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arXiv:0712.4303

Quantum-noise-limited Angular Momentum Measurement for a Micron-sized Dielectric Object

Koji Usami

Published Dec 28, 2007• 1 citation
arXivHTMLPDF

Abstract

An approach is described for observing quantum features of micron-sized spinning objects. Specifically, we consider a birefringent (uniaxial positive) dielectric object in the shape of an oblate (i.e., frisbee-like) symmetric top. It can be trapped in the air, its extraordinary axis can be aligned, and its angular momentum along the extraordinary axis can be stabilized, all optically. We show that the angular momentum quantum noise of the object perpendicular to the gigantic angular momentum along the extraordinary axis can be measured as a linear birefringent phase shift of a probe laser in an analogous fashion to the spin quantum nondemolition (QND) measurement in atomic physics.

DOI
10.48550/arxiv.0712.4303

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An approach is described for observing quantum features of micron-sized spinning objects. Specifically, we consider a birefringent (uniaxial positive) dielectric object in the shape of an oblate (i.e., frisbee-like) symmetric top. It can be trapped in the air, its extraordinary axis can be aligned, and its angular momentum along the extraordinary axis can be stabilized, all optically. We show that the angular momentum quantum noise of the object perpendicular to the gigantic angular momentum along the extraordinary axis can be measured as a linear birefringent phase shift of a probe laser in an analogous fashion to the spin quantum nondemolition (QND) measurement in atomic physics.
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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.
Quantum nondemolition (QND) measurement enhances the detection efficiency and measurement fidelity, and is highly desired for its applications in precision measurements and quantum information processing. We propose and demonstrate a QND measurement scheme for the spin states of laser-trapped atoms. On 171Yb{}^{171}\mathrm{Yb}171Yb atoms held in an optical dipole trap, a transition that is simultaneously cycling, spin-selective, and spin-preserving is created by introducing a circularly polarized beam of a control laser to optically dress the spin states in the excited level, while leaving the spin states in the ground level unperturbed. We measure the phase of spin precession of $5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ atoms in a bias magnetic field of 20 mG. This QND approach reduces the optical absorption detection noise by $\ensuremath{\sim}19\phantom{\rule{0.2em}{0ex}}\mathrm{dB}$, to an inferred level of 2.3 dB below the atomic quantum projection noise. In addition to providing a general approach for efficient spin-state readout, this all-optical technique allows quick switching and real-time programming for quantum sensing and quantum information processing.
In a recent letter [Auzinsh {\it{et. al.}} (physics/0403097)] we have analyzed the noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of NNN atomic spins by detecting optical rotation of far-detuned probe light. Here we consider maximally squeezed probe light, and carry out a detailed derivation of the contribution to the noise in a magnetometric measurement due to the differential AC Stark shift between Zeeman sublevels arising from quantum fluctuations of the probe polarization.
Quantum non-demolition measurement with an off-resonance polarized probe is a widely utilized technique for atomic sensors. Typically, QND instruments read out spin states through optical polarimetry using a linearly off-resonance probe in atomic media. This optical read-out process offers high accuracy, with potential applications in biomagnetism, inertial navigation and new physics exploration beyond the standard model. It was observed that previously unexplored spin-alignment polarization induced by the far-detuned off-resonance linear probe in an ultrasensitive optical polarimetry. The evolution of probe-generated multipole moments exacerbates probe noise due to strong magnetic couplings. A method was demonstrated to decouple spin-alignment from magnetic fields by manipulating the multipole moments in zero fields. A suppression of the probe noise by 8.2 dB at 1 Hz and 10.4 dB at 10 Hz with the proposed method, reaching the standard quantum limit, was achieved. The realized shot-noise-limited optical polarimetry shows significant potential for advancing the performance of atomic sensors, particularly in applications requiring ultra-high sensitivity, such as precision measurements and quantum metrology. These findings provide a pathway toward enhanced sensor precision in diverse scientific and technological applications.
Optical rotation detection system (ORDS) utilizing quantum nondemolition (QND) measurement methods is widely applied in the field of quantum metrology and quantum information. However, the sensitivity of ORDS is limited by the uncertainty from optical-couple noise during the measurement of the atomic spin ensemble. In this study, we specifically analyze the mechanism of optical-couple noise caused by the fluctuations of probe light’s polarization in the modulated ORDS with a new model established to describe atomic spin precession in this particular condition. It is discovered that transverse electron-spin polarization errors are generated by the residual probe photon spin polarization in the ORDS, which results in extra coupling magnetic noise. In order to suppress this noise, a novel in situ method is proposed that the resultant electron-spin errors are reduced by a specifically designed closed-loop system. The results are verified through the ORDS in a co-magnetometer. After zeroing the extra probe photon spin polarization, an angular sensitivity better than1×10−81 \times 10 ^{\mathrm {-8}}1×10−8rad/Hz1/2^{\mathrm {1/2}}1/2is achieved for frequencies higher than 5 Hz, demonstrating a probe background noise of 0.26 fT/Hz1/2^{\mathrm {1/2}}1/2@14.5 Hz, approaching electronic noise and photon shot noise (PSN). With closed-loop control, the optical rotation bias instability is promoted by 4.2 times (from 107.9 to$25.7 \mu $rad/h), and the angular noise of the ORDS is reduced by 2.4 times at 1–100 Hz. The measurement uncertainty of the realized ORDS nears the standard quantum limit, paving the road for long-term ultrasensitive measurements for new physics explorations.