Linear voltage response of non-uniform arrays of bi-SQUIDs

摘要

An amplifier and method for improving linear response includes a plurality of N bi-SQUIDs. Each bi-SQUID has a non-uniform bi-SQUID parameter βi, described by βi=2πLiIciΦ0 can be defined for each bi-SQUIDs from i=1 to N, where Li is the loop inductance, ic is the critical current, and Φ0 is a flux quantum for each bi-SQUID. The non-uniform bi-SQUIDs can be connected in series or in parallel to establish a Superconducting Quantum Interference Filter (SQIF) array of bi-SQUIDs. Once connected, a mutual inductance between the connected bi-SQUIDs can be established. If the mutual inductance between connected bi-SQUIDs is accounted for, careful manipulation of the critical current or the loop size, or both, of each bi-SQUID can result in extremely uniform behavior (linear response) of the SQIF when considered as a whole, even though the behavior of the element bi-SQUIDs is non-uniform (different βi, parameters).

主权项

1. A method for improving linearity over a wide dynamic range for an amplifier, comprising the steps of:
A) providing a plurality of N individual array cells; each said array cell having 3 Josephson Junctions to establish a bi-Superconductive Quantum Interference Device (SQUID) for said array cell, each said Josephson Junction having a critical current ic, and loop inductance Li; each said bi-SQUIDs further having a non-uniform bi-SQUID parameter βi, described by βi=2πLiici/Φ0, from i=1 to N, where Li is said loop inductance, ici is said critical current, and Φ0 is a flux quantum for each said bi-SQUID; B) connecting said array cells in series to establish a Superconducting Quantum Interference Filter (SQIF) array of N said bi-SQUIDs; wherein said step B) establishes mutual inductances between said array cells, and wherein said non-linearity parameter βi is manipulated by changing said critical current ici for each said bi-SQUID according to a predetermined Gaussian distribution pattern; and, wherein said critical current is determined according to the relationship
(L1,i+L2a,i){dot over (φ)}i,1−L2b,i{dot over (φ)}i,2−L1,i{dot over (φ)}i,3=L1b,iib+φi,2−φi,1+2πφean,i+MΦi+L1,iic3,i sin φi,3+L2b,isin φi,2−(L1,i+L2a,i)sin φi,1L2a,i{dot over (φ)}i,1−(L1,i+L2b,i){dot over (φ)}i,2−L1,i{dot over (φ)}i,3=−L1a,iib+φi,2−φi,1+2πφean,i+MΦi+L1,iic3,i sin φi,3−L2a,i sin φi,1L2a,i{dot over (φ)}i,1−L2b,i{dot over (φ)}i,2−(L3a,i+L3b,i){dot over (φ)}i,3=φi,2−φi,3+φi,1+MΦi−(L3a,i+L3b,i)ic3,i sin φi,3−L2a,i sin φi,1+L2b,i sin φi,2,where φi,j are the phases on each said Josephson Junctions Jij, i=1 to N, j=1 to 3, L1,i=(L1a,i+L1b,i), an,i is a parameter related to the loop size between Ji,1 and Ji,2, and M is the coupling strength for the phase interaction Φi between adjacent said bi-SQUIDS (one adjacent said bi-SQUID for edge said bi-SQUIDS a=1 and N, and two neighboring said bi-SQUIDs for inner said bi-SQUIDS a=2 through N−1) according toΦi={1an,2⁢(φ2,1-φ2,2-2⁢⁢π⁢⁢φe⁢an,2),for⁢⁢i=11an,i+1⁢(φi+1,1-φi+1,2-2⁢⁢π⁢⁢φe⁢an,i+1)+1an,i-1⁢(φi-1,1-φi-1,2-2⁢⁢π⁢⁢φe⁢an,i-1),for⁢⁢i=2,…⁢,N-11an,N-1⁢(φN-1,1-φN-1,2-2⁢⁢π⁢⁢φe⁢an,N-1),for⁢⁢i=N where ib is a bias current and ic3=Ic3/Ic is a normalized said critical current of a third said Josephson Junction J3 in each said bi-SQUID.