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Chinese Physics B

A Weak Value Amplification Scheme Based on Single-Particle Multi-Levels

Wenbo Su, Peng Wang, 吴春旺, Wei Wu, Pingxing Chen

Published Sep 15, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/aea75c

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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 quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, if the coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointer can not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, which makes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurement method in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement, our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped 40Ca+ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.
In this paper, we explore the possibilities of realizing weak value amplification (WVA) using purely atomic degrees of freedom. Our scheme identifies the internal electronic states and external motional states of a single trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion as the system degree and pointer degree, respectively, and their controllable weak coupling is provided by a bichromatic light field. In our experimental demonstration, by performing appropriate postselection on the internal states, a position displacement of $\ensuremath{\sim}4\AA{}$ (in phase space) of the trapped ion is amplified to $\ensuremath{\sim}10$ nm. The sensitivity of the amplification effect to the relative phase of the quantum state is also demonstrated. The high operational flexibility of this procedure allows fully exploration of the peculiarities of WVA.
In quantum weak measurement, a weak value is a quantity related to a pointer shift of a measuring device which is usually determined by pre- and postselection states. For conventional weak measurement, a single weak-value model has been well addressed in precision metrology of time delay, but it only holds for a narrowband light source. To further improve the measurement accuracy, a broad-spectrum light source is needed. We find that the single weak-value model no longer holds, due to the occurrence of modified preselection states. Here, a multiple weak-value model is established by introducing the modified preselection states in the estimation of time delay. For broad-spectrum light source with 50-nm spectral width, the multiple weak-value scheme enables us to achieve a high resolution of $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}\mathrm{as}$. Our proposed multiple weak-value amplification may have important applications in various fields involving precise time-delay detection.
Abstract Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.
Abstract Most studies for postselected weak measurement focus on using the pure Gaussian state as a pointer, which can only give an amplification limit reaching the level of the ground state fluctuation. When the pointer is initialized in a thermal state, we find that the amplification limit after the postselection can reach the level of thermal fluctuation, indicating that the amplification effect achieving the level of thermal fluctuation is also increased with the temperature growth, and also that the amplification mechanism is different from that with pure Gaussian-state pointer. To illustrate these results, we propose two schemes to implement room temperature amplification of the mechanical oscillator’s displacement caused by a single photon in the optomechanical system. The two schemes both enhance the mechanical oscillator’s original displacement by nearly seven orders of magnitude, attaining sensitivity to displacements of ∼0.26 nm. Such amplification effect can be used to observe the impact of a single photon on a room temperature mechanical oscillator, which is hard to detect in traditional measurement.
Weak measurement is a potentially powerful tool for studying post-selected quantum systems. The original approach to weak measurement requires a different von Neumann interaction between the quantum system and measurement pointer for weak values of every different observable. When studying weak values of properties of more than one particle, which is necessary for studying entanglement, these interactions can range from difficult to impossible to implement experimentally. For example, the measurement of properties on a pair of optical photons requires a strong Kerr-like nonlinearity at the two-photon level. In a recent work, we described a new method for extracting weak values of operators that can be expressed as products of two local, single-particle operators by studying the correlations in experimentally feasible local, single-particle measurements. In the present work, that theoretical approach is generalized so that weak values of products of N local, single-particle operators can be extracted from the correlations in N single-particle measurements.