Cross-Phase Modulation Enhancement Via a Resonating Cavity: Semiclassical Description

We evaluate the advantages of performing cross-phase modulation (XPM) on a very-far-off-resonance atomic system. We consider a ladder system with a weak (few-photon level) control coherent field imparting a conditional nonlinear phase shift on a probe beam. We find that by coupling to an optical resonator the optimal XPM is enhanced proportional to the finesse of the resonator by a factor of $F/4\pi$. We present a semi-classical description of the system and show that the phenomenon is optimal in the self-defined condition of off-resonance-effective-cooperativity equal to one

Practical Advantages of Almost-Balanced-Weak-Values Metrological Techniques

Precision measurements of ultra-small linear velocities of one of the mirrors in a Michelson interferometer are performed using two different weak-values techniques. We show that the technique of Almost-Balanced Weak Values (ABWV) offers practical advantages over the technique of Weak-Value Amplification (WVA), resulting in larger signal-to-noise ratios and the possibility of longer integration times due to robustness to slow drifts. As an example of the performance of the ABWV protocol we report a velocity sensitivity of 60 fm/s after 40 hours of integration time. The sensitivity of the Doppler shift due to the moving mirror is of 150 nHz

Technical advantages for weak value amplification: When less is more

The technical merits of weak value amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak value amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which uses all of them). Using the Fisher information metric, we demonstrate that weak value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time correlated noise model, and find that a Fisher information analysis indicates that while the standard method can have much larger information about the detected parameter than the postselected technique. However, the estimator needed to gather the information is technically difficult to implement, showing that the inefficient (but practical) signal-to-noise estimation of the parameter is usually superior. We also describe other technical advantages unique to imaginary weak value amplification techniques, focusing on beam deflection measurements. In this case, we discuss combined noise types (such as detector transverse jitter, angular beam jitter before the interferometer and turbulence) for which the interferometric weak value technique gives higher Fisher information over conventional methods. We go on to calculate the Fisher information of the recently proposed photon recycling scheme for beam deflection measurements, and show it further boosts the Fisher information by the inverse postselection probability relative to the standard measurement case

Cómo determinar los Parámetros de la Ecuación General de una Cuádrica a través de la Visualización

Las ecuaciones generales de las cuádricas en su forma general presentan un grado de dificultad al momento de determinar a qué tipo de cuádrica pertenece. En este sentido, la visualización juega un papel importante en la determinación y relación de la ecuación con su respectiva gráfica, dado que, al realizar una manipulación algebraica sobre la ecuación canónica de la superficie para transformarla a su forma general, se puede determinar por medio de la simple inspección de la ecuación general, no solamente a qué tipo de cuádrica pertenece, sino también se pueden determinar sus parámetros principale

Complementary weak-value amplification with concatenated postselections

We measure a transverse momentum kick in a Sagnac interferometer using weak-value amplification with two postselections. The first postselection is controlled by a polarization dependent phase mismatch between both paths of a Sagnac interferometer and the second postselection is controlled by a polarizer at the exit port. By monitoring the darkport of the interferometer, we study the complementary amplification of the concatenated postselections, where the polarization extinction ratio is greater than the contrast of the spatial interference. In this case, we find an improvement in the amplification of the signal of interest by introducing a second postselection to the system

Can Anomalous Amplification be Attained Without Postselection?

We present a parameter estimation technique based on performing joint measurements of a weak interaction away from the weak-value-amplification approximation. Two detectors are used to collect full statistics of the correlations between two weakly entangled degrees of freedom. Without the need of postselection, the protocol resembles the anomalous amplification of an imaginary-weak-value-like response. The amplification is induced in the difference signal of both detectors allowing robustness to different sources of technical noise, and offering in addition the advantages of balanced signals for precision metrology. All of the Fisher information about the parameter of interest is collected, and a phase controls the amplification response. We experimentally demonstrate the proposed technique by measuring polarization rotations in a linearly polarized laser pulse. The effective sensitivity and precision of a split detector is increased when compared to a conventional continuous-wave balanced detection technique

The Singular Perturbation Problem for a Class of Generalized Logistic Equations Under Non-classical Mixed Boundary Conditions

This paper studies a singular perturbation result for a class of generalized diffusive logistic equa- tions, dLu = uh(u, x), under non-classical mixed boundary conditions, Bu = 0 on ∂Ω. Most of the precursors of this result dealt with Dirichlet boundary conditions and self-adjoint second order elliptic operators. To over- come the new technical difficulties originated by the generality of the new setting, we have characterized the regularity of ∂Ω through the regularity of the associated conormal projections and conormal distances. This seems to be a new result of a huge relevance on its own. It actually complements some classical findings of Serrin, Gilbarg and Trudinger, Krantz and Parks, Foote, and Li and Nirenberg concerning the regularity of the inner distance function to the boundary