Active polarization stabilization of fields in an optical fiber for protective measurements

TL;DR

This work tackles polarization stabilization in fiber-based Zeno protective measurements by using the detected signal photons themselves as the stabilization error signal, implemented with SPGD on four fiber squeezers to maximize photon counts. The approach eliminates background associated with classical reference beams and increases the number of Zeno stages, achieving 13 loops and correspondingly reduced measurement uncertainty, with the temporal pointer delay encoding the polarization expectation value $\langle \hat{O} \rangle$ via $\langle \hat{O}\rangle = 2 t_{M}/\tau_{\max} - 1$. Compared with a strong measurement, the protective measurement variance $\sigma_{PM}$ is smaller for most polarization states, demonstrating a practical advantage for precision quantum state characterization. The results suggest significant practical impact for protective measurements and point toward photonic-integrated implementations to further lower losses and enable true single-photon Zeno PM with a temporal pointer.

Abstract

We have performed Zeno protective measurements of quantum polarization states by coupling the polarization to a temporal pointer (arrival time) in a birefringent optical fiber. It is necessary to actively stabilize the polarization, and we do this by using the signal photon counts themselves as the error signal in a feedback loop. We compare these measurements to a stabilization scheme using a classical reference beam as the error signal. The method using photon counts has higher signal levels and significantly reduced background. These improvements allow us to increase the number of Zeno stages in our measurements from 9 to 13, with a corresponding decrease in the measurement uncertainty.

Figures (6)

• Figure 1: Principle of a Zeno protective measurement. After each weak interaction with the measuring device, the system is projected back onto its initial state $\vert{\psi_0\rangle}$. Each dashed unit represents a Zeno stage.
• Figure 2: The experimental apparatus. The abbreviations are: linear polarizer (LP), polarization stabilizer (PS), differential group delay (DGD), electronic polarization controller (EPC), 90%/10% splitter (90:10), polarization analyzer (PA), circulator (C), computer (Comp), counter (CNT), time-to-digital converter (TDC), amplitude modulator (1x1 switch), erbium-doped-fiber amplifier (EDFA), bandpass filter (F), 2x2 switch, variable attenuator (AT) and single-photon-counting module (SPCM). The arrangement in (a) is used to characterize the performance of the active polarization stabilization. The arrangement in (b) is used to perform protective measurements.
• Figure 3: The number of photon counts in [10]s recorded when the stabilization algorithm is (a) off, and (b) on. The timing of the 2x2 switch was set to have photons propagate 5 times around the loop.
• Figure 4: Histogram of the fidelity [Eq. (\ref{['eq:fidel']})] between the mean Stokes vector and each individually measured Stokes vector. The data was acquired during the same time interval as that shown in Fig. \ref{['fig:Stable']}(b).
• Figure 5: Measured photon arrival times without background subtraction or windowing. The data in (a) was acquired after 9 loops using a reference beam for polarization stabilization Chen_2023, while the data in (b) was acquired after 13 loops using photon counts from the signal for stabilization [Fig. \ref{['fig:Expt']}(b)].