Experimental Violation of Bell-like Inequalities By Electronic Shot Noise

We report measurements of the correlations between electromagnetic field quadratures at two frequencies $f_1=7\mathrm{GHz}$ and $f_1=7.5\mathrm{GHz}$ of the radiation emitted by a tunnel junction placed at very low temperature and excited at frequency $f_1+f_2$. We demonstrate the existence of two-mode squeezing and violation of a Bell-like inequality, thereby proving the existence of entanglement in the quantum shot noise radiated by the tunnel junction.

Figure 1

Experimental setup. See details in text.

Figure 2

$\mathrm{\Delta }\mathcal{P}=\mathcal{P}{(A,B)}_{V_{\mathrm{dc}},V_{\mathrm{ac}}}-\mathcal{P}{(A,B)}_{0,0}$ (unitless): (a)–(d) difference between the normalised 2D current fluctuation distributions of the tunnel junction at $V_{\mathrm{dc}}=29.4\mu \mathrm{V}$, 18 mK, under 14.5 GHz, $V_{\mathrm{ac}}=37\mu \mathrm{V}$ microwave excitation and without excitation at $V_{\mathrm{dc}}=0$. $X$ and $P$ represent two quadratures of the observed signal while numbers 1 and 2 represent fluctuations of frequency 7 and 7.5 GHz in arbitrary units. Each distribution is made up of $2\times {10}^{11}\text{samples}$.

Figure 3

Quadrature correlators of electro-magnetic field at frequencies $f_1=7\mathrm{GHz}$, $f_2=7.5\mathrm{GHz}$ generated by a $70\mathrm{\Omega }$ tunnel junction at 18 mK under 14.5 GHz, $V_{\mathrm{ac}}=37\mu \mathrm{V}$ microwave excitation. Symbols represent experimental data and lines are theoretical expectations. Symbol sizes represent experimental uncertainty.

Figure 4

Rescaled (unitless) variances of the electro-magnetic field generated by a $70\mathrm{\Omega }$ tunnel junction at 18 mK under 14.5 GHz, $V_{\mathrm{ac}}=37\mu \mathrm{V}$ microwave excitation and without excitation, obtained using signal quadratures at frequencies $f_1=7\mathrm{GHz}$, $f_2=7.5\mathrm{GHz}$. Symbols represent experimental data and lines are theoretical expectations. Symbol sizes represent experimental uncertainty. The shaded area showcases the less-than-vacuum noise levels.