5,091 research outputs found
Validity of single-channel model for a spin-orbit coupled atomic Fermi gas near Feshbach resonances
We theoretically investigate a Rashba spin-orbit coupled Fermi gas near
Feshbach resonances, by using mean-field theory and a two-channel model that
takes into account explicitly Feshbach molecules in the close channel. In the
absence of spin-orbit coupling, when the channel coupling between the
closed and open channels is strong, it is widely accepted that the two-channel
model is equivalent to a single-channel model that excludes Feshbach molecules.
This is the so-called broad resonance limit, which is well-satisfied by
ultracold atomic Fermi gases of Li atoms and K atoms in current
experiments. Here, with Rashba spin-orbit coupling we find that the condition
for equivalence becomes much more stringent. As a result, the single-channel
model may already be insufficient to describe properly an atomic Fermi gas of
K atoms at a moderate spin-orbit coupling. We determine a characteristic
channel coupling strength as a function of the spin-orbit coupling
strength, above which the single-channel and two-channel models are
approximately equivalent. We also find that for narrow resonance with small
channel coupling, the pairing gap and molecular fraction is strongly suppressed
by SO coupling. Our results can be readily tested in K atoms by using
optical molecular spectroscopy.Comment: 6 pages, 6 figure
Deterministic Constructions of Binary Measurement Matrices from Finite Geometry
Deterministic constructions of measurement matrices in compressed sensing
(CS) are considered in this paper. The constructions are inspired by the recent
discovery of Dimakis, Smarandache and Vontobel which says that parity-check
matrices of good low-density parity-check (LDPC) codes can be used as
{provably} good measurement matrices for compressed sensing under
-minimization. The performance of the proposed binary measurement
matrices is mainly theoretically analyzed with the help of the analyzing
methods and results from (finite geometry) LDPC codes. Particularly, several
lower bounds of the spark (i.e., the smallest number of columns that are
linearly dependent, which totally characterizes the recovery performance of
-minimization) of general binary matrices and finite geometry matrices
are obtained and they improve the previously known results in most cases.
Simulation results show that the proposed matrices perform comparably to,
sometimes even better than, the corresponding Gaussian random matrices.
Moreover, the proposed matrices are sparse, binary, and most of them have
cyclic or quasi-cyclic structure, which will make the hardware realization
convenient and easy.Comment: 12 pages, 11 figure
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