Pauli-Heisenberg Oscillations in Electron Quantum Transport

We measure the current fluctuations emitted by a normal-metal–insulator–normal-metal tunnel junction with a very wide bandwidth, from 0.3 to 13 GHz, down to very low temperature $T=35\mathrm{mK}$. This allows us to perform the spectroscopy (i.e., measure the frequency dependence) of thermal noise (no dc bias, variable temperature) and shot noise (low temperature, variable dc voltage bias). Because of the very wide bandwidth of our measurement, we deduce the current-current correlator in the time domain. We observe the thermal decay of this correlator as well as its oscillations with a period $h/eV$, a direct consequence of the effect of the Pauli and Heisenberg principles in quantum electron transport.

Figure 1

Experimental setup. The symbols $\overline{)\mathsf{X}}$ and $\overline{)\mathrm{P}}$ represent, respectively, a frequency mixer and a power meter.

Figure 2

Equilibrium noise temperature vs frequency for various electron temperatures $T$. Symbols are experimental data and solid lines are theoretical expectations of Eq. (2). Inset: Experimental rescaled noise temperature $T_N/T$ vs rescaled frequency $hf/(2k_{B}T)$.

Figure 3

Out-of-equilibrium noise temperature vs frequency for different dc voltage biases $V$ at $T=35\mathrm{mK}$. Symbols are experimental data and solid lines are theoretical expectations of Eq. (3).

Figure 4

Rescaled current-current correlator in the time domain for five different voltages at $T=35\mathrm{mK}$. The data at $V=0$ correspond to the correlator at equilibrium $\mathrm{\Delta }{C}_{\mathrm{eq}}(t,T)$. Its characteristic thermal decay time is given by $\hslash /k_{B}T\sim 100\mathrm{ps}$. Solid lines are theoretical expectations.

Figure 5

Rescaled current-current correlator in the time domain vs reduced time $eVt/h$ for various bias voltages $V=25.5$, 30.6, 35.7, and $40.8\mu \mathrm{V}$ (same symbols as Fig. 4).