Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency

Abstract

Squeezed states of light belong to the most prominent nonclassical resources. They have compelling applications in metrology, which has been demonstrated by their routine exploitation for improving the sensitivity of a gravitational-wave detector since 2010. Here, we report on the direct measurement of 15 dB squeezed vacuum states of light and their application to calibrate the quantum efficiency of photoelectric detection. The object of calibration is a customized InGaAs positive intrinsic negative (p-i-n) photodiode optimized for high external quantum efficiency. The calibration yields a value of 99.5% with a 0.5% (k = 2) uncertainty for a photon flux of the order 10^17/s at a wavelength of 1064 nm. The calibration neither requires any standard nor knowledge of the incident light power and thus represents a valuable application of squeezed states of light in quantum metrology.

Figures (3)

• Figure 1: Schematic of the experimental setup. Squeezed vacuum states of light (SQZ) at a wavelength of 1064 nm were generated in a doubly resonant, type I optical parametric amplifier (OPA) operated below threshold. SHG: second harmonic generation, PBS: polarizing beam splitter; DBS: dichroic beam splitter; LO: local oscillator, PD: photodiode; MC1064: three-mirror ring cavity for spatiotemporal mode cleaning; EOM: electro-optical modulator; FI: Faraday Isolator. The phase shifter for the relative phase $\theta$ between SQZ and LO was a piezo actuated mirror. Retro reflecting mirrors were used to recycle the residual reflection from the photo diodes used for homodyne detection. An auxiliary beam (not shown) was used for the alignment of the homodyne contrast.
• Figure 2: Quantum noise and electronic dark noise at Fourier frequencies from 3 to 8 MHz. The vacuum noise reference level corresponds to local oscillator power of 26.5 mW. The measurement time for each individual trace was 211 ms. A non-classical noise reduction of up to 15 dB below vacuum noise was directly observed. The degradation of the squeezing factor towards higher frequencies is a consequence of the OPA line-width. The electronic detector dark noise was not subtracted from the data.
• Figure 3: Pump power dependence of the squeezing and anti-squeezing spectra, experiment and theory. The theoretical curves (dashed lines) were modeled with $\eta=0.975$ and $\theta_{\textrm{pn}}=1.7$ mrad for pump powers corresponding to $P/P_{\mathrm{thr}}$ of 8%, 33.9%, and 83.5% and a full-width-half-maximum linewidth $\gamma / 2\pi =$ 84 MHz. The electronic dark noise was subtracted from the data, which were subsequently normalized to the vacuum noise level. The measurement time for each individual trace was 295 ms. Already with a pump power of 1.6 mW, a nonclassical noise reduction of up to 5 dB was obtained. With 7 mW our setup produced up to 10 dB squeezing with only 11 dB antisqueezing. The model is in good agreement with the 0.3 dB increase to 15.3 dB of maximum squeezing due to subtraction of the dark noise. This effect is negligible for all other traces in this representation.