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Optics Express

Ultra-sensitive measurement of small optical rotation angles using quantum entanglement based on a quasi-Wollaston prism beam splitter

Shuai Wang, Jing Zhu, Lianqing Zhu

Published May 1, 2024• 1 citation

Abstract

The measurement of optical rotation is fundamental to optical atomic magnetometry. Ultra-high sensitivity has been achieved by employing a quasi-Wollaston prism as the beam splitter within a quantum entanglement state, complemented by synchronous detection. Initially, we designed a quasi-Wollaston prism and intentionally rotated the crystal axis of the exit prism element by a specific bias angle. A linearly polarized light beam, incident upon this prism, is divided into three beams, with the intensity of each beam correlated through quantum entanglement. Subsequently, we formulated the equations for optical rotation angles by synchronously detecting the intensities of these beams, distinguishing between differential and reference signals. Theoretical analysis indicates that the measurement uncertainty for optical rotation angles, when using quantum entanglement, exceeds the conventional photon shot noise limit. Moreover, we have experimentally validated the effectiveness of our method. In DC mode, the experimental results reveal that the measurement uncertainty for optical rotation angles is 4.7 × 10 −9 rad, implying a sensitivity of 4.7 × 10 −10 rad/Hz 1/2 for each 0.01 s measurement duration. In light intensity modulation mode, the uncertainty is 48.9 × 10 −9 rad, indicating a sensitivity of 4.89 × 10 −9 rad/Hz 1/2 per 0.01 s measurement duration. This study presents a novel approach for measuring small optical rotation angles with unprecedentedly low uncertainty and high sensitivity, potentially playing a pivotal role in advancing all-optical atomic magnetometers and magneto-optical effect research.

DOI: 10.1364/oe.525608

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The measurement of optical rotation is fundamental to optical atomic magnetometry. Ultra-high sensitivity has been achieved by employing a quasi-Wollaston prism as the beam splitter within a quantum entanglement state, complemented by synchronous detection. Initially, we designed a quasi-Wollaston prism and intentionally rotated the crystal axis of the exit prism element by a specific bias angle. A linearly polarized light beam, incident upon this prism, is divided into three beams, with the intensity of each beam correlated through quantum entanglement. Subsequently, we formulated the equations for optical rotation angles by synchronously detecting the intensities of these beams, distinguishing between differential and reference signals. Theoretical analysis indicates that the measurement uncertainty for optical rotation angles, when using quantum entanglement, exceeds the conventional photon shot noise limit. Moreover, we have experimentally validated the effectiveness of our method. In DC mode, the experimental results reveal that the measurement uncertainty for optical rotation angles is 4.7 × 10 −9 rad, implying a sensitivity of 4.7 × 10 −10 rad/Hz 1/2 for each 0.01 s measurement duration. In light intensity modulation mode, the uncertainty is 48.9 × 10 −9 rad, indicating a sensitivity of 4.89 × 10 −9 rad/Hz 1/2 per 0.01 s measurement duration. This study presents a novel approach for measuring small optical rotation angles with unprecedentedly low uncertainty and high sensitivity, potentially playing a pivotal role in advancing all-optical atomic magnetometers and magneto-optical effect research.

Ultra-sensitive measurement of the magneto-optical rotation, due to interaction of linearly-polarized light passing through room-temperature Rb85 atoms, in response to change in longitudinal magnetic field (δBz) is demonstrated using the weak measurement method. The polarization rotation angle measurement sensitivity (δϕ) of 16 μrad and hence of the magnetometer of 1 nT, achieved using the weak measurement method is better than the balanced optical polarimetry results by a factor of three. The improvement in the measurement sensitivity is realized via optical amplification of the polarization rotation angle via spin-orbit coupled light beam-field. The method is devoid of external rf(/ac) modulation, allows for optimal tunability of sensitivity depending on the dynamic range of the applied magnetic field and the sensitivity can be further enhanced by operating in the spin exchange relaxation free regime of alkali spin polarization.

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 than

1 \times 10 ^{\mathrm {-8}}

rad/Hz

^{\mathrm {1/2}}

is achieved for frequencies higher than 5 Hz, demonstrating a probe background noise of 0.26 fT/Hz

^{\mathrm {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.

Application of nonlinear magneto-optical (Faraday) rotation to magnetometry is investigated. Our experimental setup consists of a modulation polarimeter that measures rotation of the polarization plane of a laser beam resonant with transitions in Rb. Rb vapor is contained in an evacuated cell with antirelaxation coating that enables atomic ground-state polarization to survive many thousand wall collisions. This leads to ultranarrow features $(\ensuremath{\sim}{10}^{\ensuremath{-}6} \mathrm{G})$ in the magnetic-field dependence of optical rotation. The potential sensitivity of this scheme to sub-$\ensuremath{\mu}\mathrm{G}$ magnetic fields as a function of atomic density, light intensity, and light frequency is investigated near the

^{\mathrm {1/2}}

and

D2

lines of

{}^{85}\mathrm{Rb}.

It is shown that through an appropriate choice of parameters the shot-noise-limited sensitivity to small magnetic fields can reach $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12} \mathrm{G}/\sqrt{\mathrm{Hz}}.$

A self-oscillating magnetometer based on nonlinear magneto-optical rotation using amplitude-modulated pump light and unmodulated probe light (AM-NMOR) in 87Rb has been constructed and tested towards a goal of airborne detection of magnetic anomalies. In AM-NMOR, stroboscopic optical pumping via amplitude modulation of the pump beam creates alignment of the ground electronic state of the rubidium atoms. The Larmor precession causes an ac rotation of the polarization of a separate probe beam; the polarization rotation frequency provides a measure of the magnetic field. An anti-relaxation coating on the walls of the atomic vapor cell results in a long lifetime of 56 ms for the alignment, which enables precise measurement of the precession frequency. Light is delivered to the magnetometer by polarization-maintaining optical fibers. Tests of the sensitivity include directly measuring the beat frequency between the magnetometer and a commercial instrument and measurements of Earth's field under magnetically quiet conditions, indicating a sensitivity of at least 5 pT/νHz. Rotating the sensor indicates a heading error of less than 1 nT, limited in part by residual magnetism of the sensor.

An atomic magnetometer detects atomic responses to the magnetic field, and its sensitivity is ultimately limited by quantum noise fluctuations. For magnetometers based on nonlinear magneto-optical rotation (NMOR), the possible concurrent generation of light squeezing due to polarization self-rotation complicates the optimization for magnetometer sensitivity. Here, we study NMOR magnetometers with frequency-modulated light in a paraffin coated 87Rb vapor cell in the low and high power regimes corresponding to situations with and without light squeezing, respectively, with detection observables being different Stokes components reflecting the magnetic-field-induced atomic circular dichroism or birefringence. We found that the overall best sensitivity is achieved in the low power regime when there is no light squeezing and for circular dichroism measurement. We provide a general insight on parameter optimization and the choice of detection observables, from the delicate trade-off between the atomic responses and the noises including the technical and quantum optical noises. Our results could have practical significance in optical atomic magnetometry.

Magneto-optical (Faraday) rotation is a process in which the plane of light polarization rotates as light propagates through a medium along the direction of a magnetic field. In atomic vapors where ground state atomic polarization relaxes very slowly (relaxation rates ≳1 Hz), there arise ultranarrow, light-power-dependent (nonlinear) features in the magnetic field dependence of Faraday rotation. The shot-noise-limited sensitivity of a magnetometer based on nonlinear Faraday rotation can exceed 10−11 G/Hz, corresponding to a sensitivity of ∼10−6 Hz/Hz to Zeeman sublevel shifts. Here we discuss recent progress in magnetometry based on nonlinear optical rotation and consider the application of these methods to searches for fundamental-symmetry-violating interactions.