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Chinese Physics

Investigation of spontaneous magnetization of coupled 2 2 superconducting ring array

Zhuangzhi Li, Furen Wang, Yang Tao, Xinyuan Liu, Ping Ma, Xie Fei-Xiang, Nie Rui-Juan, Dai Yuan-Dong

Published Mar 25, 2004• 4 citations
Publisher

Abstract

We present the theoretical investigation of spontaneous magnetization of a coupled 2 × 2 π ring array. It is indicated by free energy calculation that the system has the lowest energy when the four π rings have the full antiparallel configuration. Furthermore, the numerical evaluation results show that the system which favours full antiparallel spontaneous magnetization is a quantum effect deriving from the phase cohering of the superconducting quantum wavefunctions in the four superconducting rings through the shared Josephson junctions.

DOI
10.1088/1009-1963/13/4/021

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arXiv:cond-mat/9510059•Physical review. B, Condensed matter•Jul 1, 1996•18 citations
We present the theoretical investigation of spontaneous magnetization of a coupled 2 × 2 π ring array. It is indicated by free energy calculation that the system has the lowest energy when the four π rings have the full antiparallel configuration. Furthermore, the numerical evaluation results show that the system which favours full antiparallel spontaneous magnetization is a quantum effect deriving from the phase cohering of the superconducting quantum wavefunctions in the four superconducting rings through the shared Josephson junctions.
We have analyzed the quantum interference effects in the macroscopic “superconducting molecule.” The composite system consists of two massive superconducting rings, each interrupted by a Josephson junction, which are at the same time weakly coupled with one another. The special case of coupling via the Josephson four-terminal junction is considered. The structure of the macroscopic quantum states in an applied magnetic field is calculated. It is shown that, depending on the values of the magnetic fluxes through each ring, the system displays two groups of states, the “orthostates” with both induced currents going in the same direction, and the “parastates” with the opposite currents and with the total induced flux locked to zero value. The transition to the flux locked state with changing of the total applied flux is sudden and is preserved in a certain interval which is determined by the difference of the fluxes applied through each ring. It makes the system sensitive to small gradients of the external magnetic field.
The presence of spontaneous currents in unconventional Josephson junctions gives rise to the possibility of using zero magnetic field magnetization states in an unconventional loop as qubit states in a Josephson quantum computing device. However, the advantage of zero field may be insufficient to overcome the problems arising in the design and fabrication of low-noise, low-dissipation, reproducible devices. On the other hand, low-T/sub c/ "flux" devices suffer the same problems though their perspectives are more promising. The solution could be an increase in the device complexity, but with the gain of an effective advantage on the external noise rejection of the system during quantum evolution. Using advanced fabrication techniques it is now possible to build Josephson junction arrays made of superconducting unconventional loops. On this basis, a new qubit device can be designed as a ring array of unconventional loops. From a theoretical point of view this device is analogous to an annular Josephson junction, but with a "built in" natural degeneracy. For their topological and energetical properties, such arrays could be excellent devices for the qubit circuitry usable as the basic building blocks for quantum computing devices. In this work, we show how some of the principles of qubit design could be implemented in such devices.
Reentrant superconducting behavior of the critical supercurrent temperature dependencies has been observed for the Nb–Cu/Ni–Nb Josephson SFS (superconductor–ferromagnet–superconductor) junctions. The Ic(T) oscillations detected are associated with a crossover of the SFS junctions from '0'- to 'π'-state that is related to a special feature of superconducting pair flow through a ferromagnet (spatial oscillations of induced superconducting order parameter in presence of the exchange field). A triangular array of the junctions in the π-state shows evidence for a phase shift of π on the Ic(H) dependence. We have argued advantages of the SFS π-junction use for the quantum bit implementation based on the superconducting loop with quantum Josephson junctions. While designs proposed previously are based on magnetically frustrated superconducting loops, we discuss the advantages offered by the π-junctions in obtaining naturally degenerate two-level systems.
We study quantum phase-slip (QPS) processes in a superconducting ring containing NNN Josephson junctions and threaded by an external static magnetic flux ${\ensuremath{\Phi}}_{B}$. In such a system, a QPS consists of a quantum tunneling event connecting two distinct classical states of the phases with different persistent currents [Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson coupling energy EJ{E}_{J}EJ​ of the junctions is larger than the charging energy EC=e2/2C{E}_{C}={e}^{2}/2CEC​=e2/2C, where CCC is the junction capacitance, the quantum amplitude for the QPS process is exponentially small in the ratio EJ/EC{E}_{J}/{E}_{C}EJ​/EC​. At given magnetic flux, each QPS can be described as the tunneling of the phase difference of a single junction of almost $2\ensuremath{\pi}$, accompanied by a small harmonic displacement of the phase difference of the other $N\ensuremath{-}1$ junctions. As a consequence, the total QPS amplitude ${\ensuremath{\nu}}_{\mathrm{ring}}$ is a global property of the ring. Here, we study the dependence of ${\ensuremath{\nu}}_{\mathrm{ring}}$ on the ring size NNN, taking into account the effect of a finite capacitance C0{C}_{0}C0​ to ground, which leads to the appearance of low-frequency dispersive modes. Josephson and charging effects compete and lead to a nonmonotonic dependence of the ring's critical current on NNN. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the system converges either towards a superconducting or an insulating state, depending on the ratio between the charging energy E0=e2/2C0{E}_{0}={e}^{2}/2{C}_{0}E0​=e2/2C0​ and the Josephson coupling energy EJ{E}_{J}EJ​.
We propose a qubit consisting of a superconducting ring with two zero junctions and one ferromagnetic π junction. In the system, degenerate states appear in the phase space without an external magnetic field because of a competition between the zero and π states. Quantum tunneling between the degenerate states leads to a formation of bonding and antibonding states which are used as a bit. For manipulating the states, only a small magnetic field around zero is required. This feature leads to a large-scale integration and a construction of the smaller-sized qubit which is robust to the decoherence by external noises.
We investigate uniform one-dimensional arrays of small Josephson junctions [EJ{\mathit{E}}_{\mathit{J}}EJ​\ensuremath{\ll}EC{\mathit{E}}_{\mathit{C}}EC​, EC{\mathit{E}}_{\mathit{C}}EC​=(2e)2{)}^{2})2/2C] with a realistic Coulomb interaction U(x)=EC{\mathit{E}}_{\mathit{C}}EC​\ensuremath{\lambda}exp(-|x|/\ensuremath{\lambda}) (here \ensuremath{\lambda}\ensuremath{\gg}1 is the screening length in units of the lattice constant of the array). At low energies this system can be described in terms of interacting Bose particles (extra single Cooper pairs) on the lattice. With increasing concentration \ensuremath{\nu} of extra Cooper pairs, a crossover from the Bose gas phase to the Wigner crystal phase and then to the superlattice regime occurs. The phase diagram in the superlattice regime consists of commensurable insulating phases with \ensuremath{\nu}=1/l (l is integer) separated by superconducting regions where the current is carried by excitations with fractional electric charge q=\ifmmode\pm\else\textpm\fi{}2e/l. The Josephson current through a ring-shaped array pierced by magnetic flux is calculated for all of the phases. \textcopyright{} 1996 The American Physical Society.