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arXiv:2105.12349 · Physical Review A

Weak-value amplification and the lifetime of a decaying particle

Yuichiro Mori, Izumi Tsutsui

Published Sep 1, 2021• 3 citations
arXivHTMLPDF

Abstract

We study the possibility of varying the measured lifetime of a decaying particle based on the technique of weak value amplification in which an additional filtering process called postselection is performed. Our analysis made in a direct measurement scheme presented here shows that, for simple two-level systems, the lifetime may be prolonged more than three times compared to the original one, while it can also be shortened arbitrarily by a proper choice of postselection. This result is consistent with our previous analysis on the possible prolongation of the lifetime of $B$ mesons that may be observed in laboratories, and suggests room for novel applications of weak-value amplification beyond precision measurement conventionally considered.

DOI
10.1103/physreva.104.032202

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We study the possibility of varying the measured lifetime of a decaying particle based on the technique of weak value amplification in which an additional filtering process called postselection is performed. Our analysis made in a direct measurement scheme presented here shows that, for simple two-level systems, the lifetime may be prolonged more than three times compared to the original one, while it can also be shortened arbitrarily by a proper choice of postselection. This result is consistent with our previous analysis on the possible prolongation of the lifetime of BBB mesons that may be observed in laboratories, and suggests room for novel applications of weak-value amplification beyond precision measurement conventionally considered.
The technique of weak value amplification, proposed by Aharonov et al. in 1988, has been applied for various fields of physics for the purpose of precision measurement, which is made possible by exploiting the freedom of ``postselection'' specifying actively the final state in the physical process. Here we report the feasibility of utilizing the technique of weak value amplification in high-energy particle physics, especially in measuring the CPCPCP-violating parameters in BBB meson decays, where the effective lifetime of the decay mode is expected to be prolonged statistically due to the postselection. Our analysis shows that, when adopted in the Belle II experiment at the SuperKEKB collider, the effective lifetime may be prolonged up to 2.6 times, and that the measurement precision of the CPCPCP-violating parameters will also be improved by its effect.
Novel Approach to Measuring CPCPCP Violation in BBB Meson Decays: A Case Study of Weak Measurement in High Energy Physics
The weak measurement, proposed by Aharonov {\it et al.} in 1988, has been applied for various fields of physics for the purpose of precision measurement, which is made possible with the help of the 'postselection' specifying actively the final state in the physical process. Here we report for the first time the feasibility of applying the weak measurement in high energy particle physics, especially in measuring the CPCPCP-violating parameters in BBB meson decays, where the effective lifetime of the decay mode is expected to be prolonged statistically due to the postselection. Our analysis shows that, when adopted in the Belle II experiment at the SuperKEKB collider, the effective lifetime may be prolonged up to 2.62.62.6 times, and that the measurement precision of the CPCPCP-violating parameters will be improved by about 20\%.
Abstract Weak measurements have many applications in the field of quantum information due to the peculiar properties of weak values. Quantum weak measurement can be performed by two particles or two degree of freedom of single particle. The former needs complex operations, the latter require the reconstruction of the motion state wavepacket, which consumes substantial quantum resources. This paper presents a novel weak measurement scheme that encodes multiple internal energy levels of a single particle into the measured system and the measuring pointer, while defining a finite-coupling postselected pointer ratio (FCPR). The FCPR obtained from this scheme enables both weak value amplification and rapid experimental results. To verify these advantages, we measured the FCPR using a trapped 40 Ca + experimental setup and monitored fluctuations of the laser power within the experimental system. The results show that our scheme can detect weaker laser power fluctuations, thus providing higher precision for laser power locking.
In a weak measurement with postselection, a measurement value, called the weak value, can be amplified beyond the eigenvalues of an observable. However, there are some controversies whether weak-value amplification is practically useful in increasing the sensitivity of the measurement, in which fundamental quantum noise dominates. In this paper, we investigate the sensitivity limit of an optical interferometer when weak-value amplification is implemented, properly accounting for quantum shot noise and radiation-pressure noise. To do so, we formulate weak-value amplification in the Heisenberg picture instead of in the Schr\"odinger picture, which is conventionally used. This formulation enables us to understand intuitively what happens when the measurement outcome is postselected and the weak value is amplified. As a result, we find that the sensitivity limit is given by the standard quantum limit that is the same as in a standard interferometry. We also discuss a way to circumvent the standard quantum limit.
The novel notion of a physical quantity called 'weak value', which was proposed by Aharonov et al. in 1988, has attracted much attention in the fields of quantum foundations and quantum measurement.In particular, the fact that through proper state selections the weak value can be made arbitrarily large, exceeding the conventional bound set by the maximum eigenvalue of the physical observable, has been widely regarded as a promising source for precision measurement.Indeed, in recent years we have seen increasingly many reports of successful applications of the weak value in photonic systems with various instances of observables amplified effectively.However, it has also been recognized that there are two major obstacles in realizing this weak value amplification (WVA).First, it is unclear under what conditions the WVA becomes effective due to the conflict between the ambiguity caused by the state selections and the amplification effect.Second, the required state selections may not be available depending on the systems one is dealing with.In order to expand the applicability of the WVA, one must solve these problems properly.In this dissertation, we first review the basics of precision measurement and the WVA and then present our method of evaluation for the WVA considering the measurement uncertainty including the ambiguity of the WVA.We applied our method of evaluation for the two celebrated experiments to confirm the basic validity of the results of the two experiments.In addition, as a new application of the WVA, we consider the time evolution of unstable particles to find that the decay time distribution is generally characterized by the weak value of the Hamiltonian and that the state selections can indeed be performed by measuring the particles produced during the decay.Our result indicates that the WVA may also be applicable to the system of unstable particles.
Weak measurements offer insights into the behavior of quantum systems. Combined with postselection, quantum mechanics predicts a range of experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent preselected and postselected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of postselection and the choice of final state. The generalized law is illustrated for two interesting choices of postselection.