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Physical Review A

Observation of spin echoes of laser-cooled Rb atoms

Yoshiro Takahashi, Takayuki Shimizu, N. Tanaka, Keita HONDA, K. Toyoda, T. Yabuzaki

Published May 1, 1999• 4 citations
Publisher

Abstract

We have observed gradient spin echoes in the ground state of $\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{r}\ensuremath{-}\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{d}{}^{85}\mathrm{Rb}$ atoms through paramagnetic Faraday rotation. We have obtained the exact expression for the behavior of the echo signal under the assumption that the motion of the cold atoms is ballistic. The qualitative behaviors predicted by the theory have been confirmed experimentally. We demonstrate the usefulness of the spin echo method for the diagnosis for the atomic density distribution of cold atoms. We discuss various advantages of the spin echo as a novel method for temperature measurement.

DOI
10.1103/physreva.59.3761

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We have observed gradient spin echoes in the ground state of laser\ensuremath−cooled85Rb\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{r}\ensuremath{-}\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{d}{}^{85}\mathrm{Rb}laser\ensuremath−cooled85Rb atoms through paramagnetic Faraday rotation. We have obtained the exact expression for the behavior of the echo signal under the assumption that the motion of the cold atoms is ballistic. The qualitative behaviors predicted by the theory have been confirmed experimentally. We demonstrate the usefulness of the spin echo method for the diagnosis for the atomic density distribution of cold atoms. We discuss various advantages of the spin echo as a novel method for temperature measurement.
We have observed gradient spin echoes in the ground state of laser-cooled 85Rb atoms through paramagnetic Faraday rotation. We have obtained the exact expression for the behavior of the echo signal under the assumption that the motion of the cold atoms is ballistic. The qualitative behaviors predicted by the theory have been confirmed experimentally. We demonstrate the usefulness of the spin echo method for the diagnosis for the atomic density distribution of cold atoms. We discuss various advantages of the spin echo as a novel method for temperature measurement.
We have observed Larmor spin precession in the ground state of laser-cooled 85Rb{}^{85}\mathrm{Rb}85Rb atoms through paramagnetic Faraday rotation. We have been able to obtain a precision of 18pT18\mathrm{pT}18pT in the determination of the applied magnetic field, which proves the usefulness of laser-cooled atoms as an atomic magnetometer.
We report noninvasive detection of spin coherence in a collection of Raman-driven cold atoms using dispersive Faraday rotation fluctuation measurements, which opens possibilities of probing spin correlations in quantum gases and other similar systems. We demonstrate five orders of magnitude enhancement of the measured signal strength as compared to traditional spin noise spectroscopy with thermal atoms in equilibrium. Our observations are in good agreement with the comprehensive theoretical modeling of the driven atoms at various temperatures. The extracted spin relaxation rate of cold rubidium atoms with atom number density $\ensuremath{\sim}10{\phantom{\rule{0.16em}{0ex}}}^{9}/{\mathrm{cm}}^{3}$ is of the order of $3\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}10{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ at 150 $\ensuremath{\mu}\mathrm{K}$, two orders of magnitude less than $3\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}10{\phantom{\rule{0.16em}{0ex}}}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ of that of a thermal atomic vapor with atom number density $\ensuremath{\sim}10{\phantom{\rule{0.16em}{0ex}}}^{12}/{\mathrm{cm}}^{3}$ at 373 K.
Central spin decoherence is useful for detecting many-body physics in environments and moreover, the spin echo control can remove the effects of static thermal fluctuations so that the quantum fluctuations are revealed. The central spin decoherence approach, however, is feasible only in some special configurations and often requires uniform coupling between the central spin and individual spins in the baths, which are very challenging in experiments. Here, by making analogue between central spin decoherence and depolarization of photons, we propose a scheme of Faraday rotation echo spectroscopy (FRES) for studying quantum fluctuations in interacting spin systems. The echo control of the photon polarization is realized by flipping the polarization with a birefringence crystal. The FRES, similar to spin echo in magnetic resonance spectroscopy, can suppress the effects of the static magnetic fluctuations and therefore reveal dynamical magnetic fluctuations. We apply the scheme to a rare-earth compound LiHoF4 and calculate the echo signal, which is related to the quantum fluctuations of the system. We observe enhanced signals at the phase boundary. The FRES should be useful for studying quantum fluctuations in a broad range of spin systems, including cold atoms, quantum dots, solid-state impurities, and transparent magnetic materials.
We measured the diffusion coefficient of Rb atoms in N2{\mathrm{N}}_{2}N2​ buffer gas by the constant-gradient spin-echo method. At a temperature of $60\ifmmode^\circ\else\textdegree\fi{}\mathrm{C},$ our measured diffusion coefficient is D0=0.159cm2/s,{D}_{0}=0.159 {\mathrm{cm}}^{2}/\mathrm{s},D0​=0.159cm2/s, which is consistent with values found from polarization decay. We report also the tipping angle dependence of the phase-relaxation time of Rb atoms at high density.