The study of entanglement in quantum systems is an area of much recent experimental and theoretical work and is of central importance in the implementation of various protocols in quantum information science. The dynamical properties of entanglement are examined in the context of the XY spin 1/2 chain model with a staggered magnetic field. The quality of entangled state transfer is found to be comparable to the uniform field XY spin 1/2 chain in the strong field regime. The effects of anisotropy on state transfer is also considered, as well as the interaction between entanglement waves and the possibility of transmission of multiple bits of quantum information. As an additional system where these quantum entanglement dynamics might play out, a large array of mesoscopic junctions made out of gapless unconventional superconductors is also studied. In this model, the tunneling processes of both particle-hole and Cooper pairs give rise to a strongly retarded effective action which, contrary to the case of conventional superconductors, cannot be readily characterized in terms of a local Josephson energy. This is an action that describes, for example, grain boundary and c-axis junctions in layered high-Tc superconductors. The emergent collective phenomena in this system are obtained, along with the phase diagram and the electrical conductivity of the model.
We study the dynamics of entanglement in an
XY spin chain subject to a staggered magnetic field and contrast it to the previously discussed uniform field case. We find that in the isotropic
(XX) limit a staggered field can provide almost equally favorable conditions for a high-fidelity transfer of entanglement, while even a modest amount of exchange anisotropy appears to have a strong detrimental effect. We also study interactions between different waves of entanglement and assess the possibility of simultaneous transmission of multiple bits of quantum information.
Conventional tunnel Josephson junctions form the basic building blocks of superconducting electronics. Their operation is based on comparatively simple dynamics where the superconducting phases across the junctions is the only dynamical degree of freedom. The goal of the project on which this thesis is based, is to understand the physics and develop a consistent theoretical description of the quantum dynamics of unconventional Josephson structures: spin active junctions, junctions containing low energy quasiparticles, and junctions composed of
d-wave superconductors. Spin active Josephson junctions involve the additional degree of freedom of quasiparticle spin. Here we theoretically investigate the spin-structure of the current carrying interface bound states - Andreev Bound States (ABS), and induced ground state spin polarization of a short (shorter than the superconducting coherence length) nanowire junction containing a localized magnetic moment. We show that temporal variation of the superconducting phase difference and magnetic moment induce rotations in spin polarized and unpolarized subspaces respectively, which is manifested by temporal oscillation of the Josephson current.The interlevel transitions obey a selection rule that forbids manipulations in a certain region ofexternal parameters and results from specific properties of Andreev bound states in magnetic contacts where, in a certain regime of phase bias and strength of magnetic scatterer, ABS belong to different eigenstates of the combined charge and parity inversion symmetry operator.A general framework is developed to include low energy quasiparticle states into the dynamics of Josephson junctions. Such states exist in e.g. constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. The existence of such states prevent the separation of energy scales which in conventional tunnel junctions freezes out the quasiparticle degrees of freedom. We show that the resonant interaction with such low energy states rather than the Josephson potential defines the nonlinear Josephson dynamics at small amplitudes.The framework is applied to high temperature Josephson junctions, whose unconventional order parameter admits ABS with energies in the middle of the superconducting gap - Mid Gap States (MGS). In addition to the non-linear dynamics induced by the MGS, we identify a reentrance effect in the transition between thermal activation and macroscopic quantum tunneling associated with the MGS, and connect this phenomenon to experimental observations.
We study theoretically a variety of collective quantum phases occurring in frustrated sawtooth chains of Josephson junctions embedded in a dissipationless transmission line. The basic element of a system, i.e., the triangular superconducting cell, contains two 0 and one $\ensuremath{\pi}$ Josephson junctions characterized by
EJ and $\ensuremath{\alpha}{E}_{J}$ Josephson energies, accordingly. In the frustrated regime the low-energy quantum dynamics of a single cell is determined by anticlockwise or clockwise flowing persistent currents (vortex or antivortex). The direct embedding of $\ensuremath{\pi}$ Josephson junctions in a transmission line allows us to establish a short or long-range interaction between (anti)vortices of well-separated cells. By making use of the variational approach, we map the superconducting circuit Hamiltonian to an effective
XX spin model with an exchange spin-spin interaction decaying with the distance
x as ${x}^{\ensuremath{-}\ensuremath{\beta}}$, and the local ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x,n}$ terms corresponding to the coherent quantum beats between vortex and antivortex in a single cell. We obtain that, in long arrays such as $N\ensuremath{\gg}{\ensuremath{\ell}}_{0}\ensuremath{\simeq}\sqrt{C/{C}_{0}}$, where
C and
C0 are capacitances of a 0 Josephson junction and a transmission line, respectively, the amplitude of quantum beats is strongly suppressed. By means of exact numerical diagonalization, we study the interplay between the coherent quantum beats and the exchange spin-spin interaction leading to the appearance of various collective quantum phases such as the paramagnetic (
P), compressible superfluid (
CS), and weakly compressible superfluid ($w\text{\ensuremath{-}}CS$) states.
Magnetic and topological properties along with quantum correlations in terms of several entanglement measures have been investigated for an antiferromagnetic (AFM) spin-1/2 XY model in the presence of transverse magnetic field and XZX-YZY type of three-spin interactions. Symmetries of the spin Hamiltonian have been identified. Under the Jordan-Wigner transformation, the spin Hamiltonian converted into spinless superconducting model with nearest neighbor (NN) hopping and Cooper pairing terms in addition to next NN Cooper pairing potential. Long range AFM order has been studied in terms of staggered spin-spin correlation functions, while the topological orders have been characterized by winding numbers. Magnetic and topological phase diagrams have been prepared. Faithful coexistence of magnetic and topological superconducting phases is found in the entire parameter regime. Boundaries of various quantum phases have been marked and positions of bicritical points have been identified.
Quantum dynamics of in-plane Josephson junctions between two d-wave superconducting films is described by the anisotropic XY -model, where both quasiparticle and Cooper pair tunnelling terms appear to be equally non-local. Applying a combination of the weak and strong coupling analyses to this model, we find compelling evidence of a dissipative phase transition. The corresponding critical behaviour is studied and contrasted with that found previously in the conventional (s-wave) Josephson junctions.
We study quantum dynamics of and phase transitions in a Josephson junction between two planar d-wave superconductors where the processes of both quasiparticle and Cooper pair tunneling give rise to nonlocal dissipative terms in the effective action. By combining a perturbative weak coupling analysis in the charge representation with a variational approach in the phase representation at strong coupling, we ascertain a layout of the junction's phase diagram and discuss the corresponding behaviors.