Nonlocal Cancellation of Optical Rotations in Fructose Solutions

TL;DR

The paper demonstrates nonlocal cancellation and addition of optical rotations using polarization-entangled photons in fructose solutions, enabling remote probing of optical activity through joint measurements. By modeling rotation as a unitary $\hat{U}(\theta)=e^{-i\hat{\sigma}_y\theta}$ and employing Bell states $|\psi_{\pm}\rangle$, the authors show that entangled probes can exhibit either cancellation ($\theta_- =0$ when $\theta_A=\theta_B$ in $|\psi_-\rangle$) or additive effects ($\theta_+ = \theta_A+\theta_B$ in $|\psi_+\rangle$), observable via $M_{zz}^{\pm}$ and $M_{xz}^{\pm}$ with characteristic $\cos(2\theta_{\pm})$ and $\sin(2\theta_{\pm})$ dependences. The experiments include a 795 nm setup with fructose and a long-distance 300 m fiber configuration at 1535/1560 nm, validated by quantum state tomography and CHSH tests (S up to $2.818\pm0.0094$). The results agree with theory and suggest enhanced sensitivity scaling with photon number $N$ (Heisenberg limit $F_Q(N)=4N^2$) for nonlocal optical-rotation measurements, with implications for sensing a range of chiral molecules and potential miniaturization via lab-on-a-chip technologies.

Abstract

Entanglement, one of the most representative phenomena in quantum mechanics, has been widely used for fundamental studies and modern quantum technologies. In this paper, we report the observation of nonlocal cancellation and addition of optical rotations with polarization-entangled photons in fructose solutions. The entanglement also enables probing optical activities at a distance by joint measurements on the entangled photons. The good agreement between the experimental results and theoretical predictions demonstrates the potential for extending these measurements to other chiral molecules, with a sensitivity that improves as the number of entangled photons increases.

Figures (4)

• Figure 1: Experimental setups for observing nonlocal cancellation and addition of optical rotations with entangled photons. (a) In the experiment with fructose solutions, 795 nm polarization-entangled photons are generated using cavity-enhanced SPDC and a beam splitter (BS) via post selection Wu2017Wu2019Cheng2020. A quarter-wave plate (QWP) and half-wave plate (HWP) are then used to adjust the phase between $\ket{\text{H}}_{\rm A}\ket{\text{V}}_{\rm B}$ and $\ket{\text{V}}_{\rm A}\ket{\text{H}}_{\rm B}$. (b) In the experiment across two buildings, polarization-entangled photons at 1535 and 1560 nm are generated with a thermally stabilized PPLN crystal in a Sagnac interferometer KimPRA2006. A 773.8 nm picosecond laser is exploited as the pump laser. The polarization analyzers in both setups consist of a HWP, a QWP and a polarization beam splitter (PBS) before the photons are collected into the single-photon detectors (SPDs). Coincident events are analyzed and recorded by time digitizers (CCUs).
• Figure 2: Reconstructed density matrices of the polarization-entangled photons with one photon passing through (a) air (where the state is prepared in $\ket{\phi_{+}}=\frac{1}{\sqrt{2}}(\ket{\rm H}_A \ket{\rm H}_B+\ket{\rm V}_A \ket{\rm V}_B)$), (b) purified water, and (c) fructose solution (of which the molarity corresponds to an optical rotation of $\theta_A = 20.08^{\circ}$). (d) The predicted density matrix of the entangled photons, in which the presence of fructose is modeled by $\hat{U}\left(\theta_{\rm A}\right)=e^{-i{\hat{\sigma}}_y\theta_{\rm A}}$, has a cosine similarity of 0.94 compared to the density matrix in (c). The reconstructed density matrices of Bell states $\ket{\psi_{+}}$ used in the experiments with fructose solutions (measured in front of the solutions) and across two buildings (measured at the input of the 300-m-long fiber) are shown in (e) and (f), respectively.
• Figure 3: (a) Optical rotation of a linearly polarized laser beam measured for different molarities of fructose solution. The standard deviation is $\pm 0.04^{\rm o}$. (b) Measurement of $\theta_{\pm}$ with entangled photons prepared in $\ket{\psi_{\pm}}$. The shaded yellow and blue regions indicate quantum levorotation ($\theta_{\pm} > 0$) and quantum dextrorotation ($\theta_{\pm} < 0$), respectively. All data are available in the Supplementary Materials.
• Figure 4: Joint measurements (a) $M^{\pm}_{zz}$ and (b) $M^{\pm}_{xz}$ for different $\theta_{\text{B}}$ and $\theta_{\text{A}}=20^\circ$. The curves are the fitting using trigonometric functions. The high visibility implies the nonlocal effect of entangled photons. (c) Observation of nonlocal cancellation ($\theta_-=0$) and nonlocal addition of optical rotations. The standard deviation is $\pm 0.3^{\rm o}$. (d) Nonlocal measurements of $\theta_{\text{A}}$ (square) and $\theta_{\text{B}}$ (circles) compared to the experimentally prepared $\theta_{\text{A}}=20^{\circ}$ (black line) and $\theta_{\text{B}}$ (red line). The standard deviation is $\pm 0.21^{\rm o}$. All data are available in the Supplementary Materials.