Direct frequency-comb-driven Raman transitions in the terahertz range

We demonstrate the use of a femtosecond frequency comb to coherently drive stimulated Raman transitions between terahertz-spaced atomic energy levels. More specifically, we address the $3d~^2D_{3/2}$ and $3d~^2D_{5/2}$ fine structure levels of a single trapped $^{40}$Ca$^+$ ion and spectroscopically resolve the transition frequency to be $\nu_D = 1{,}819{,}599{,}021{,}534 \pm 8$ Hz. The achieved accuracy is nearly a factor of five better than the previous best Raman spectroscopy, and is currently limited by the stability of our atomic clock reference. Furthermore, the population dynamics of frequency-comb-driven Raman transitions can be fully predicted from the spectral properties of the frequency comb, and Rabi oscillations with a contrast of 99.3(6)\% and millisecond coherence time has been achieved. Importantly, the technique can be easily generalized to transitions in the sub-kHz to tens of THz range and should be applicable for driving, e.g., spin-resolved rovibrational transitions in molecules and hyperfine transitions in highly charged ions.Comment: 9 pages, 8 figure

Divorce Reform—One State’s Solution

Although New York has long been a leader in reform legislation, it has also had one of the most ineffective divorce laws in the nation. Therefore, it was not unrealistic to hope that when New York recently revised its divorce laws the new product would serve as a model for future reforms in other jurisdictions. While the new law as finally enacted is defective in several respects, its provisions reflect an attempt to accommodate the basic reform trends in current divorce law. This comment investigates briefly the evolution of governmental controls of divorce, the American tradition prior to the New York reform, and the implications of the procedures finally adopted by that state

Bolza quaternion order and asymptotics of systoles along congruence subgroups

We give a detailed description of the arithmetic Fuchsian group of the Bolza surface and the associated quaternion order. This description enables us to show that the corresponding principal congruence covers satisfy the bound sys(X) > 4/3 log g(X) on the systole, where g is the genus. We also exhibit the Bolza group as a congruence subgroup, and calculate out a few examples of "Bolza twins" (using magma). Like the Hurwitz triplets, these correspond to the factoring of certain rational primes in the ring of integers of the invariant trace field of the surface. We exploit random sampling combined with the Reidemeister-Schreier algorithm as implemented in magma to generate these surfaces.Comment: 35 pages, to appear in Experimental Mathematic

Spatial and temporal aspects of visual backward masking in children and young adolescents

We thank Marc Repnow for his help setting up the experiments. In addition, we thank two anonymous reviewers for their very thoughtful and helpful comments. This work was supported by the Volkswagen Foundation project “Between Europe and the Orient—A Focus on Research and Higher Education in/on Central Asia and the Caucasus” and by the VELUX Foundation project “Perception, Cognition and Healthy Brain Aging.”Peer reviewedPublisher PD