Localization and antiresonance in disordered qubit chains PRB

Localization and antiresonance in disordered qubit chains PRB 68, 214410 (03) JPA 36, L 561 (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 ELECTRONS QCs with perpetually coupled qubits: THE HAMILTONIAN n 0 localized excitation one magnon 2 J CONFINING ELECTRODES Localized state on the defect: no threshold in an infinite chain. g e 0 e 1 Energy: Qubit energy difference can be controlled n 0 -1 e 1 +(g 2+J 2)1/2 HELIUM Nuclear spins with dipolar coupling Josephson junction systems Electrons on helium e 0 ONE EXCITATION e 0 n 0+1 n 0+2 Localization length: Strong anisotropy: D>>1 study many-body effects in a disordered spin system TWO EXCITATIONS: IDEAL CHAIN Strong anisotropy D>>1 Narrow band of bound pairs J/D 2 e 1+g+JD ANTIRESONANT DECOUPLING g ~ JD Resonanting bound pairs and states with one excitation on the defect DO NOT mix bound pair NEXT to the defect bound pair (n 0 +2, n 0 +3) (n 0 +1, n 0 +2) + localized delocalized pair (n 0 , n 0 +3) J/D LDP 2 e 1+g 2 e 1 n 0 n SCATTERING PROBLEM FOR ANTIRESONANCE The coefficient of reflection of the propagating magnon from the defect R=1 Initial state: n 0 … + 2 e 1+JD n 0 +1 n 0+2 doublet BP J/D 2 J 2 e 1+g + LDP n 0+2 Localization length: when JD – g = J/2 2 e 1 4 J TIME EVOLUTION (numerical results - 10 sites) nonoverlapping bands, a pair NEXT to the defect mixes with bound pairs only … Final state: n 0 4 J g ~ JD The bound pair NEXT to the defect becomes strongly hybridized with 2 e 1+g+JD the LDPs n 0 Localized - delocalized pairs 4 J RESONANT DEFECT: 2 J n 0 +1 n 0+2 two magnons 2 e 1 doublet 2 e 1+JD n 0+1 localized BP next to the defect (surface-type) Unbound magnons g < JD ONE DEFECT AT n 0 Localized BOUND PAIRS: one excitation on the defect bound pairs 2 e 1+JD NON-RESONANT DEFECT : overlapping bands: a pair NEXT to the defect mixes with localized-delocalized pairs only g=JD/4 g=JD