarization can be completely modified. Those predictions are successfully compared with measurements of spin-noise signals using three different transitions of an ensemble of metastable 4He^{4}\mathrm{He}4He at room temperature.
Spin noise spectroscopy (SNS) allows optically detect the fluctuations of a spin ensemble. Such fluctuations induce noise in the birefringence of the medium, which can be probed by recording polarization fluctuations of a laser beam after its propagation through the sample. As spin fluctuations are centered on the zero frequency, a transverse magnetic field is applied: spin precession then shifts the spin noise resonance at the Larmor frequency, so that it is not hidden by technical noises. The first SNS experiment was reported in the early 1980s by Alexandrov and Zapasskii, but it is only in 2004 that advances in narrow linewidth lasers and low noise electronics allow using this technique to probe various systems, such as thermal atomic vapors, semiconductors, or quantum wells. It was also proposed for magnetic field sensing, and possible measurements of correlations beyond the second-order raise a lot of interest, as they can give access to new quantum phenomena. We have performed spin noise spectroscopy in a metastable helium gas cell, and show that we can get two polarization dependent noise peaks when we record the linear instead of the circular birefringence fluctuations. Moreover, the relatively simple structure of helium allows us to show that it depends on the closest optical transition even when we are detuned by more than the Doppler broadening. We can also show that the behavior of the polarization dependence is strongly affected by time dependent B-field fluctuations. We performed simulations using a density matrix time evolution model, with added random fluctuations. It reproduces quite well the experimental results, including the transition dependence and the time dependent B-field noise effect, which have not been reported yet.
State of the art atomic sensors operate near the standard quantum limit (SQL) of projection noise, and overcoming this limit by using atom-atom entanglement such as spin squeezing is a major goal in quantum metrology. By coupling an ensemble of approximately 1000 Yb-171 atoms to a high-finesse asymmetric micromirror cavity with single-atom cooperativity of 1.8., we produce a near-unitary spin squeezed state. The observed spin noise suppression and metrological gain are limited by the state readout to 9.4(4) dB and 6.5(4) dB, respectively, while the generated states offer a spin noise suppression of 15.9(6) dB and a metrological gain of 12.9(6) dB over the standard quantum limit, limited by the curvature of the Bloch sphere. When requiring the squeezing process to be within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2).
We investigate theoretically and experimentally a nondestructive interferometric measurement of the state population of an ensemble of laser-cooled and trapped atoms. This study is a step toward generation of (pseudo)spin squeezing of cold atoms targeted at the improvement of the cesium clock performance beyond the limit set by the quantum projection noise of atoms. We calculate the phase shift and the quantum noise of a near-resonant optical probe pulse propagating through a cloud of cold 133Cs^{133}\mathrm{Cs}133Cs atoms. We analyze the figure of merit for a quantum nondemolition (QND) measurement of the collective pseudospin and show that it can be expressed simply as a product of the ensemble optical density and the pulse-integrated rate of the spontaneous emission caused by the off-resonant probe light. Based on this, we propose a protocol for the sequence of operations required to generate and utilize spin squeezing for the improved atomic clock performance via a QND measurement on the probe light. In the experimental part we demonstrate that the interferometric measurement of the atomic population can reach a sensitivity of the order of Nat\sqrt{{N}_{\mathrm{at}}}Nat​​ in a cloud of Nat{N}_{\mathrm{at}}Nat​ cold atoms, which is an important benchmark toward the experimental realization of the theoretically analyzed protocol.