Exploring the non-equilibrium fluctuation relation for quantum mechanical tunneling of electrons across a modulating barrier

We experimentally explore the phenomenon of electron tunneling across a modulated tunneling barrier which is created between an STM tip and an Au film deposited on a vibrating piezo surface. Measurements of the time series of the quantum mechanical tunneling current across the modulating barrier show large fluctuations. Analysis of the average work done in establishing tunneling current in finite time interval shows a distribution of both positive and negative work events. The negative work events suggest tunneling against the bias voltage direction. We show that these distributions obey the Gallavotti Cohen Non-equilibrium Fluctuation Relations (GC-NEFR) valid for systems driven through a dissipating environment. Typically, while the GC-NEFR has been shown for non -equilibrium classical systems we show its validity for the quantum mechanical tunneling process too. The GC-NEFR analysis also gives us a way to measure the dissipation present in this quantum tunneling system. We propose the modulated barrier behaves like a lossy scattering medium for the tunneling electrons resulting in a tendency to randomize of the tunneling process.