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arXiv:1204.6701 · Optics Express

Weak interference in the high-signal regime

Juan P. Torres, Graciana Puentes, Nathaniel Hermosa, Luis José Salazar-Serrano

Published Aug 2, 2012• 11 citations
arXivHTMLPDF

Abstract

Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on: a) the existence of a weak interaction which couples a property of a system (the system) with a separate degree of freedom (the pointer), and b) 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. Unfortunately, the weak amplification process is generally accompanied by severe losses of the detected signal, which limits its applicability. However, we will show here that since weak amplification is essentially the result of an interference phenomena, it should be possible to use the degree of interference (weak interference) to get relevant information about the physical system under study in a more general scenario, where the signal is not severely depleted (high-signal regime).

DOI
10.1364/oe.20.018869

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Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on: a) the existence of a weak interaction which couples a property of a system (the system) with a separate degree of freedom (the pointer), and b) 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. Unfortunately, the weak amplification process is generally accompanied by severe losses of the detected signal, which limits its applicability. However, we will show here that since weak amplification is essentially the result of an interference phenomena, it should be possible to use the degree of interference (weak interference) to get relevant information about the physical system under study in a more general scenario, where the signal is not severely depleted (high-signal regime).
Abstract Weak measurement (WM) based on post-selection is a useful tool for precision metrology due to the ability of amplifying weak physical effects. In this paper, we reveal the underlying mechanism of the amplification in the post-selected WM based on the weak-value amplification (WVA) and the almost balanced weak-values amplification (ABWVA) strategies. We find that the amplification stems from the interference between the local oscillator and signal components which are respectively associated with the initial system state and the state disturbance induced by the weak coupling. The magnitude of the amplification is proportional to the interference strength which is dominated by the post-selection and the coupling strength. Furthermore, our theory can perfectly explain the amplification limit in the WVA strategy and the anomalous amplification in the ABWVA strategy.
We discuss interferometric parameter estimation of the amplitude, instead of the phase, via weak value amplification. The considered weak interaction introduces modulation on the amplitude of the wave function; therefore, the two-party state experiences a nonunitary evolution. With the same pre- and postselection states as those of original weak value amplification, a much larger anomalous amplification factor can be attained. The shift in the intensity profile at the dark port and the signal-to-noise ratio for the parameter of interest get further amplified by the weak value, compared to phase-based weak value amplification. Although the nonunitary evolution introduces loss, more information about the parameter of interest can be extracted. Thus the weak value amplification is extended to measurement of amplitude and nonunitary processes. We also discuss possible applications of this idea for precisely measuring tiny rotations or enhancing the image contrast of transparent objects.
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 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.
We show using statistically rigorous arguments that the technique of weak value amplification (WVA) does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection. Specifically we prove that post-selection, a necessary ingredient for WVA, decreases estimation accuracy and, moreover, arranging for anomalously large weak values is a suboptimal strategy. In doing so, we explicitly provide the optimal estimator, which in turn allows us to identify the optimal experimental arrangement to be the one in which all outcomes have equal weak values (all as small as possible) and the initial state of the meter is the maximal eigenvalue of the square of the system observable. Finally, we give precise quantitative conditions for when weak measurement (measurements without post-selection or anomalously large weak values) can mitigate the effect of uncharacterized technical noise in estimation.
The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is larger for the post-selected state more orthogonal to the initial state. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wavefunction and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound in contrast to the Gaussian probe wavefunction and that the amplified signal is sharp.