Quantum Radiometric Calibration

TL;DR

The paper tackles the challenge of calibrating photodiode quantum efficiencies at high photon flux for optical quantum technologies. It introduces quantum radiometric calibration (QRC), which uses squeezed-light states and the Heisenberg uncertainty principle in a in-situ balanced homodyne detector setup to infer photodiode efficiencies from frequency-specific noise measurements. The authors derive the calibration signal theory, quantify the various loss channels (escape, propagation, mode-matching, and detection), and demonstrate an absolute calibration with 0.37% uncertainty on 1550 nm photodiodes, obtaining η_DE ≈ 97.20% and η_QE ≈ 96.9%. Despite reaching near-99% efficiency, the results show a gap to the stringent requirements of optical quantum computing and low-frequency gravitational-wave detectors, underscoring the need for higher squeezing and lower optical losses to achieve fault-tolerant performance.

Abstract

Optical quantum computing, as well as quantum communication and sensing technology based on quantum correlations are in preparation. These require photodiodes for the detection of about 10^16 photons per second with close to perfect quantum efficiency. Already the radiometric calibration is a challenge. Here, we provide the theoretical description of the quantum radiometric calibration method. Its foundation is squeezed light and Heisenberg's uncertainty principle, making it an example of quantum metrology based on quantum correlations. Unlike all existing radiometric calibration methods, ours is in situ and provides both the detection efficiency and the more stringent quantum efficiency directly for the measurement frequencies of the user application. We calibrate a pair of the most efficient commercially available photodiode at 1550 nm to a system detection efficiency of (97.20 + 0.37)% using 10-dB-squeezed vacuum states. Our method has great potential for significantly higher precision and accuracy, but even with this measurement, we can clearly say that the available photodiode efficiencies for 1550 nm are unexpectedly low, too low for future gravitational wave detectors and for optical quantum computing.

Figures (4)

• Figure 1: Decoherence due to imperfect efficiency --- The ellipses represent the product of the standard deviations $\Delta \!\hat{X}$ and $\Delta \hat{Y}$ of squeezed states. The circle refers to the ground state (of the same optical mode). (a) Representation of the squeezed state measured in this work with imperfect total setup efficiency $\eta$. (b) Representation of the same squeezed state as inferred for perfect efficiency (zero optical loss). The inference corrects for the imperfect efficiency of $\eta = 94.5$% (photon loss of 5.5%) according to Eq. (\ref{['eq:3']}) yielding a higher squeeze factor and a decreased uncertainty area being at the lower bound of the Heisenberg uncertainty relation in Eq. (\ref{['eq:2']}).
• Figure 2: Schematic of the QRC setup --- 0.1 W of the output power of a 1550 nm fibre laser was converted into a 775 nm laser beam by resonator-enhanced second harmonic generation (SHG). This light was used to pump our parametric down-conversion (PDC) resonator to generate squeezed vacuum states (SQZ). Two identical photodiodes (PD) to be calibrated were used for the BHD with transimpedance amplifier (TIA). The local oscillator (LO) for the BHD of about 20 mW came from the same fibre laser. The BHD measured the electric field strength of the squeezed states, while the differential phase $\theta$ was continuously driven with a phase shifter (PS). The PS was placed in front of a spatial mode cleaner (MC) to avoid beam jitter on the PDs. EOM: electro-optical modulator for Pound-Drever-Hall locking of the length of the MC and SHG resonators, FI: Faraday isolator to avoid self-interference of the second harmonic (SH) light, here 775 nm, PID: proportional-integral-derivative controller.
• Figure 3: Determining the escape efficiency --- Left: Squeezing resonator whose escape efficiency $\eta_{\rm esc}$ needs to be determined in a separate measurement. $\eta_{\rm esc}$ is imperfect due to intra-cavity photon scattering ($\ell^2_\mathrm{scat}$) and absorption ($\ell^2_\mathrm{abs}$) at all three intra-cavity surfaces and during crystal transmission. Further photon losses are the residual transmission ($\ell^2_\mathrm{trans}$) and reflection ($\ell^2_\mathrm{refl}$) of the convex and plane crystal surfaces, respectively. Exactly the same loss sources also reduce the reflectivity of the resonator according to Eq. (\ref{['eq:9']}), which is accessible through an in-situ measurement of mode-matched, retro-reflected light. AR, PR, HR: anti-, partial, and high-reflectivity coating. Top right: Measurement of the retro-reflected light while the resonator's length is scanned. Dips occur on resonance when the light couples and experiences the intra-cavity loss (to be up-scaled by the imperfect modematching). The black line in the measurement graph is the theoretical model with fitted coupling mirror reflectivity and round trip loss. Bottom right: Simultaneous measurement of transmitted light provides the imperfect mode matching.
• Figure 4: Measurement of the uncertainty product --- The voltage from the BHD was converted to a zero-span noise power at 5 MHz with 300 kHz resolution bandwidth using a spectrum analyzer. The traces shown are normalized to the noise power of the optical mode's ground state. The BHD's readout phase $\theta$ was continuously swept by applying a saw tooth voltage to a piezo electric element behind a steering mirror in the beam path (PS in Fig. \ref{['fig:2']}. The lowest noise power corresponds to $\Delta\!^2 \!\hat{X}$, the highest to $\Delta\!^2 \hat{Y}$. Per sweep (gray), 32,001 data points were recorded. The red trace corresponds to the same data but 500 Hz low-pass filter on linear scale. The black line shows a model fit, which determined for this single measurement $\Delta\!^2 \!\hat{X} \!\approx 0.10$ and $\Delta\!^2 \hat{Y} \!\approx 19.7$.