Michigan State University Localization and antiresonance in disordered qubit chains PRB 68, 214410 (03) JPA 36, L561 (03) L. F. Santos and M. I. Dykman Michigan State University Quantum computer modeled with an anisotropic spin-1/2 chain A defect in the chain a multiple localized many-excitation states Many particle antiresonance    THE MODEL QCs with perpetually coupled qubits: Nuclear spins with dipolar coupling Josephson junction systems Electrons on helium THE HAMILTONIAN ONE EXCITATION e1 localized excitation 2J one magnon e1 +(g2+J2)1/2 ELECTRONS HELIUM Energy: CONFINING ELECTRODES Qubit energy difference can be controlled Localized state on the defect: no threshold in an infinite chain. Localization length: g e0 e0 e0 e0 n0-1 n0 n0+1 n0+2 Strong anisotropy: D>>1 study many-body effects in a disordered spin system    TWO EXCITATIONS: IDEAL CHAIN NON-RESONANT DEFECT : g < JD RESONANT DEFECT: g ~ JD ONE DEFECT AT n0 The bound pair NEXT to the defect becomes strongly hybridized with the LDPs Strong anisotropy D>>1 Localized BOUND PAIRS: one excitation on the defect next to the defect (surface-type) 2J J/D 4J doublet LDP 2e1+g+JD 2e1+JD 2e1+g 2e1 BP doublet 2e1+g+JD Narrow band of bound pairs bound pairs localized BP n0 n0+1 2e1+JD J/D J/D 2e1+JD n0 +1 n0+2 LDP + 2J 2e1+g n0 +1 n0+2 n0 n0+2 two magnons Localized - delocalized pairs Unbound magnons Localization length: 4J 2e1 2e1 n0 n 4J when JD – g = J/2    ANTIRESONANT DECOUPLING g ~ JD SCATTERING PROBLEM FOR ANTIRESONANCE TIME EVOLUTION (numerical results - 10 sites) Resonanting bound pairs and states with one excitation on the defect DO NOT mix g=JD/4 g=JD nonoverlapping bands, a pair NEXT to the defect mixes with bound pairs only overlapping bands: localized-delocalized pairs only The coefficient of reflection of the propagating magnon from the defect R=1 bound pair NEXT to the defect Initial state: (n0 +1, n0 +2) … bound pair + n0 localized delocalized pair Final state: (n0 +2, n0 +3) + … (n0 , n0 +3) n0