606 research outputs found
On Nori's Fundamental Group Scheme
We determine the quotient category which is the representation category of
the kernel of the homomorphism from Nori's fundamental group scheme to its
\'etale and local parts. Pierre Deligne pointed out an error in the first
version of this article. We profoundly thank him, in particular for sending us
his enlightning example reproduced in Remark 2.4 2).Comment: 29 page
Inverse Landau-Zener-Stuckelberg problem for qubit-resonator systems
We consider theoretically a superconducting qubit - nanomechanical resonator
(NR) system, which was realized by LaHaye et al. [Nature 459, 960 (2009)].
First, we study the problem where the state of the strongly driven qubit is
probed through the frequency shift of the low-frequency NR. In the case where
the coupling is capacitive, the measured quantity can be related to the
so-called quantum capacitance. Our theoretical results agree with the
experimentally observed result that, under resonant driving, the frequency
shift repeatedly changes sign. We then formulate and solve the inverse
Landau-Zener-Stuckelberg problem, where we assume the driven qubit's state to
be known (i.e. measured by some other device) and aim to find the parameters of
the qubit's Hamiltonian. In particular, for our system the qubit's bias is
defined by the NR's displacement. This may provide a tool for monitoring of the
NR's position.Comment: 10 pages, 7 figure
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