2,363 research outputs found
Quantum memory coupled to cavity modes
Inspired by spin-electric couplings in molecular magnets, we introduce in the
Kitaev honeycomb model a linear modification of the Ising interactions due to
the presence of quantized cavity fields. This allows to control the properties
of the low-energy toric code Hamiltonian, which can serve as a quantum memory,
by tuning the physical parameters of the cavity modes, like frequencies, photon
occupations, and coupling strengths. We study the properties of the model
perturbatively by making use of the Schrieffer-Wolff transformation and show
that, depending on the specific setup, the cavity modes can be useful in
several ways. They allow to detect the presence of anyons through frequency
shifts and to prolong the lifetime of the memory by enhancing the anyon
excitation energy or mediating long-range anyon-anyon interactions with tunable
sign. We consider both resonant and largely detuned cavity modes.Comment: 16 pages, 6 figure
Physical solutions of the Kitaev honeycomb model
We investigate the exact solution of the honeycomb model proposed by Kitaev
and derive an explicit formula for the projector onto the physical subspace.
The physical states are simply characterized by the parity of the total
occupation of the fermionic eigenmodes. We consider a general lattice on a
torus and show that the physical fermion parity depends in a nontrivial way on
the vortex configuration and the choice of boundary conditions. In the
vortex-free case with a constant gauge field we are able to obtain an
analytical expression of the parity. For a general configuration of the gauge
field the parity can be easily evaluated numerically, which allows the exact
diagonalization of large spin models. We consider physically relevant
quantities, as in particular the vortex energies, and show that their true
value and associated states can be substantially different from the one
calculated in the unprojected space, even in the thermodynamic limit
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