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arXiv:1403.0420 · Scientific Reports

Faraday rotation echo spectroscopy and detection of quantum fluctuations

Shao-Wen Chen, Ren-Bao Liu

Published Apr 15, 2014• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/srep04695

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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.
Abstract The correlations of fluctuations are key to studying fundamental quantum physics and quantum many‐body dynamics. They are also useful information for understanding and combating decoherence in quantum technology. Nonlinear spectroscopy and noise spectroscopy are powerful tools to characterize fluctuations, but they can access only very few among the many types of higher‐order correlations. A systematic quantum sensing approach, called quantum nonlinear spectroscopy (QNS), is recently proposed for extracting arbitrary types and orders of time‐ordered correlations, using sequential weak measurement via a spin quantum sensor. However, the requirement of a central spin as the quantum sensor limits the versatility of the QNS since usually a central spin interacts only with a small number of particles in proximity and the measurement of single spins needs stringent conditions. Here, the aim is to employ the polarization (a pseudo‐spin) of a coherent light beam as a quantum sensor for QNS. After interacting with a target system (such as a transparent magnetic material), the small Faraday rotation of the linearly polarized light can be measured, which constitutes a weak measurement of the magnetization in the target system. Using a Mach–Zehnder interferometer with a designed phase shift, one can post‐select the effects of the light–material interaction to be either a quantum evolution or a quantum measurement of the material magnetization. This way, the correlated difference photon counts of a certain number of measurement shots, each with a designated interference phase, can be made proportional to a certain type and order of correlations of the magnetic fluctuations in the material. The analysis of the signal‐to‐noise ratios shows that the second‐order correlations are detectable in general under realistic conditions and higher‐order correlations are significant when the correlation lengths of the fluctuations are comparable to the laser spot size (such as in systems near the critical points). Since the photon sensor can interact simultaneously with many particles and interferometry is a standard technique, this protocol of QNS is advantageous for studying quantum many‐body systems.
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.
Detailed experimental analysis of photon echo polarization in a longitudinal magnetic field is performed for the first time at the simplest quantum transition J = 1 ↔ J = 0 for which the non-Faraday rotation of photon echo polarization plane was predicted. The echo was generated at the intercombination transition (6s6p) 3P1 → (6s2) 1S0 of 174Yb by two resonant laser pulses of linear (parallel or mutually orthogonal) polarization, and the angled echo optical scheme was applied for the detection. At the magnetic field strength ℬ ⩽ 5 G the photon echo has polarization very close to linear one; its polarization plane rotates around magnetic field vector, and photon echo polarization components and integral echo power oscillate versus ℬ from its maximum value to zero, in agreement with theory. At a stronger magnetic field ℬ ∼ 40 G photon echo power oscillations disappear, no preferable orientation of polarization vector is observed; the fluctuations of exciting radiation spectrum are supposed to be responsible for this "non-polarized" echo.
It is known that linear birefringence of the medium essentially hinders measuring the Faraday effect. For this reason, optically anisotropic materials have never been considered as objects of the Faraday-rotation-based spin noise spectroscopy. We show, both theoretically and experimentally, that strong optical anisotropy that may badly suppress the regular Faraday rotation of the medium, practically does not affect the measurement of the spatially uncorrelated spin fluctuations. We also show that the birefringent media provide additional opportunity to measure spatial spin correlations. Results of the experimental measurements of the spin-noise spectra performed on Nd^{3+} ions in the uniaxial crystal matrices well agree with the theory.
We have implemented a continuous measurement of the mean magnetic moment of an ensemble of atoms trapped in a far-off-resonance optical lattice, by detecting the Faraday rotation of one of the lattice beams after it has passed through the atom cloud. In a first demonstration experiment we have observed Larmor precession with high signal-to-noise ratio, and compared the performance of the measurement with a simple theory. Faraday spectroscopy offers an ideal method to monitor the atomic dynamics and will be applied to the study of quantum chaos in magneto-optical lattices. In principle the measurement sensitivity can be increased to the point where quantum backaction becomes significant, thereby opening the door to studies of quantum feedback, spin squeezing and the role played by quantum measurement in quantum/classical correspondence.
We describe a relatively non-invasive optical spectroscopy technique, known as spin noise spectroscopy (SNS), to probe spontaneous magnetization fluctuations in an alkali atomic vapor at thermal equilibrium. The atomic magnetization at a non-zero temperature fluctuates about its equilibrium value, and such magnetization (spin) noise imparts fluctuation in the measured Faraday rotation of a far-detuned, linearly polarized probe laser beam passing through the vapor. This Faraday rotation fluctuation reveals the intrinsic spin dynamics of the electrons in the alkali vapor. We present a systematic experimental study of the SNS realized in thermal rubidium vapor and illustrate how one can measure various magnetic and chemical properties of the sample with minimal perturbation. We also demonstrate the applicability of this spectroscopy technique in measuring the spin populations and their dynamics in different hyperfine and magnetic levels by optically pumping the atomic system.