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A one-shot deviation principle for stability in matching problems
This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation
A one-shot deviation principle for stability in matching problems
This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation
A one-shot deviation principle for stability in matching problems
This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation
Locking Local Oscillator Phase to the Atomic Phase via Weak Measurement
We propose a new method to reduce the frequency noise of a Local Oscillator
(LO) to the level of white phase noise by maintaining (not destroying by
projective measurement) the coherence of the ensemble pseudo-spin of atoms over
many measurement cycles. This scheme uses weak measurement to monitor the phase
in Ramsey method and repeat the cycle without initialization of phase and we
call, "atomic phase lock (APL)" in this paper. APL will achieve white phase
noise as long as the noise accumulated during dead time and the decoherence are
smaller than the measurement noise. A numerical simulation confirms that with
APL, Allan deviation is averaged down at a maximum rate that is proportional to
the inverse of total measurement time, tau^-1. In contrast, the current atomic
clocks that use projection measurement suppress the noise only down to the
level of white frequency, in which case Allan deviation scales as tau^-1/2.
Faraday rotation is one of the possible ways to realize weak measurement for
APL. We evaluate the strength of Faraday rotation with 171Yb+ ions trapped in a
linear rf-trap and discuss the performance of APL. The main source of the
decoherence is a spontaneous emission induced by the probe beam for Faraday
rotation measurement. One can repeat the Faraday rotation measurement until the
decoherence become comparable to the SNR of measurement. We estimate this
number of cycles to be ~100 cycles for a realistic experimental parameter.Comment: 18 pages, 7 figures, submitted to New Journal of Physic
Millimeter-long Fiber Fabry-Perot cavities
We demonstrate fiber Fabry-Perot (FFP) cavities with concave mirrors that can
be operated at cavity lengths as large as 1.5mm without significant
deterioration of the finesse. This is achieved by using a laser dot machining
technique to shape spherical mirrors with ultralow roughness and employing
single-mode fibers with large mode area for good mode matching to the cavity.
Additionally, in contrast to previous FFPs, these cavities can be used over an
octave-spanning frequency range with adequate coatings. We also show directly
that shape deviations caused by the fiber's index profile lead to a finesse
decrease as observed in earlier attempts to build long FFP cavities, and show a
way to overcome this problem
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