Creation of NOON states by double Fock-state/Bose-Einstein condensates

NOON states (states of the form $|N>_{a}|0>_{b}+|0>_{a}|N>_{b}$ where $a$ and $b$ are single particle states) have been used for predicting violations of hidden-variable theories (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state/Bose-Einstein condensates as sources in a modified Mach Zender interferometer can lead to the creation of the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$ is the total number of particles in the two condensates. The modification of the interferometer involves making conditional ``side'' measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter. The result is equivalent to the quantum experiment in which a large molecule passes through two slits. The NOON states are combined in a final beam splitter and show interference. Attempts to detect through which ``slit'' the condensates passed destroys the interference.Comment: 8 pages 5 figure

Feedback control of spin systems

The feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems.Comment: 16 pages, 15 figure

Paramagnetic Faraday rotation with spin-polarized ytterbium atoms

We report observation of the paramagnetic Faraday rotation of spin-polarized ytterbium (Yb) atoms. As the atomic samples, we used an atomic beam, released atoms from a magneto-optical trap (MOT), and trapped atoms in a far-off-resonant trap (FORT). Since Yb is diamagnetic and includes a spin-1/2 isotope, it is an ideal sample for the spin physics, such as quantum non-demolition measurement of spin (spin QND), for example. From the results of the rotation angle, we confirmed that the atoms were almost perfectly polarized.Comment: 8 pages, 20 figure

The structural and mechanical properties of the Achilles tendon 2 years after surgical repair

Background Acute ruptures of the Achilles tendon affect the tendon's structural and mechanical properties. The long-term effects of surgical repair on these properties remain unclear. Purpose To evaluate effects of early mobilization versus traditional immobilization rehabilitation programs 2 years after surgical Achilles tendon repair, by comparing force-elongation and stress-strain relationships of the injured tendon to those of the uninjured tendon. Methods A group of males with previous Achilles tendon rupture (n = 18) and a group of healthy male controls (n = 9) participated. Achilles tendon rupture group consisted of patients that had received early mobilization (n = 9) and patients that had received traditional immobilization with a plaster cast (n = 9). Comparisons of tendon structural and mechanical properties were made between Achilles tendon rupture and healthy control groups, and between the uninjured and injured sides of the two rehabilitation groups in Achilles tendon rupture group. Ultrasound was used to determine bilaterally tendon cross-sectional area, tendon resting length, and tendon elongation as a function of torque during maximal voluntary plantar flexion. From these data, Achilles tendon force-elongation and stress-strain relationships were determined. Findings The Achilles tendon rupture group uninjured side was not different from healthy control group. Structural and mechanical parameters of the injured side were not different between the Achilles tendon rupture early mobilization and the immobilization groups. Compared to the uninjured side, the injured side showed a reduction in stress at maximal voluntary force, in Young's modulus and in stiffness. Interpretation Two years post-surgical repair, the Achilles tendon mechanical properties had not returned to the uninjured contralateral tendon values

Robust optimization with simulated annealing

Robust optimization, Simulated annealing, Global optimization, Nonconvex optimization,