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 properties of phase escape in a dc superconducting quantum interference device ͑SQUID͒ at 25 mK, which is well below quantum-to-classical crossover temperature T cr , in the presence of strong resonant ac driving have been investigated. The SQUID contains two Nb/ Al-AlO x / Nb tunnel junctions with Josephson inductance much larger than the loop inductance so it can be viewed as a single junction having adjustable critical current. We find that with increasing microwave power W and at certain frequencies and / 2, the single primary peak in the switching current distribution, which is the result of macroscopic quantum tunneling of the phase across the junction, first shifts toward lower bias current I and then a resonant peak develops. These results are explained by quantum resonant phase escape involving single and two photons with microwave-suppressed potential barrier. As W further increases, the primary peak gradually disappears and the resonant peak grows into a single one while shifting further to lower I. At certain W, a second resonant peak appears, which can locate at very low I depending on the value of . Analysis based on the classical equation of motion shows that such resonant peak can arise from the resonant escape of the phase particle with extremely large oscillation amplitude resulting from bifurcation of the nonlinear system. Our experimental result and theoretical analysis demonstrate that at T Ӷ T cr , escape of the phase particle could be dominated by classical process, such as dynamical bifurcation of nonlinear systems under strong ac driving.

Salinity is a major abiotic stress that limits plant productivity and quality throughout the world. Roots are the sites of salt uptake. To better understand salt stress responses in maize, we performed a comparative proteomic analysis of seedling roots from the salt-tolerant genotype F63 and the salt-sensitive genotype F35 under 160 mM NaCl treatment for 2 days. Under salinity conditions, the shoot fresh weight and relative water content were significantly higher in F63 than in F35, while the osmotic potential was significantly lower and the reduction of the K+/Na+ ratio was significantly less pronounced in F63 than in F35. Using an iTRAQ approach, twenty-eight proteins showed more than 2.0- fold changes in abundance and were regarded as salt-responsive proteins. Among them, twenty-two were specifically regulated in F63 but remained constant in F35. These proteins were mainly involved in signal processing, water conservation, protein synthesis and biotic cross-tolerance, and could be the major contributors to the tolerant genotype of F63. Functional analysis of a salt-responsive protein was performed in yeast as a case study to confirm the salt-related functions of detected proteins. Taken together, the results of this study may be helpful for further elucidating salt tolerance mechanisms in maize.