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Title: Parameter optimization for transitions between memory states in small arrays of Josephson junctions

Abstract

Coupled arrays of Josephson junctions possess multiple stable zero voltage states. Such states can store information and consequently can be utilized for cryogenic memory applications. Basic memory operations can be implemented by sending a pulse to one of the junctions and studying transitions between the states. In order to be suitable for memory operations, such transitions between the states have to be fast and energy efficient. Here in this article we employed simulated annealing, a stochastic optimization algorithm, to study parameter optimization of array parameters which minimizes times and energies of transitions between specifically chosen states that can be utilized for memory operations (Read, Write, and Reset). Simulation results show that such transitions occur with access times on the order of 10–100 ps and access energies on the order of 10 -19–5×10 -18 J. Numerical simulations are validated with approximate analytical results.

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [3]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computing and Computational Sciences Directorate; Univ. of Delaware, Newark, DE (United States). Dept. of Mathematical Sciences
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computing and Computational Sciences Directorate
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computing and Computational Sciences Directorate; ; Univ. of Tennessee, Knoxville, TN (United States). Dept. of Mechanical, Aerospace, and Biomedical Engineering
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1407744
DOE Contract Number:
AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physica. A; Journal Volume: 474; Journal Issue: C
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Josephson junction; Memory cell; Parameter optimization; Nonlinear dynamical systems

Citation Formats

Rezac, Jacob D., Imam, Neena, and Braiman, Yehuda. Parameter optimization for transitions between memory states in small arrays of Josephson junctions. United States: N. p., 2017. Web. doi:10.1016/j.physa.2017.01.044.
Rezac, Jacob D., Imam, Neena, & Braiman, Yehuda. Parameter optimization for transitions between memory states in small arrays of Josephson junctions. United States. doi:10.1016/j.physa.2017.01.044.
Rezac, Jacob D., Imam, Neena, and Braiman, Yehuda. Wed . "Parameter optimization for transitions between memory states in small arrays of Josephson junctions". United States. doi:10.1016/j.physa.2017.01.044.
@article{osti_1407744,
title = {Parameter optimization for transitions between memory states in small arrays of Josephson junctions},
author = {Rezac, Jacob D. and Imam, Neena and Braiman, Yehuda},
abstractNote = {Coupled arrays of Josephson junctions possess multiple stable zero voltage states. Such states can store information and consequently can be utilized for cryogenic memory applications. Basic memory operations can be implemented by sending a pulse to one of the junctions and studying transitions between the states. In order to be suitable for memory operations, such transitions between the states have to be fast and energy efficient. Here in this article we employed simulated annealing, a stochastic optimization algorithm, to study parameter optimization of array parameters which minimizes times and energies of transitions between specifically chosen states that can be utilized for memory operations (Read, Write, and Reset). Simulation results show that such transitions occur with access times on the order of 10–100 ps and access energies on the order of 10-19–5×10-18 J. Numerical simulations are validated with approximate analytical results.},
doi = {10.1016/j.physa.2017.01.044},
journal = {Physica. A},
number = C,
volume = 474,
place = {United States},
year = {Wed Jan 11 00:00:00 EST 2017},
month = {Wed Jan 11 00:00:00 EST 2017}
}
  • Here, we study memory states of a circuit consisting of a small inductively coupled Josephson junction array and introduce basic (write, read, and reset) memory operations logics of the circuit. The presented memory operation paradigm is fundamentally different from conventional single quantum flux operation logics. We calculate stability diagrams of the zero-voltage states and outline memory states of the circuit. We also calculate access times and access energies for basic memory operations.
  • Cited by 1
  • We have studied the phase diagram of two capacitively coupled Josephson junction arrays with charging energy, E{sub c}, and Josephson coupling energy, E{sub J}. Our results are obtained using a path integral Quantum Monte Carlo algorithm. The parameter that quantifies the quantum fluctuations in the ith array is defined by {alpha}{sub i}{identical_to}E{sub c{sub i}}/E{sub J{sub i}}. Depending on the value of {alpha}{sub i}, each independent array may be in the semiclassical or in the quantum regime: We find that thermal fluctuations are important when {alpha}{<=}1.5 and the quantum fluctuations dominate when 2.0{<=}{alpha}. Vortices are the dominant excitations in the semiclassicalmore » limit, while in the quantum regime the charge excitations are important. We have extensively studied the interplay between vortex and charge dominated individual array phases. The phase diagrams for each array as a function of temperature and interlayer capacitance were determined from results for their helicity modulus, {upsilon}({alpha}), and the inverse dielectric constant, {epsilon}{sup -1}({alpha}). The two arrays are coupled via the capacitance C{sub inter} at each site of the lattices. When one of the arrays is in the quantum regime and the other one is in the semiclassical limit, {upsilon}(T,{alpha}) decreases with T, while {epsilon}{sup -1}(T,{alpha}) increases. This behavior is due to a duality relation between the two arrays: e.g., a manifestation of the gauge invariant capacitive interaction between vortices in the semiclassical array and charges in the quantum array. We find a re-entrant transition in {upsilon}(T,{alpha}), at low temperatures, when one of the arrays is in the semiclassical limit (i.e., {alpha}{sub 1}=0.5) and the quantum array has 2.0{<=}{alpha}{sub 2}{<=}2.5, for the values considered for the interlayer capacitance of C{sub inter}=0.26087, 0.52174, 0.78261, 1.04348, and 1.30435. Similar results were obtained for larger values of {alpha}{sub 2}=4.0 with C{sub inter}=1.04348 and 1.30435. For smaller values of C{sub inter} the superconducting-normal transition was not present. In addition, when 3.0{<=}{alpha}{sub 2}<4.0, and for all the interlayer couplings considered above, a novel re-entrant phase transition occurs in the charge degrees of freedom, i.e., there is a re-entrant insulating-conducting transition at low temperatures. Finally, we obtain the corresponding phase diagrams that have some features that resemble those seen in experiment.« less
  • We have measured the temperature dependence and magnetic field dependence of the zero-bias resistance ({ital R}{sub 0}) as well as the current-voltage ({ital I}-{ital V}) characteristics for several two-dimensional arrays of small aluminum Josephson junctions. {ital R}{sub 0}({ital T}) decreases with decreasing temperature, which can be described in terms of two types of vortex motion: flux, flow, and vortex tunneling. At temperatures higher than the Kosterlitz-Thouless transition temperature ({ital T}{gt}{ital T}{sub {ital c}}) or at a bias current greater than the current corresponding to the onset of the nonlinear {ital I}-{ital V} characteristics ({ital I}{gt}{ital I}{sub {ital d}}), the effectivemore » damping resistance which characterizes flux-flow motion is found to be approximately equal to the junction normal-state resistance {ital R}{sub {ital N}}. At low temperatures and at small bias current, {ital R}{sub 0} is temperature independent and remains finite down to our minimum attainable temperature. This finite resistance is found to be dependent on the array size as well as the junction parameters. {copyright} {ital 1996 The American Physical Society.}« less
  • We analyze Fiske resonances of one-dimensional parallel arrays of underdamped Josephson tunnel junctions. They appear in the current voltage (I{endash}V) characteristics as resonant current singularities (steps) at finite voltages V{sub m} when a magnetic field H is applied perpendicular to the array cells. We present measurements of current step amplitudes I{sub cm}, and of the maximum Josephson current I{sub c0} as a function of H, for arrays made of four, six, and ten small Josephson junctions. The I{endash}V characteristics of the arrays exhibit three, five, and eight resonant current steps, respectively, at increasing voltages. In all devices we find thatmore » the current amplitude of the highest order step has just one maximum occurring at H{approx}1/2H{sup {asterisk}}, being H{sup {asterisk}} the first field value where I{sub c0}(H{sup {asterisk}}){approx}I{sub c0}(0). Numerical simulations of the phase dynamics in small parallel arrays as a function of the applied magnetic flux are performed. The results of the simulation reproduce the experimentally observed features. {copyright} {ital 1997 American Institute of Physics.}« less