Quantum Brownian Motion at Strong Dissipation Probed by Superconducting Tunnel Junctions

Abstract

We have studied the temporal evolution of a quantum system subjected to strong dissipation at ultra-low temperatures where the system-bath interaction represents the leading energy scale. In this regime, theory predicts the time evolution of the system to follow a generalization of the classical Smoluchowski description, the quantum Smoluchowski equation, thus, exhibiting quantum Brownian motion characteristics. For this purpose, we have investigated the phase dynamics of a superconducting tunnel junction in the presence of high damping. We performed current-biased measurements on the small-capacitance Josephson junction of a scanning tunneling microscope placed in a low impedance environment at milli-Kelvin temperatures. We can describe our experimental findings by a quantum diffusion model with high accuracy in agreement with theoretical predications based on the quantum Smoluchowski equation. In this way we experimentally demonstrate that quantum systems subjected to strong dissipation follow quasi-classical dynamics with significant quantum effects as the leading corrections. PACS numbers: 74.50.+r, 74.55.+v, Introduction.-Brownian motion -that is the fate of a heavy particle immersed in a fluid of lighter particles -is the prototype of a dissipative system coupled to a thermal bath [1]. Its quantum mechanical analogue can be found in open quantum systems, which have received considerable attention in the last decade [2]. This is mainly due to the experimental progress in fabricating quantum devices on ever growing scales with the intention to control their quantum properties to an unprecedented accuracy. Efforts have thus focused to tame the impact of decoherence and noise in order to preserve fragile features such as entanglement as possible resources for technological applications [3].

An entropy production based method for determining the position diffusion’s coefficient of a quantum Brownian motion

“…In this article, D xx is found to be proportional to 1/(2mω) coth[ω/(2k B T )] ( = 1) and together with the condition k B T /ω 1 we have in the first-order Taylor series approximation that D xx ∼ k B T /(mω 2 ). However, the linear dependence of D xx on the temperature has not been detected yet in typical experiments, see for example optomechanical systems [29] or superconducting tunnel junctions [30]. The most convenient result is the minimum value defined by Dekker's inequality, which is small compared to the coefficient of the momentum diffusion D pp .…”

Quantum partition of energy for a free Brownian particle: Impact of dissipation

“…Lately, kinetic energy of a trappped Fermi gas has been considered [11]. Many other aspects of quantum Brownian motion has been intensively studied in last few years [12][13][14][15][16][17][18][19][20]. However, the previous results have not been directly related to the energy equipartition theorem.…”

Single Channel Josephson Effect in a High Transmission Atomic Contact

“…is implies non-negligible charging e ects and quantum uctuations of the phase [8][9][10]. Still, thermal uctuations can be reduced by operating in the low mK regime [11]. In this new scenario, the e ect of the electromagnetic environment seen by the junction leads to dynamical Coulomb blockade (DCB) type physics [12,13], which has remained largely unexplored until recently as it requires both signi cant charging e ects as well as a high transparency channel in order to be visible.…”