Entanglement-Enhanced Quantum Nano-Vibrometry

Abstract

The study of dynamic systems at the nanometer scale can benefit from the loss and background resilience offered by quantum two-photon interference. However, fast measurements with the required resolution are difficult to realize. As a solution, we introduce extreme energy entanglement between the photons undergoing interference. Using a flux probing analysis technique, we recover vibrational signals with frequencies as high as 21 kHz. Along with validating nanometer-scale precision and accuracy, we observe a significant quantum advantage when measuring in the presence of loss and background.

Figures (3)

• Figure 1: (a) Apparatus schematic. PBS, polarizing beamsplitter; HWP, half-wave plate; DM, dichroic mirror; BS, 50:50 beamsplitter. (b) Coincidences as a function of time for an input sinusoid with a 25-Hz oscillation between 50 and 100 Hz. The peak-to-peak amplitude also oscillates between $\sim$36 nm and $\sim$22 nm, respectively. The anti-coincidences are not shown. (c) The probed spectrum (2.1 million detected pairs, 10 s). The dashed line indicates the threshold set by $p_{\rm FA}= 0.1\%$; see text. (d-e) The original and reconstructed signals, respectively. The recovered amplitude is $\sim$35 ($\sim$23) nm for the 50-Hz (100-Hz) portion.
• Figure 2: (a) Signals used for amplitude validation, driving at 10 Hz. (b--d) Estimated mean amplitudes and frequencies (10 trials), along with amplitude precision ($\sigma_x$) and accuracy $(\Delta x \equiv |x_\text{true} - x_\text{measured}|$). The amplitude estimation accounts for the factor of 2 resulting from retro-reflection. Error bars in (b) and (d) show the standard deviation (i.e., precision). Each 1-s trial involved $\sim$190,000 detected pairs. (e--f) Estimated amplitudes and frequencies from a single discrete sine sweep (1--21 kHz in 1-kHz steps). We probe each frequency with $\sim$1 million detected pairs (5 s). We attribute the consistent $\sim$0.142% frequency offset error to imperfections in the piezoelectric speaker playback pipeline; a similar error is observed when recording the acoustic signal with a microphone.
• Figure 3: Demonstration of quantum advantage. The test signal is a 10-Hz square wave with a true peak-to-peak amplitude of $\sim$55 nm. The quantum measurement is robust against (a) imbalanced path loss ($L$) and (b) optical background ($B$), whereas the classical measurement is not.