Simultaneous bicolor interrogation in thulium optical clock providing very low systematic frequency shifts

Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty, demonstrating incredible control over external perturbations of the clock transition frequency. At the same time, there is an increasing demand for atomic (ionic) transitions and new interrogation and readout protocols providing minimal sensitivity to external fields and possessing practical operational wavelengths. One of the goals is to simplify the clock operation while maintaining the relative uncertainty at a low 10−18 level achieved at the shortest averaging time. This is especially important for transportable and envisioned space-based optical clocks. Here, we demonstrate implementation of a synthetic frequency approach for a thulium optical clock with simultaneous optical interrogation of two clock transitions. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of the tensor lattice Stark shift in thulium can also be reduced to below 10−18 in fractional frequency units. This makes the thulium optical clock almost free from hard-to-control systematic shifts. The “simultaneous” protocol demonstrates very low sensitivity to the cross-talks between individual clock transitions during interrogation and readout.

Investment Choice with Managerial Incentive Schemes

In this paper, we show that firms might get an additional strategic benefit from using marginal-cost-reducing investments in conjunction with strategic delegation. While both these instruments allow firms to “aggressively” participate in product market competition, we show that they act as substitutes or complements depending on whether they are chosen simultaneously or sequentially. Given that the use of such instruments is inseparably linked with a Prisoner’s Dilemma kind of situation, our analysis shows a way to mitigate at least to some extent such effects, through their simultaneous use. We find that the unique Nash equilibrium of the game with commitment comprises both players choosing the instruments simultaneously. In case the instruments are chosen without commitment, an asymmetric equilibrium is shown to exist in addition to the simultaneous protocol, yielding unequal payoffs.

Distortion Product Otoacoustic Emissions: Comparison of Sequential versus Simultaneous Presentation of Primary-Tone Pairs

This Grason-Stadler GSI-60 system for measuring distortion product otoacoustic emissions (DPOAEs) allows the examiner to present one set of primary-tone pairs at a time (i.e., sequential presentation), or to present as many as four sets of primary-tone pairs at a time (i.e., simultaneous presentation). The Sequential and Simultaneous protocols were used to compare administration times, DPOAEs, and noise floors (NFs) on normal-hearing subjects at three frequencies (f2 = 1000, 2000, and 4000 Hz) and eight intensities (L1 = 40–75 dB SPL in 5 dB steps; L2 = 30–65 dB SPL). The Simultaneous protocol was completed in less than half the time (mean = 2 minutes, 21 seconds) required for the Sequential protocol (mean = 5 minutes, 13 seconds). When stimulus intensity (L1) was <60 dB SPL, the Sequential and Simultaneous protocols yielded similar DPOAEs and NFs. However, at the higher L1 intensities, the NFs for the Simultaneous protocol were larger than those for the Sequential protocol. The higher Simultaneous NFs reflect the greater system distortion/noise generated by the GSI-60 instrumentation. Reliability was assessed using the standard error of measurement of the difference between two scores. The data revealed no significant differences between protocols, and suggest that differences between two DPOAEs are statistically significant if they exceed ~7 dB (95% confidence interval). Este sistema Grason-Stadler (GSI-60) para la medición de emisiones otoacústicas por productos de distorsión (DPOAE) permite al examinador la presentación de un juego de pares de tonos primarios al mismo tiempo (p.e., presentación secuencial), o presentar hasta cuatro juegos de pares de tonos primarios a la vez (p.e., presentación simultánea). Se utilizaron los protocolos Secuencial y Simultáneo para comparar los tiempos de administración, las DPOAE y los pisos de ruido (NF) en sujetos normo-oyentes, en tres frecuencias (f2 = 1000, 2000 y 4000 Hz) y ocho intensidades (L1 = 40-75 dB en pasos de 5 dB; L2 = 30-65 dB SPL). El protocolo Simultáneo se completó en menos de la mitad del tiempo (media = 2 minutos, 21 segundos) requerido por el protocolo Secuencial (media = 5 minutos, 13 segundos). Cuando la intensidad del estímulo (L1) fue £60 dB SPL, los protocolos Secuencial y Simultáneo rindieron DPOAE y NF similares. Sin embargo, en las intensidades L1 más altas, los NF para el protocolo Simultáneo fueron mayores que aquellas para el protocolo Secuencial. Los NF Simultáneos más altos reflejan la mayor distorsión/ruido del sistema, generado por la instrumentación del GSI-60. La confiabilidad fue evaluada utilizando el error estándar de medición de la diferencia entre los dos puntajes. Los datos revelaron que no había diferencias significativas entre los protocolos, y sugieren que las diferencias entre dos DPOAE son estadísticamente significativas si exceden ~7 dB (intervalo de confianza del 95%).