Quantum Phase Diffusion in a Small Underdamped Josephson Junction

Abstract

Quantum phase diffusion in a small underdamped Nb/AlO x /Nb junction (∼ 0.4 µm 2 ) is demonstrated in a wide temperature range of 25-140 mK where macroscopic quantum tunneling (MQT) is the dominant escape mechanism. We propose a two-step transition model to describe the switching process in which the escape rate out of the potential well and the transition rate from phase diffusion to the running state are considered. The transition rate extracted from the experimental switching current distribution follows the predicted Arrhenius law in the thermal regime but is greatly enhanced when MQT becomes dominant. PACS numbers: 74.50.+r, 85.25.Cp Classical and quantum diffusion of Brownian particles in titled periodic potential plays a fundamental role in the dynamical behavior of many systems in science and engineering [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Examples include current biased Josephson junctions [1][2][3][4][5][6][7][8][9], colloidal particles in arrays of laser traps [10,11], cold atoms in optical lattice or Bose-Einstein condensates [12][13][14], and various biology-inspired systems known as Brownian motors (molecular motors or life engines), which receive considerable attention in physics [15] and chemistry [16]. Because of the design flexibility, manufacturability, and controllability Josephson junctions provide an excellent test bed for making quantitative comparison of experimental data with theoretical predictions and unraveling possible new physics in the tilted periodic potential systems.The dynamics of a current biased Josephson junction can be visualized as a fictitious phase particle of mass C moving in a tilted periodic potential U(ϕ) = −E J (iϕ + cos ϕ). Here, C is junction capacitance, i = I/I c is the junction's bias current normalized to its critical current, the phase particle's position ϕ is the gauge invariant phase difference across the junction, and E J = I c /2e is the Josephson coupling energy with e and being the electron charge and Planck's constant, respectively. Previous experiments using Josephson junctions have identified three distinctive dynamical states, as shown schematically in Fig. 1. In the first state, the phase particle is trapped in one of the metastable potential wells and undergoes small oscillation around the bottom of the well with plasma frequency ω p . Because of thermal and/or quantum fluctuations the particle has a finite rate Γ 1 escaping from the trapped state. The escape rate becomes significant when the barrier height ∆U is not much greater than k B T or ω p , where k B is the Boltzmann constant and T denotes the temperature, respectively. After the particle escapes from the initial well, depending on the energy gain δU = Φ 0 I (Φ 0 being the flux quantum) and the loss E D due to damping (cf. Fig. 1), it could enter either the second dynamical state called phase diffusion (PD) or the final running state. In the former case as the bias current I is increased further the particle will eventually make a transition, characterized by a rat...

Thermal hopping and retrapping of a Brownian particle in the tilted periodic potential of a NbN/MgO/NbN Josephson junction

“…An example is given by a recent experiment on submicron Nb/AlOx/Nb junctions 40 . Data show an anomalous σ(T ) dependence with a negative dσ/dT over the entire temperature range and a saturation at low temperatures.…”

Fabrication of $\hbox{Nb/Al}_{2}\hbox{O}_{3}/\hbox{Nb}$ Josephson Junctions Using In Situ Magnetron Sputtering and Atomic Layer Deposition

“…The specific resistance of this junction is R N A ~ 14.7 Ωµm 2 , where R N and A are the normal resistance and area of the junction, respectively. Assuming I c R N product is proportional to ∆ [17], the critical current I c of the reference junction can be estimated using eI c R N /∆ = 1.27, which is determined from a large number of Nb/AlO x /Nb junctions previously measured in our lab [18]. We hence obtain I c R N ~ 1.4 mV for the reference junction.…”

Macroscopic quantum tunneling and retrapping processes in moderately damped YBaCuO Josephson junctions

“…At low bias the process of escape and retrapping may occur multiple times generating diffusion of the phase until an increase of the tilt of the potential, due to a change in the bias current, raises the velocity of the particle and the transition to the running state occurs. This is known as PD regime [11,[13][14][15][16][18][19][20][21]. The experimental observation of such regimes in a JJ is based on the measurement of the SCDs and the study of the behavior of its first and second momenta (the mean I and the width ) σ as function of temperature.…”

“…In LTS systems, MDR is more frequently the natural consequence of a reduction of the critical current c I . Low c I are induced or by size reduction typically in the submicron regime [11][12][13][14][15] or by very low critical current density c J [16][17][18]. Lower critical currents result in lower Josephson energies.…”

“…Lower critical currents result in lower Josephson energies. These devices are charac-terized by intermediate levels of dissipation and by phase diffusion (PD) phenomena [11,[13][14][15][16][18][19][20][21]. The low critical current c I limit seems to be characteristic also of all futuristic nanohybrids devices incorporating nanowires or unconventional barriers [18,[22][23][24], and MDR is intrinsically more common than it could be expected.…”