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Experimental Demonstration of Fully Atomic Weak Value Amplification

Chun-Wang Wu, Jie Zhang, Yi Xie, Bao-Quan Ou, Wei Wu, Ping‐Xing Chen

Published Nov 15, 2018• 1 citation
OpenAlex

Abstract

In this Letter, we experimentally demonstrate the first realization of weak value amplification (WVA) using purely atomic degrees of freedom. Our measurement model identifies the internal electronic states and external motional states of a single trapped $^{40}$Ca$^+$ ion as the system degree and pointer degree respectively, and their controllable weak coupling is provided by a bichromatic light field. By performing appropriate postselection on the internal states, a tiny position displacement of 4 angstroms of the trapped ion is amplified to 10 nanometers in our experiment. The extreme sensitivity of the amplification effect to the relative phase of the quantum state is also demonstrated, which may have relation to the phase estimation applications. This work has potential to advance the abundant metrological applications related to the atomic interferometric process, and allows fully exploration of the peculiarities of WVA owing to the high operational flexibility of this procedure .

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Scheme and experimental demonstration of fully atomic weak-value amplification

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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 $^{40}\mathrm{Ca}^{+}$ 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.

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We introduce an ultrasensitive interferometric protocol that combines weak value amplification (WVA) with traditional interferometry. This protocol WVA+interferometry uses weak value amplification of the relative delay between two paths to enhance interferometric sensitivity. As an example, we demonstrate a proof-of-principle experiment that achieves few-attosecond timing resolution (few nanometer path length resolution) with a double-slit interferometer using only common optical components. Since our example uses only the spatial shift of double-slit interference fringes, its precision is not limited by the timing resolution of the detectors but is instead limited by the fundamental shot noise associated with classical light and the diminished technical noise. We experimentally demonstrate that the signal-to-noise ratio can be improved by one to two orders of magnitude relative to a measurement that does not use WVA. Two key conclusions are drawn: (i) Most conventional interferometric techniques primarily rely on determining the path difference (time delay or longitudinal phase), with their precision constrained by technical noise. Our protocol offers a robust solution for minimizing the technical noise in traditional interferometry, with precision in principle approaching the shot-noise limit. (ii) Although WVA has achieved significant advancements in ultrasensitive longitudinal phase measurement, its applicability is constrained by the need for broad spectral bandwidths and high-resolution spectrometers. Contrary to previous assumptions, we demonstrate that quantum-limited WVA time delay measurements are achievable with narrow band light using real weak values. Thus, the cost-effectiveness and practicality of the proposed WVA+interferometry protocol using narrow band light broaden the scope of WVA applications. This protocol holds potential for broad applications in optical metrology, quantum optics and quantum information, biomedical imaging, and interferometric telescopes for astrophysics.

arXiv:2404.00531•Physical Review Letters•Feb 27, 2025•11 citations
In this Letter, we experimentally demonstrate the first realization of weak value amplification (WVA) using purely atomic degrees of freedom. Our measurement model identifies the internal electronic states and external motional states of a single trapped 40^{40}40Ca+^++ ion as the system degree and pointer degree respectively, and their controllable weak coupling is provided by a bichromatic light field. By performing appropriate postselection on the internal states, a tiny position displacement of 4 angstroms of the trapped ion is amplified to 10 nanometers in our experiment. The extreme sensitivity of the amplification effect to the relative phase of the quantum state is also demonstrated, which may have relation to the phase estimation applications. This work has potential to advance the abundant metrological applications related to the atomic interferometric process, and allows fully exploration of the peculiarities of WVA owing to the high operational flexibility of this procedure .
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.
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.
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.
The weak-value-amplification (WVA) effect, which is also called weak measurement, has been developed extensively in various sensing systems. Here, we report the actual realization of the WVA effect in spin-exchange relaxation-free atomic magnetometer system, wherein the slight separation of transverse momentum of the probe light is amplified by introducing orthogonal pre- and post-selection states. A differential detector is used to obtain the transverse position of the probe light accurately in real time. The weak coupling of the magneto-optical interaction with atoms will be reflected in the differential signal. The WVA effect is observed and demonstrated directly and a high sensitivity of 8 fT/Hz is achieved. Also, we obtain the stable and distinct simulated magnetocardiography signal through our system. The present successful implementation of this probe method paves the way for further technical noise suppression and sensitivity improvement of quantum sensors.
We introduce an ultrasensitive interferometric protocol that combines weak value amplification (WVA) with traditional interferometry. This protocol WVA+interferometry uses weak value amplification of the relative delay between two paths to enhance interferometric sensitivity. As an example, we demonstrate a proof-of-principle experiment that achieves few-attosecond timing resolution (few nanometer path length resolution) with a double-slit interferometer using only common optical components. Since our example uses only the spatial shift of double-slit interference fringes, its precision is not limited by the timing resolution of the detectors but is instead limited by the fundamental shot noise associated with classical light and the diminished technical noise. We experimentally demonstrate that the signal-to-noise ratio can be improved by one to two orders of magnitude relative to a measurement that does not use WVA. Two key conclusions are drawn: (i) Most conventional interferometric techniques primarily rely on determining the path difference (time delay or longitudinal phase), with their precision constrained by technical noise. Our protocol offers a robust solution for minimizing the technical noise in traditional interferometry, with precision in principle approaching the shot-noise limit. (ii) Although WVA has achieved significant advancements in ultrasensitive longitudinal phase measurement, its applicability is constrained by the need for broad spectral bandwidths and high-resolution spectrometers. Contrary to previous assumptions, we demonstrate that quantum-limited WVA time delay measurements are achievable with narrow band light using real weak values. Thus, the cost-effectiveness and practicality of the proposed WVA+interferometry protocol using narrow band light broaden the scope of WVA applications. This protocol holds potential for broad applications in optical metrology, quantum optics and quantum information, biomedical imaging, and interferometric telescopes for astrophysics.