Quasienergy anholonomy and its application to adiabatic quantum state manipulation

Abstract

The parametric dependence of a quantum map under the influence of a rank-1 perturbation is investigated. While the Floquet operator of the map and its spectrum have a common period with respect to the perturbation strength $\lambda$, we show an example in which none of the quasienergies nor the eigenvectors obey the same period: After a periodic increment of $\lambda$, the quasienergy arrives at the nearest higher one, instead of the initial one, exhibiting an anholonomy, which governs another anholonomy of the eigenvectors. An application to quantum state manipulations is outlined.

10pages, 1figure. To be published in Phys. Rev. Lett.

References in corpus (9)

• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Holonomic Quantum Computation
• Geometric quantum computation with NMR
• Time Dependent Floquet Theory and Absence of an Adiabatic Limit
• Symmetry, Duality and Anholonomy of Point Interactions in One Dimension
• Exponential complexity of an adiabatic algorithm for an NP-complete problem
• Connection Conditions and the Spectral Family under Singular Potentials
• Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction
• Double Spiral Energy Surface in One-dimensional Quantum Mechanics of Generalized Pointlike Potentials

Cited by in corpus (24)

• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Quantized Adiabatic Transport in Momentum Space
• Floquet Semimetal with Floquet-band Holonomy
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• Topological swing in Bloch oscillations
• A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds
• New anatomy of quantum holonomy
• Quantum holonomy in Lieb-Liniger model
• Cheon's anholonomies in Floquet operators
• Exotic quantum holonomy in Hamiltonian systems
• Adiabatic quantum computation along quasienergies
• Exotic quantum holonomy induced by degeneracy hidden in complex parameter space
• Adiabatic excitation of a confined particle in one dimension with a variable infinitely sharp wall
• Bloch vector, disclination and exotic quantum holonomy
• Quantum anholonomies in time-dependent Aharonov-Bohm rings
• Gauge invariants of eigenspace and eigenvalue anholonomies: Examples in hierarchical quantum circuits
• Exotic quantum holonomy and non-Hermitian degeneracies in two-body Lieb-Liniger model
• Complete population inversion of Bose particles by an adiabatic cycle
• Eigenvalue and eigenspace anholonomies in hierarchical systems
• Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions
• Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops
• Generating nonequilibrium stationary state from ground state condensate through an almost-adiabatic cycle
• Topological adiabatic dynamics in classical mass-spring chains with clamps
• A topological formulation for exotic quantum holonomy