Quantum Accelerator Modes from the Farey Tree

TY - JOUR

T1 - Quantum Accelerator Modes from the Farey Tree

AU - Buchleitner, A.

AU - d'Arcy, M.B.

AU - Fishman, S.

AU - Gardiner, S.A.

AU - Guarneri, I.

AU - Ma, Z.-Y.

AU - Rebuzzini, L.

AU - Summy, G.S.

PY - 2006

Y1 - 2006

N2 - We show that mode locking finds a purely quantum nondissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode locking. A hierarchy for the rational numbers known as the Farey tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.

AB - We show that mode locking finds a purely quantum nondissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode locking. A hierarchy for the rational numbers known as the Farey tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.

U2 - 10.1103/PhysRevLett.96.164101

DO - 10.1103/PhysRevLett.96.164101

M3 - Article

SN - 1079-7114

VL - 96

JO - Physical Review Letters

JF - Physical Review Letters

IS - 16

M1 - 164101

ER -