An admissible level $$\widehat{\mathfrak {osp}} \left( 1 \big \vert 2 \right) $$-model: modular transformations and the Verlinde formula

The modular properties of the simple vertex operator superalgebra associated with the affine Kac–Moody superalgebra \(\widehat{{\mathfrak {osp}}} (1|2)\) at level \(-\frac{5}{4}\) are investigated. After classifying the relaxed highest-weight modules over this vertex operator superalgebra, the characters and supercharacters of the simple weight modules are computed and their modular transforms are determined. This leads to a complete list of the Grothendieck fusion rules by way of a continuous superalgebraic analog of the Verlinde formula. All Grothendieck fusion coefficients are observed to be non-negative integers. These results indicate that the extension to general admissible levels will follow using the same methodology once the classification of relaxed highest-weight modules is completed.     

Large area light-pulse atom interferometry

We report the experimental demonstration of a large area atom interferometer based on extended sequences of light pulses. We characterize the interferometer through measurement of the acceleration due to gravity and demonstrate a threefold enhancement in intrinsic acceleration sensitivity. The technique is applicable to many atom interferometer configurations, including those used for measurement of rotations, gravity gradients, and Planck's over 2pi/m.     

Injection-locking technique for heterodyne optical phase locking of a diode laser

A novel technique is demonstrated for heterodyne optical phase locking of a diode laser to a single-frequency source by injection seeding. By modulation of the drive current of the diode laser at as much as several gigahertz, FM sidebands are imposed upon the output. We demonstrate that it is possible to phase lock either sideband to an injected beam. The carrier of the diode laser output is therefore locked in phase with the injected light but with a frequency difference given by the modulation of the drive current. The phase fluctuations between the lasers are analyzed, and the variance is found to be (4.4( degrees ))(2) , corresponding to 99.4% of the diode carrier light locked to the injected beam.