The physics of Josephson junctions at the microscopic level

A project of the Theoretical Chemical and Quantum Physics Group


Mr. Tim DuBois, Mr. Martin Cyster, Dr. Nicolas Vogt, A/Prof. Jared Cole, Prof. Salvy Russo


J. Lisenfeld, M. Marthaler, A. Ustinov: Karlsruhe Institute of Technology

C. Müller: University of Queensland

Brief Project Outline

Although superconducting devices are based on the dissipation-less properties of metals below the superconducting transition, they suffer from a fundamental drawback. The quantum effects on which these devices rely stem from Josephson junctions, which are ultra-small, ultra-thin insulating barriers. At present the best method for fabricating these junctions is to take advantage of the native amorphous oxide, which forms on many superconducting metals when exposed to oxygen. This oxide layer in turn contains defects, due to its amorphous nature, which provides a new and dominant dissipation channel. Although much is known about the effects of these defects, very little is known about their precise microscopic origins.

The TCQP group is working on this problem from several directions:

  • Developing microscopic models of Josephson junctions themselves to better understand the formation of the junction and their amorphous nature.
  • Developing effective models of two-level defects with the aim of comparing to microscopic parameters.
  • Working with our experimental collaborators to test theoretical models and design new experiments to more accurately measure junction defects.

Two-state defects are a generic feature of disorder crystals. An amorphous crystal can be thought of as a conventional periodic crystal where there are small random perturbations to the bond lengths and angles. This tends to disrupt the long range periodicity, resulting in the amorphous nature of the solid. At the same time, this localised disorder in the bonds allows for degenerate atomic positions, ie. one or more atoms can take two equivalent positions which are very close in energy. The formation of these two-state defects profoundly modifies the thermodynamic and electrical properties of the material.

Anatomy of phase qubit spectroscopy

Anatomy of a phase-qubit/two-level fluctuator spectrum. A phase qubit circuit is a very sensitive probe of coherent two-level systems embedded in the circuit itself (typically within the Josephson junction). The physics of the two-state system can be probed via dynamical spectroscopy experiments where typically such experiments have a number of different "free' parameters which must be precisely measured in order to characterise the system precisely. Using a series of measurements, each of the parameters can be independently determined, providing more information on the nature of the two-level fluctuator.
Cole et al., Appl. Phys. Lett. 97, 252501 (2010)

Oxide deposition simulation

A Josephson junction is formed using a controlled oxidation of aluminium metal. The oxidation is performed at relatively low temperatures and pressures which result in an amorphous aluminium oxide layer. This movie shows a detailed simulation of the growth of aluminium oxide produced by simulating the impact and equilibration of each oxygen atom individually. For particular sets of pressure, temperature and thermostat configurations, we see formation of either amorphous or crystalline layers which can be then compared to experimental measurements of example junctions.

Recent Publications

T. C. DuBois, S. P. Russo and J. H. Cole, Atomic delocalization as a microscopic origin of two-level defects in Josephson junctions, New Journal of Physics 17 23017 (2015)

J. Lisenfeld, G. Grabovskij, C. Muller, J. H. Cole, G. Weiss and A. V. Ustinov, Observation of directly interacting coherent two-level systems in an amorphous material, Nature Communications 6 6182 (2015)

T. C. DuBois, M. Per, S. P. Russo and J. H. Cole, Delocalized Oxygen as the Origin of Two-Level Defects in Josephson Junctions, Physical Review Letters 110 077002 (2013)

J. H. Cole, C. Müller, P. Bushev, G. J. Grabovskij, J. Lisenfeld, A. Lukashenko, A. V. Ustinov and A. Shnirman, Quantitative evaluation of defect-models in superconducting phase qubits, Appl. Phys. Lett. 97, 252501 (2010)

For more information about this project, please contact Jared Cole.

Electronic properties of phosporous-doped silicon nanostructures

A project of the Theoretical Chemical and Quantum Physics Group


Mr. Jackson Smith, Mr. Jesse Vaitkus, Dr. Daniel Drumm, A/Prof. Jared Cole, and Prof. Salvy Russo

Brief Project Outline

We are rapidly approaching the lithography limit for manufacturing nanoelectronic devices. As these devices get smaller, their quantum properties become important. These properties can be used by quantum computers, which have the potential to revolutionise the field of computing and information processing.

To make components for a quantum computer, we must use bottom-up approaches to manufacturing. And, while we are not at a stage where large-scale commercial manufacturing is feasible, this technology has developed to the point where it is possible to have control over the manufacturing process with atomic precision. For example, new structures such as quantum dots, layers, and wires have all been made experimentally by doping silicon with phosphorus atoms at extremely high concentrations.

To understand how we can use these devices, we first need to understand their electronic structure. One of the strengths of our group is in performing highly accurate density-functional theory (DFT) calculations to find the ground-state electronic properties of nano-scale structures. The results of these DFT calculations are then used to build effective models for these devices using effective-mass theory, the nonequilibrium Green's functions formalism, and tight-binding theory. This many-pronged approach allows us to model systems that are of direct relavance to current experiments.

Illustration of a Si:P delta-doped layer

Illustration of a phosphorus (red atoms) in silicon (grey bonds) [Si:P] delta-doped layer. The ratio of phosphorus atoms to silicon atoms is equal to 1/4 inside the layer. These high doping densities and the strong spatial confinement of the phosphorus atoms leads to the interesting physical properties of these structure.

Isosurface of the donor electron wavefunction for a single P donor in Si

Isosurface (blue/red) of the donor electron wavefunction for a single phosphorus donor in silicon (yellow). By the doping of a single phosphorus atom into silicon, one electron is donated to the silicon lattice. Although this electron is bound to the phosphorus atom, the isosurface shows it is partially delocalised and spread throughout the silicon. The distance from the edge to the center of the picture is almost 3 nm. The fact the electron is spread out in space is a consequence of the wave-like nature of this fundamental particle.

Probability density of the donor electrons in a Si:P delta-doped wire

Probability density (black) of the donor electrons in an Si:P delta-doped wire. This picture gives us an idea of the shape of the wire and the space within which a current will flow through the device.

Recent Publications

J. S. Smith, J. H. Cole and S. P. Russo, Electronic properties of d-doped Si:P and Ge:P layers in the high-density limit using a Thomas-Fermi method, Phys. Rev. B 89 035306 (2014)

D. W. Drumm, J. S. Smith, M. C. Per, A. Budi, L. C. L. Hollenberg, and S. P. Russo, Ab initio Electronic Properties of Monolayer Phosphorus Nanowires, Phys. Rev. Lett. 110 126802 (2013)

For more information about this project, please contact Jared Cole or Salvy Russo.

Spin physics, spin-chains, quantum magnonics and entanglement theory

A project of the Theoretical Chemical and Quantum Physics Group


Mr. Muhammad Ahmed, Dr. Jan Jeske, A/Prof. Jared Cole, Prof. Andrew Greentree


C. Müller, M. Marthaler, Prof. Schön: Karlsruhe Institute of Technology

S. Huelga: University of Ulm

L. Hall, L. Hollenberg: University of Melbourne

S. Devitt: NII, Tokyo, Japan

Brief Project Outline

The study of spins and their interactions (be they electron-, nuclear- or pseudo-spins) is one of the central components of quantum mechanics. In recent years, the new fields of quantum computing and quantum information processing have link the physics of spins to the fields of information theory, computing theory and cryptography. In this project, we consider the behaviour of interacting few spin systems to study entanglement, transport and measurement. This has applications to quantum computing, quantum sensing as well as the fundamental theory of quantum mechanics. Specific topics of recent interest include:

  • The interplay between decoherence and entanglement theory, the connection between entanglement quantification and entanglement sudden birth and death.
  • Hamiltonian characterisation and measurement, the extraction of system information (system calibration) from a quantum system.
  • Spin transport and the direct control of single magnons.

Geometric entanglement evolution

Evolution of the absolute geometric entanglement hierarchy within a system consisting to two atom-photon pairs, showing the inter-conversion between different classes of entanglement.
J. Cole, J. Phys. A: Math. Theor. 43 135301 (2010)

Entanglement generation

The maximum entanglement which can be generated by an interaction, governed by its position in the Weyl chamber. An arbitrary two-qubit interaction can always be expressed as a trajectory in the Weyl chamber, giving a graphical method for study the creation and destruction of entanglement during coherent evolution.

Spin-wave guiding via time-varying local magnetic potential. By varying the shape and translational speed of the potential, the spin-wave behaves in a similar manner to the light field in an optic fibre. Provided the translation of the potential is adiabatic enough, the spin-wave can be steered while staying as a coherent excitation.
Makin et al. Phys. Rev. Lett. 108 017207 (2012)

Recent Publications

J. H. Cole, Understanding entanglement sudden death through multipartite entanglement and quantum correlations, J. Phys. A: Math. Theor. 43 135301 (2010)

M. I. Makin, J. H. Cole, C. D. Hill and A. D. Greentree, Spin Guides and Spin Splitters: Waveguide Analogies in One-Dimensional Spin Chains, Phys. Rev. Lett. 108 017207 (2012)

Muhammad H. Ahmed and Andrew D. Greentree, Guided magnon transport in spin chains: Transport speed and correcting for disorder, Phys. Rev. A 91 022306 (2015)

For more information about this project, please contact Jared Cole or Andrew Greentree.

Atom-photon interactions and the boundary between quantum optics and condensed-matter

A project of the Theoretical Chemical and Quantum Physics Group


Dr. Jan Jeske, A/Prof. Jared Cole, Prof. Andrew Greentree


P. Longo: Heidelberg University

K. Busch: TU Berlin

Brief Project Outline

Quantum optics and condensed-matter are traditionally two separate branches of physics. The former being concerned with the interactions between atoms and photons, the latter with the effects of multi-particle systems in which local and non-local effects are observed. Recently, these two fields have started to overlap, resulting in such concepts as circuit-QED and quantum optics experiments in solid-state systems. We are interested in how quantum optics concepts can be implemented in solid-state systems as well as how condensed-matter effects can be observed in interacting atom-photon systems. Recent work includes:

  • The study of "solid-light", the prediction of Mott-Insulator type transitions in systems of coupled photonic cavities and strongly coupled atoms.
  • The propagation of excitations in nonlinear photonic cavity systems and their use in simulating classical and quantum optical elements.
  • The interaction of coherent and incoherent processes within a Jaynes-Cummings lattice system and the resulting correlated emission.

Phase diagram of a coupled-cavity system

Phase diagram of a Jaynes-Cummings lattice system, consisting of an array of coupled photonic cavities, each one strongly coupled to a two-level atom. The superfluid order parameter shows distinctive lobes which are charateristic of a Mott-Insulator/Superfluid quantum phase transition. In this case, this phase transition stems from the induced photon-photon interaction, via the atoms.
Greentree et al., Nature Physics 2, 856 - 861 (2006).

Excitation propagation in a coupled-atom-cavity array

Evolution of an initial excitation in a one-dimensional Jaynes-Cummings lattice consisting of 100 cavities. The atoms are detuned from the photonic cavities, resulting in a separation of velocities for the photonic and atomic excitations. The dashed lines are giving by an approximate analytic expression derived in the dispersive limit.
Makin et al., Phys. Rev. A 80, 043842 (2009).

Emission spectrum from an atom-cavity system

Fluorescence spectra of a laser-driven and dissipative two-cavity system resonant (top) and off-resonant (bottom) atom-photon coupling. The incoherent driving strength is adjusted such that the steady-state particle density is, 0.25, 0.5, 0.75 and 1.0. In addition to the spectra, the light gray (vertical) lines indicate single-particle excitations of the non-dissipative system from (0→1) excitation subspace transitions. These excitations yield the main contributions to the spectra.
Knap et al., Phys. Rev. A 83, 023821 (2011).

Recent Publications

M. Knap, E. Arrigoni, W. von der Linden, J. H. Cole Emission characteristics of laser-driven dissipative coupled-cavity systems, Phys. Rev. A 83, 023821 (2011)

M.I. Makin, Jared H. Cole, Charles D. Hill, Andrew D. Greentree, Lloyd C. L. Hollenberg Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian, Phys. Rev. A 80, 043842 (2009)

A. D. Greentree, C. Tahan, J. H. Cole, L. C. L. Hollenberg Quantum phase transitions of light, Nature Physics, 2, 856 (2006)

For more information about this project, please contact Jared Cole or Andrew Greentree.

Open quantum systems and decoherence theory

A project of the Theoretical Chemical and Quantum Physics Group


Mr. David Ing, Dr. Nicolas Vogt, Dr. Jan Jeske, A/Prof. Jared Cole


M. Marthaler, G. Schön: Karlsruhe Institute of Technology

S. Huelga, M. Plenio: University of Ulm

C. Müller, T. Stace: University of Queensland

Brief Project Outline

What defines the boundary between the quantum and classical worlds is one of the most fundamental questions of modern physics. Quantum theory has proven to be spectacularly successful at small length scales, short times and very cold temperatures. Yet, in our everyday world the equations of classical physics have a fundamentally different form and interpretation. How do we smoothly swap between these descriptions? - this is one of the central points of decoherence theory. How do we perturb an otherwise phase coherent theory (quantum mechanics) in order to include the effects of the wider environmental, ie. the effects of dephasing and dissipation.

The TCQP group studies this problem in a range of different physical systems and with several different mathematical techniques. Problems of current interest include:

  • Mathematical methods for describing spatial correlations in noise processes and there ramifications of these correlations in quantum system dynamics
  • The cross-over from Markovian to non-Markovian dynamics and the effects of finite bath effects
  • Extensions to the usual decoherence models for more efficient and scalable numerical simulation

A linear chain of spins is an ideal system to study effects due to spatially correlated noise. Here we show the transmission probability of so-called "perfect state transfer" as a function of correlation length of environmental dephasing.  We see that for noise which is correlated on length scales longer than the spin chain, the noise has little effect on the excitation transfer process.

The distribution of charge states in an single-electron transistor evolving as a function of time, computed using stochastic Bloch-Redfield theory. As the system evolves, the statistical distribution of charge states broadens due to the interplay of coherent and incoherent processes which are modelled consistently within a stochastic master equation.

Recent Publications

J. Jeske and J. H. Cole, Derivation of Markovian master equations for spatially correlated decoherence, Physical Review A 87 052138 (2013)

J. Jeske, N. Vogt and J. H. Cole, Excitation and state transfer through spin chains in the presence of spatially correlated noise, Physical Review A 88 062333 (2013)

N. Vogt, J. Jeske and J. H. Cole, Stochastic Bloch-Redfield theory: Quantum jumps in a solid-state environment, Physical Review B 88 174514 (2013)

For more information about this project, please contact Jared Cole.