Weak value amplification (WVA) is a concept that has been extensively used in a myriad of applications with the aim of rendering measurable tiny changes of a variable of interest. In spite of this, there is still an on-going debate about its true nature and whether is really needed for achieving high sensitivity. Here we aim at helping to clarify the puzzle, using a specific example and some basic concepts from quantum estimation theory, highlighting what the use of the WVA concept can offer and what it can not. While WVA cannot be used to go beyond some fundamental sensitivity limits that arise from considering the full nature of the quantum states, WVA can notwithstanding enhance the sensitivity of real and specific detection schemes that are limited by many other things apart from the quantum nature of the states involved, i.e. technical noise. Importantly, it can do that in a straightforward and easily accessible manner.
Weak value amplification (WVA) is a concept that has been extensively used in a myriad of applications with the aim of rendering measurable tiny changes of a variable of interest. In spite of this, there is still an on-going debate about its true nature and whether is really needed for achieving high sensitivity. Here we aim at helping to clarify the puzzle, using a specific example and some basic concepts from quantum estimation theory, highlighting what the use of the WVA concept can offer and what it can not. While WVA cannot be used to go beyond some fundamental sensitivity limits that arise from considering the full nature of the quantum states, WVA can notwithstanding enhance the sensitivity of real and specific detection schemes that are limited by many other things apart from the quantum nature of the states involved, i.e. technical noise. Importantly, it can do that in a straightforward and easily accessible manner.
Abstract Even though weak measurements and weak value amplification (WVA) are founded on the principles of quantum mechanics and quantum measurements, these have found widespread applications in optics due to their inherent origin in wave interference. Besides their use in addressing foundational questions of quantum mechanics or for resolving quantum paradoxes, weak measurements and WVA have thus been used for numerous metrological applications, e.g., quantification of small optical beam displacement, tiny angular rotation, determination of extremely small phase shifts, spectral shifts, unraveling weak fundamental optical effects, improved optical imaging, amplifying weak signal and extracting small physical parameters and so forth. In this review, after providing the mathematical foundation of weak measurement and WVA, some of the metrological applications of weak measurements in the classical optics domain are briefly summarized, and the controversies and debates on the potential advantages of WVA in the estimation and detection of weak signal are discussed, and the interferometric philosophy of WVA is elucidated. The experimental weak measurement and WVA schemes in the domain of quantum optics are also discussed and highlighted the new perspectives and emerging trends of weak measurements in both the classical and quantum optics domain and their prospects in the development of next‐generation ultra‐sensitive optical devices.
Weak Value Amplification (WVA) is a signal enhancement technique proposed in 1988 by Aharonov, Albert, and Vaidman that has been widely used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on: i) the existence of a weak interaction which couples a property of a system (the system) with a separate degree of freedom (the pointer), and ii) the measurement of an anomalously large mean value of the pointer state (weak mean value), after appropriate pre and post-selection of the state of the system. The usefulness of weak value amplification for measuring extremely small quantities has been demonstrated under a great variety of experimental conditions to measure very small transverse displacements of optical beams, beam deflections, angular shifts, temporal shifts, phase shifts, frequency shifts, velocity measurements and temperature differences, among others. In this thesis we make use of this concept to improve current technologies and analyse the true usefulness of this technique with respect to other experimental alternatives. In particular, we have applied the concept to measure femtosecond temporal delays between pulses much smaller than their pulse width. From the theoretical model we estimate that the ultimate sensitivity of this scheme will allow to measure delays of the order of attoseconds using femtosecond laser sources. In addition, we have developed an innovative experimental scheme that makes use of the interference effect present in a WVA scheme to generate a highly-sensitive tunable beam displacer that can outperform the limitations imposed by the use of movable optical elements. From the experimental results, we were able to perform a scan of a Gaussian beam with waist 600 μm over an interval of 240 μm in steps of 1 μm. Moreover, we have implemented a proof-of-concept experiment aimed at increasing the sensitivity of Fiber Bragg Grating (FBG) temperature sensors. The sensors behave as frequency filters whose center is determined by its surrounding temperature. By means of a WVA scheme we were able to measure a polarization dependent frequency shift that is small compared to the width of each FBG spectrum, and from that value we were able to obtain a four-fold enhancement of the sensitivity with respect to current schemes. Finally, we address the question of what can offer the concept of WVA and what can not in terms of achieving high sensitivity measurements. By using a specific example and some basic concepts from quantum estimation theory, we have found that while WVA cannot be used to go beyond some fundamental sensitivity limits that arise from considering the full nature of the quantum states, WVA can notwithstanding enhance the sensitivity of real and specific detection schemes that are limited by many other things apart from the quantum nature of the states involved, i.e. technical noise. Weak Value Amplification (WVA) es una técnica experimental propuesta en 1988 por Aharonov, Albert, y Vaidman que ha sido ampliamente utilizada para medir pequeños cambios de variables físicas que en principio no podrían medirse usando otras metodologías debido a limitaciones técnicas. La técnica se basa en: i) la existencia de una interacción débil que acopla una propiedad de un sistema (el sistema) con otro grado de libertad (el metro), y ii) la medición de un valor promedio particularmente grande del metro (weak mean value), después de realizar una selección adecuada de los estados inicial y final del sistema. La utilidad de la técnica para la medición de cantidades extremadamente pequeñas ha sido demostrada en una gran variedad de condiciones experimentales para medir, por ejemplo, desplazamientos transversales de haces ópticos muy pequeños, deflexiones en haces, corrimientos angulares, retardos temporales, cambios de fase, cambios de frecuencia, mediciones de velocidad y diferencias de temperaturas, entre otros. En esta tesis, hacemos uso del concepto de Weak Value Amplification para mejorar el desempeño de algunos esquemas experimentales actuales y también para analizar la verdadera utilidad de esta técnica con respecto a otras alternativas experimentales. En particular, aplicamos el concepto para medir retardos temporales entre pulsos del orden de femtosegundos mucho más pequeños que su duración y mediante un modelo teórico, determinamos un límite en la sensibilidad del sistema que permite medir retardos del orden de attosegundos utilizando pulsos del orden de femtosegundos. También desarrollamos un dispositivo que hace uso de la interfencia presente en los esquemas basados en WVA para generar un desplazador de haz sintonizable que puede superar las limitaciones impuestas en resolución por el uso de elementos ópticos móviles. En particular, reportamos el resultado de realizar un barrido de la posición de un haz Gaussiano, con ancho 600 μm, a lo largo de un intervalo de 240 μm en pasos de 1 μm. Por otro lado, demostramos la viabilidad del uso del concepto de WVApara aumentar la sensibilidad en sensores de temperatura basados en Fiber Bragg Gratings (FBG) a través de un experimento. Teniendo en cuenta de que este tipo de sensores se comportan como filtros espectrales cuya frecuencia central está determinada por la temperatura a su alrededor, con el esquema implementado, hemos podido medir corrimientos en frecuencia que son pequeños en comparación con el ancho del espectro de cada FBG. En particular reportamos que el esquema implementado permite mejorar en un factor de cuatro la sensibilidad de los esquemas de medición corrientes. Por último, buscamos dar respuesta a la pregunta: ¿qué puede y qué no puede ofrecer el concepto de WVA cuando se utiliza en mediciones de gran precisión? Mediante el uso de un ejemplo especifico y algunos conceptos básicos de la mecánica cuántica, hemos encontrado que los esquemas basados en WVA no son de utilidad para superar limites fundamentales que surgen al considerar la naturaleza cuántica de la luz. Sin embargo, hemos encontrado que el concepto de WVA puede ser de gran utilidad para mejorar la sensibilidad de esquemas experimentales específicos en donde la sensibilidad puede estar limitada por otros factores diferentes a la naturaleza cuántica de la luz, como por ejemplo el ruido técnico.
Weak-value amplification (WVA) is a metrological protocol that amplifies ultrasmall physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photodetection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is 6 times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.
Weak-value amplification (WVA) provides a way for amplified detection of a tiny physical signal at the expense of a lower detection probability. Despite this trade-off, due to its robustness against certain types of noise, WVA has advantages over conventional measurements in precision metrology. Moreover, it has been shown that WVA-based metrology can reach the Heisenberg limit using entangled resources, but preparing macroscopic entangled resources remains challenging. Here, we demonstrate a novel WVA scheme based on iterative interactions, achieving the Heisenberg-limited precision scaling without resorting to entanglement. This indicates that the perceived advantages of the entanglement-assisted WVA are in fact due to iterative interactions between each particle of an entangled system and a meter, rather than coming from the entanglement itself. Our work opens a practical pathway for achieving the Heisenberg-limited WVA without using fragile and experimentally demanding entangled resources.
Weak value amplification (WVA) is a technique by which one can magnify the apparent strength of a measurement signal. Some have claimed that WVA can outperform more conventional measurement schemes in parameter estimation. Nonetheless, a significant body of theoretical work has challenged this perspective, suggesting WVA to be fundamentally suboptimal. Optimal measurements may not be practical, however. Two practical considerations that have been conjectured to afford a benefit to WVA over conventional measurement are certain types of noise and detector saturation. Here, we report a theoretical study of the role of saturation and pixel noise in WVA-based measurement, in which we carry out a Bayesian analysis of the Fisher information available using a saturable, pixelated, digitized, and/or noisy detector. We draw two conclusions: first, that saturation alone does not confer an advantage to the WVA approach over conventional measurement, and second, that WVA can outperform conventional measurement when saturation is combined with intrinsic pixel noise and/or digitization.
Recently, the weak-value amplification (WVA) has been extensively investigated as a promising quantum technique for improving an accuracy of a precision measurement.The basic idea of WVA comes from the weak measurement introduced by Aharonov, Albert, and Vaidman in 1988.The weak measurement is the indirect quantum measurement with the weak interaction and postselection of the final state of the measured system.The attention point is that we can measure the quantity called the weak value, which appears in the shift of the measuring probe given by the weak measurement.Because the weak value can be outside the range of the eigenvalues, the shift of the measuring probe obtained by the weak measurement becomes larger than the one given by the conventional measurement.This shift amplification effect by the weak value is the WVA, which has been studied for precisely measuring the small coupling constant.In this thesis, we propose the two possible applications of the WVA.First, we analytically obtain the optimal probe wave function for a given weak value by the variational method.It is shown that the amplification factor obtained by the optimal probe has noupper bound while the one in the Gaussian probe already reported by some researchers has the upper bound.Furthermore, the variance of the optimal probe after the measurement can be zero.We can derive the optimal probe by the Lagrange multiplier method for maximizing the shift of the probe position or minimizing the variance of the final distribution.Second we have developed the way which has a technical advantage of the WVA from the viewpoint of statistics.It is often argued that the WVA is not helpfull for the parameter estimation.Therefore we consider the statistical inferences that the WVA will be advantageous.We propose a method to determine whether the interaction is present or not and evaluate the capability of the WVA for this interaction detection problem by using the hypothesis testing in statistics.As the main result, it is shown that the merit of the WVA is the reduction of the possibility to miss the presence of the interaction more than the conventional measurement while keeping the probability of a misdetection, when the absolute value of the weak value is outside the range of the eigenvalues.In this discussion, we assume that the number of the obtained data is infinitely large and we neglect the data loss by the failure of the postseleciton.iii the deepest appreciation to my ex-supervisor