50-km fiber interferometer for testing gravitational signatures in quantum interference

Abstract

Quantum mechanics and general relativity are the foundational pillars of modern physics, yet experimental tests that combine the two frameworks remain rare. Measuring optical phase shifts of massless photons in a gravitational potential provides a unique quantum platform to probe gravity beyond Newtonian descriptions, but laboratory-based interferometers have not yet reached the sensitivity needed to access this regime. Here, we report the realization of a 50-km table-top Mach-Zehnder fiber interferometer operating at the single-photon level, achieving a phase sensitivity of $4.42\times10^{-6}$ rad root-mean-square (RMS) within the frequency range of 0.01 Hz to 5 Hz. We demonstrate that this sensitivity is sufficient to resolve a phase-shift signal of $(6.18 \pm 0.44)\times10^{-5}$ rad RMS at 0.1 Hz, associated with a modulated gravity-induced signal. Our results establish a milestone for quantum sensing with large-scale optical interferometry, demonstrating the capability to detect gravitational redshifts in a local laboratory, thereby paving the way for testing quantum phenomena within general relativistic frameworks.

Figures (3)

• Figure 1: Layout of the Mach-Zehnder fiber interferometer, with both interferometer arms maintained at the same height. The interferometer is composed of two 50/50 fiber beam splitters (BS) and two 50-km low-loss fiber spools (yellow), each maintained under active temperature control. Single photons centered at 1550nm, generated from a Type-0 photon source, are used to probe the interferometer phase sensitivity. A weak continuous-wave (CW) laser field at 1542nm is used to lock the interferometer phase. This classical field co-propagates with the single photons through the interferometer before being separated by dense wavelength division multiplexers (DWDM) and directed to a homodyne detector. To stabilize both fast and slow phase fluctuations, the error signal from the homodyne detector is sent to an acousto-optic modulator (AOM) driven by a voltage-controlled oscillator (VCO) and to a fiber stretcher, respectively. The interferometer phase is extracted from the heralded photon number counts detected by superconducting nanowire single-photon detectors (SNSPDs). The core interferometer elements are placed in a thermally and acoustically isolated enclosure (blue shaded region).
• Figure 2: Phase noise spectra of the single-photon interferometer from a 160-hour measurement, spanning the frequency band from e-4Hz to 5Hz. The dim blue and green traces show the phase noise sensitivity calibrated from heralded single-photon counts at each interferometer output. The red trace shows the half-difference between the phase noises measured at the two interferometer outputs, rejecting common-mode noise of the interferometer. The peak at 0.25Hz corresponds to the injected dither tone for calibration; The peak observed at 0.1Hz corresponds to the simulated gravitationally-induced phase shift signal, with an expected root-mean-square (RMS) amplitude of 6.48e-5rad, in agreement with the measured value of 6.18(44)e-5rad. The signal is clearly resolved above the noise floor, which is primarily limited by photon shot noise. Additional peaks at 1Hz and its harmonics arise from cryostat compressor noise.
• Figure 3: (a) Measurements of injected signal amplitudes at 0.1Hz. We use three different dithers with calibrated RMS amplitudes of 2.59e-04, 1.3e-04, and 6.48e-05rad (green dashed lines). The measurement durations are 18.2, 33.1, and 160 hours, respectively. The measured signal values are 2.4(13)e-4, 1.3(09)e-4, 6.18(44)e-5rad (red dots with error bars). The data for the smallest dither was combined from two separate runs (68.8 h and 91.2 h), yielding independent estimates of 6.33(73)e-5 and 6.06(54)e-5rad (red dotted box). This demonstrates the repeatability of the measurement and the stability of the apparatus. The thresholds for signal-to-noise ratios (SNR) of 5 and 10 are shown in the plot to indicate the required measurement times for different signal levels. (b) Allan deviation (ADEV) of the in-phase component obtained from lock-in analysis of the simulated signal, showing the phase stability $\sigma$ versus the averaging time $\tau$. The blue dots with error bars show overlapping ADEV values calculated from the 160-hour measurement. The data follows a $1/\sqrt{\tau}$ trend (blue line) and is consistent with a white noise process, indicating that the measured signal is stationary. The red triangle shows an estimate statistical uncertainty of the measurement from the demodulated time series. It is consistent with an extrapolation of the ADEV trend, as expected for a white noise process.