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arXiv:1108.4498

Magnetic flux induce dissipation effect on the quantum phase diagram of mesoscopic SQUID array

Sujit Sarkar

Published Aug 23, 2011• 0 citations
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Abstract

We present the quantum phase diagram of mesoscopic SQUID array. We predict different quan- tum phases and the phase boundaries along with several special points. We present the results of magnetic flux induced dissipation on these points and also on the phase boundaries. The Josephson couplings at these points are dependant on the system parameter in a more complicated fashion and differ from the Ambegaokar and Baratoff relation. We derive the analytical relation between the dissipation strength and Luttinger liquid parameter of the system. We observe some interesting behaviour at the half-integer magnetic flux quantum and also the importance of co-tunneling effect.

DOI
10.48550/arxiv.1108.4498

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We present the quantum phase diagram of mesoscopic SQUID array. We predict different quan- tum phases and the phase boundaries along with several special points. We present the results of magnetic flux induced dissipation on these points and also on the phase boundaries. The Josephson couplings at these points are dependant on the system parameter in a more complicated fashion and differ from the Ambegaokar and Baratoff relation. We derive the analytical relation between the dissipation strength and Luttinger liquid parameter of the system. We observe some interesting behaviour at the half-integer magnetic flux quantum and also the importance of co-tunneling effect.
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We analyze the quantum phases of a superconducting quantum dot array. Superconducting quantum dots are connected through Josephson junction. We study the effect of finite range Josephson coupling and also finite range interactions between the dots. Our field-theoretical study predicts different kinds of phases near the charge degeneracy point. We predict two different kinds of repulsive Luttinger liquid phases originate from different sources: one from the commensurate-incommensurate transition and the other from the XYXYXY criticality. Apart from the charge-density wave, we also predict the possibility of dimer-order density wave from the interplay of long-range interaction between the dots and Cooper-pair density. We observe different multicritical points with interesting phases and also two special points. The renormalization group flow diagram also shows many interesting phases.
By means of perturbation analysis, assuming small inductance values, the dynamical equations for the gauge-invariant superconducting phase differences in a dc superconducting quantum interference device (SQUID), containing junctions with different resistive and coupling parameters, are reduced to a single nonlinear differential equation. The resulting effective reduced potential shows that degenerate phase states exist for half-integer values of the applied flux number ${\ensuremath{\Psi}}_{\mathit{ex}}$ and for zero bias current. It can be also shown that, by small variations of the externally applied flux, this degeneracy can be removed and, for sufficiently low values of the SQUID parameter $\ensuremath{\beta}$, different magnetic states, characterized by opposite magnetic moments, can be reversibly realized.
We consider SQUIDs containing a 0°–45° d-wave (D) Josephson junction with tunneling in the a–b plane through a thin ferromagnetic (F) barrier. In the clean case and for high barrier transparency, the coexistence of stable 0, π and metastable π/2 states in such DFD junctions could give a temperature-induced coexistence between stable integer, half-integer and quarter-integer fluxoid configurations in SQUIDs. This coexistence may take place in a finite range of barrier thicknesses (for a given value of the exchange field in the ferromagnet), resulting in two (double) flux jumps per one external flux quantum in the diagram Φeq(Φe) of equilibrium flux as a function of external flux. Novel quantum devices can be based on such SQUIDs.
Two states of a flux qubit with three Josephson junctions were shown in a single measurement with a dc-SQUID. The qubit is an aluminum superconductor loop surrounded by a dc-SQUID for readout. It has two states, which have persistent currents flowing in opposite directions. The readout data for three samples with different junction sizes suggest that the probability distribution for the double-well potential depends on the ratio of E J / E C , where E J is the Josephson energy and E C is the charging energy. The probability distribution was estimated by calculating the wavefunctions and energy levels for the measured samples. We measured the retrapping current of a dc-SQUID without the qubit as a function of the magnetic field. It was found that the relative phase relation for the magnetic field dependence of the retrapping current jumped from 0 to π at E J ≈ E C . This jump can be explained phenomenologically by taking into account the two kinds of dissipation arising from ac currents flowing through the lead and along the SQUID loop. The fact that the jump occurred at E J ≈ E C strongly suggests that the quantum nature of the electromagnetic environment needs to be taken into account in order to understand the origin of the dissipation.