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...

The self-heating effect on intrinsic tunneling spectra ͑ITSs͒ is investigated using stacks of intrinsic Josephson junctions ͑IJJs͒ in near optimally doped Bi 2 Sr 2 CaCu 2 O 8+␦ crystals. The area of the stacks S ranges from 12 down to 0.16 m 2 . For IJJs with larger S, ITSs are distorted by self-heating, but become progressively less size dependent as S decreases down to submicrometer level. Analysis based on the ballistic phonon model of Krasnov et al. indicates a temperature rise of ϳ5 K for the smallest junctions at the bias voltage corresponding to the conductance peak. A brief comparison between the ITSs and spectra from other techniques is presented.

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