Localization and antiresonance in disordered qubit chains 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 multiple localized many-excitation states • Many particle antiresonance
PRB 68, 214410 (03) JPA 36, L561 (03)
int0 HHH THE HAMILTONIAN
),(84 111int
nnnn n
znn
zn
JJH
znn nH
2
10 0,0 nnn g
ONE EXCITATION
)exp(')exp(1 niCniC
Energy: cos11 JE
Localized state on the defect:no threshold in an infinite chain.
Localization length:
)/|(|sinh/1 1 Jgld
1
localizedexcitation
2Jone magnon
1g2+J2)1/2
TWO EXCITATIONS: IDEAL CHAIN
)(2
)(12
1221 mnimni eCeC Strong anisotropy 1
cos22
2 1
JJJEBP
Narrow band of bound pairs
Unbound magnons
J/
1
1+J
4J
bound pairs
two magnons
ANTIRESONANT DECOUPLING g ~ JResonanting bound pairs and states with one excitation on the defect DO NOT mix
(n0 +2, n0 +3)
bound pair(n0 +1, n0 +2)
bound pair NEXT to the defect
(n0 , n0 +3)
localized delocalized pair+
NON-RESONANT DEFECT : g < J
Localized - delocalized pairs
ONE DEFECT AT n0
n0 n0+1
n0 n
n0 +1 n0+2
RESONANT DEFECT: g ~ J
2J
J/
4J
doublet
LDP
21+g+J
21+J21+g
BP
n0 n0+2
n0 +1 n0+2
+
The bound pair NEXT to the defect becomes strongly hybridized with the LDPs
Localization length:
sLDPl when J–g = J/2
SCATTERING PROBLEMFOR ANTIRESONANCE The coefficient of reflection of the propagating magnon from the defect R=1
Initial state:
n0 …
n0
Final state:
… +
TIME EVOLUTION(numerical results - 10 sites)
nonoverlapping bands,a pair NEXT to the defect mixes with bound pairs only
overlapping bands:a pair NEXT to the defect mixes with localized-delocalized pairs only
THE MODEL
QCs with perpetually coupled qubits:Nuclear spins with dipolar couplingJosephson junction systemsElectrons on helium
HELIUM
CONFINING ELECTRODES
ELECTRONS
Qubit energy difference can be controlled
study many-body effects in a disordered spin system
n0-1 n0 n0+2n0+1
g
Localized BOUND PAIRS:one excitation on the defect
next to the defect (surface-type)
Stronganisotropy: >>1
J/
2J
4J
LDP
21+g
21+J
doublet21+g+J
localized BP
g=J g=J
