Transport of Quantum Noise through Random Media

We present an experimental study of the propagation of quantum noise in a multiple scattering random medium. Both static and dynamic scattering measurements are performed: the total transmission of noise is related to the mean free path for scattering, while the noise frequency correlation function determines the diffusion constant. The quantum noise observables are found to scale markedly differently with scattering parameters compared to classical noise observables. The measurements are explained with a full quantum model of multiple scattering.

Figure 1

Experimental setup for measuring the transmission of quantum noise through a multiple scattering medium. Two different measurements were carried out by inserting either detector D1 or D2. The total transmission was recorded with an integrating sphere onto detector D1. With detector D2, the noise in a single speckle spot was measured.

Figure 2

Total transmission of noise as a function of measurement frequency $\Omega$ for two different sample thicknesses. The spectral densities were recorded with a resolution bandwidth of $30\mathrm{kHz}$ and a video bandwidth of $10\mathrm{kHz}$ and by averaging each trace 100 times. Radically different transmissions are observed for technical noise (below $1\mathrm{MHz}$) compared to shot noise (above $1.5\mathrm{MHz}$). The spikes around $1.3\mathrm{MHz}$ are due to oscillations in the detector power supply and are abandoned in the analysis.

Figure 3

Left panel: inverse total transmission of quantum noise as a function of sample thickness. The line is a linear fit to the experimental data. Right panel: inverse total transmission of classical noise and a quadratic fit to the data. The different scales in the two plots clearly demonstrate that classical and quantum noise are transmitted differently.

Figure 4

Measured correlation function for shot noise (triangles) and technical noise (squares) as a function of frequency offset. The experimental data are compared to $⟨⟨C_{ab}^{\mathrm{SN}}⟩⟩$ (full curve) and $⟨⟨C_{ab}^{\mathrm{TN}}⟩⟩$ (dashed curve), respectively. Note the different magnitude of the correlation for quantum noise (left axis) and classical noise (right axis). The inset shows the complete shot noise data set of the photocurrent spectral density $|\delta i{|}^2$ in a speckle spot. Each data point was obtained by averaging the noise spectra over the measurement frequency $\Omega$ within the limits of the shot noise region.