Single Mode Number Research Articles

Sagnac effect enhancement with single-mode number squeezing in the presence of photon loss

The precision of gyroscope can be improved with Sagnac effect enhancement. We show that Sagnac effect can be enhanced with single-mode number squeezing technique by calculating the quantum Fisher information (QFI) of coherent state and Fock state and obtain the minimum phase uncertainty with parity measurement in ideal case. Considering that photon losses almost cannot be avoidable in the practical application, a lossy interferometer is modeled by inserting a beam splitter theoretically to calculate the QFI in the presence of photon losses. Through theoretical analysis, the effective transmission rate (or the maximum loss rate) which can enhance Sagnac effect is obtained. For instance, if the average photon number of coherent state \(|\alpha |^{2}\) is far more than the average photon number of Fock state \(N\) and \(N = 20\), sub-shot-noise phase uncertainty can be achieved when loss rate is less than 85%, which indicates the prospect of practical application with the proposed scheme.

Estimates of the power per mode number of broadband ULF waves at geosynchronous orbit

AbstractIn studies of radial diffusion processes in the magnetosphere it is well known that ultralow frequency (ULF) waves of frequency mωd can resonantly interact with particles of drift frequency ωd, where m is the waves' azimuthal mode number. Due to difficulties in estimating m, an oversimplifying assumption is often made in simulations, namely that all ULF wave power is located at a single mode number. In this paper a technique is presented for extracting information on the distribution of ULF power in a range of azimuthal mode numbers. As a first step, the cross power and phase differences between time series from azimuthally aligned magnetometers are calculated. Subsequently, through integrating the ULF power at particular ranges of phase differences that correspond to particular mode numbers, estimates of the fraction of the total power at each phase difference range or mode number are provided. Albeit entwined with many ambiguities, this technique offers critical information that is currently missing when estimating radial diffusion of energetic particles. As proof‐of‐concept, the technique is first tested successfully for a well‐studied case of narrowband ULF Field Line Resonances (FLR) for which the mode number was calculated simultaneously through ground‐based and space measurements. Subsequently, the technique is demonstrated for the broadband ULF waves that accompanied the 2003 “Halloween” magnetospheric storms. The temporal evolution of power at each mode number gives insight into the evolution of ULF waves during a storm as well as more accurate characterization of broadband ULF waves that can be used in radial diffusion simulations.

Collapse and pinch-off of a non-axisymmetric impact-created air cavity in water

AbstractThe axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long-term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single mode number $m$ and amplitude ${a}_{m} $. For small initial distortion amplitude (1 or 2 % of the mean disc radius), the cavity walls oscillate linearly during collapse, with nearly constant amplitude and increasing frequency. As the amplitude is increased, higher harmonics are triggered in the oscillations and we observe more complex pinch-off modes. For small-amplitude disturbances we compare our experimental results with the model for the amplitude of the oscillations by Schmidt et al. (Nature Phys., vol. 5, 2009, pp. 343–346) and the model for the collapse of an axisymmetric impact-created cavity previously proposed by Bergmann et al. (J. Fluid Mech., vol. 633, 2009b, pp. 381–409). By combining these two models we can reconstruct the three-dimensional shape of the cavity at any time before pinch-off.