Optimal signal recovery for pulsed balanced detection

We demonstrate a tool for filtering technical and electronic noises from pulses of light, especially relevant for signal processing methods in quantum optics experiments as a means to achieve the shot-noise level and reduce strong technical noise by means of a pattern function. We provide the theory of this pattern-function filtering based on balance detection. Moreover, we implement an experimental demonstration where 10 dB of technical noise is filtered after balance detection. Such filter can readily be used for probing magnetic atomic ensembles in environments with strong technical noise.

Figure 1

Scheme of the experimental setup. M, mirror; FC, fiber coupling; HWP, half-wave plate. See text for details.

Figure 2

Average pulse shapes of the original pulse $p\left(t\right)$ at 150 MHz (blue dashed line) and the amplified one $p^{\prime }\left(t\right)$ at 5 MHz (green solid line). For the sake of comparison, both pulses are normalized.

Figure 3

Example of pulses seen by the balanced detector (a) without technical noise, and (b) with technical noise introduced.

Figure 4

Scheme of the electronic circuit used to introduce technical noise into the AOMs. See text for details.

Figure 5

Illustration of noise contributions in the power spectrum of a train of pulses. Thin red curve shows the electronic noise of the detector, i.e., with no optical signal introduced. Blue medium curve shows power spectrum with no introduced technical noise. This shows narrow peaks at harmonics of the pulse repetition frequency rising from a shot-noise background. The rolloff in signal strength is due to the 5 MHz bandwidth of the detector. Thick green curve shows power spectrum with an introduced technical noise with central frequency of 5 MHz and FWHM bandwidth of 1 MHz.

Figure 6

Power spectral density from a train of 800 pulses, considering three cases: signal without technical noise (blue line), signal with technical noise (bold green line), and electronic noise (red thin line).

Figure 7

Example of cutting of the pulses (blue thin line) and the corresponding pattern function (red thick line).

Figure 8

Computed noise estimation as a function of the optical signal power (a) without and (b) with technical noise introduced. Circles: experimental data; solid line: quadratic fit.

Figure 9

Computed noise estimation using the optimal pattern estimator as a function of the optical power for shot-noise limited pulses (blue circles) and pulses with technical noise (green stars). Their corresponding quadratic fits are shown in red dashed and cyan lines, respectively.

Figure 10

Noise angle estimation as a function on the optical power. Raw estimators with technical noise (green bold line) and without (blue medium line). Wiener estimator with technical noise (pink diamonds). Model-based estimators with technical noise (green stars) and without (blue circles). For the sake of visualization the results are presented in a semilog graph.