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Observation of the weak-to-strong transition of quantum measurement in trapped ions

Yiming Pan, Jie Zhang, Eliahu Cohen, Chun-Wang Wu, Ping‐Xing Chen, Nir Davidson

Published Oct 24, 2019• 1 citation
OpenAlex

Abstract

Quantum measurement remains puzzling through the mist of their stormy history from the early birth of quantum mechanics to state-of-the-art quantum technologies. Here, we report the observation of measurement transition from weak to strong in a single trapped $40Ca^+$ ion system. By realizing a cat state of the ion's vibrational motion by pre- and post-selecting its internal electronic state, we observed the transition from weak value asymptotics to expectation value asymptotics. More precisely, the weak-to-strong measurement transition is characterized by a universal transition factor $\exp(-\Gamma^2/2)$, where $\Gamma$ is a dimensionless coupling parameter related to the system-apparatus interaction. This transition, which continuously connects Aharonov's weak measurement and von Neumann' strong projective measurement, is capable of opening new experimental possibilities for testing quantum foundations, as well as novel applications for computation in trapped ions and other physical systems.

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•Oct 24, 2019•4 citations
Quantum measurement remains puzzling through the mist of their stormy history from the early birth of quantum mechanics to state-of-the-art quantum technologies. Here, we report the observation of measurement transition from weak to strong in a single trapped 40Ca+40Ca^+40Ca+ ion system. By realizing a cat state of the ion's vibrational motion by pre- and post-selecting its internal electronic state, we observed the transition from weak value asymptotics to expectation value asymptotics. More precisely, the weak-to-strong measurement transition is characterized by a universal transition factor exp⁡(−Γ2/2)\exp(-\Gamma^2/2)exp(−Γ2/2), where Γ\GammaΓ is a dimensionless coupling parameter related to the system-apparatus interaction. This transition, which continuously connects Aharonov's weak measurement and von Neumann' strong projective measurement, is capable of opening new experimental possibilities for testing quantum foundations, as well as novel applications for computation in trapped ions and other physical systems.
In this work, we study the measurement transition for a coherent squeezed pointer state through a transition factor $\mathrm{\ensuremath{\Gamma}}$ that involves a system-pointer coupling by using an arbitrary measured observable AAA. In addition, we show that the shift in the pointer's position and momentum establishes a relationship with a new value defined as the transition value, which generalizes the weak value as well as the conditional expectation value. Furthermore, a strategy is introduced to achieve different measurement regimes by just adjusting the rrr and ${\ensuremath{\phi}}_{\ensuremath{\xi}}$ parameters of the coherent squeezed pointer state, opening an interesting way to test quantum mechanics foundations. Our scheme has been theoretically applied in a trapped ion illuminated by a bichromatic laser beam, with a high potential to be implemented in future experimental setups.
Although quantum mechanics has been able to explain a wide range of physical, chemical, and even biological events with unprecedented accuracy, fundamental problems remain. For instance, the problem of quantum measurement and quantum entanglement, which are the most perplexing problems that have persisted since the foundation of quantum mechanics. Both are crucial quantum resources with broad applications in quantum information science, quantum computing and quantum optics. For this reason, this thesis is devoted to research the quantum measurement from the weakest regime to the strongest one as well as the dynamics of entanglement of different quantum systems. In this work, we study the measurement transition for a coherent-squeezed pointer state through a transition factor Γ that involves a system-pointer coupling by using an arbitrary measured observable A. In addition, we show that the shift in the pointer’s position and momentum establishes a relationship with a new value defined as the transition value, which generalizes the weak value as well as the conditional expectation value. Furthermore, a new strategy is introduced to achieve different measurement regimes by just adjusting the r and ϕξ parameters of the coherent-squeezed pointer state, opening an interesting way to test quantum mechanics foundations. Our scheme has been theoretically applied in a trapped ion illuminated by a bichromatic laser beam, with a high potential to be implemented in future experimental setups. Besides, we propose a method to regulate the quantum entanglement in the system mentioned before as well as a dispersive-hybrid system where a qubit is directly coupled to a cavity and a mechanical resonator. Entanglement can be controlled by only tuning the squeezing parameters associated with the vibrational mode. As the squeezing amplitude becomes larger, the maximal entanglement abruptly falls to zero at specific squeezing phases. For the hybrid system, it is also possible to generate entanglement for bipartitions from the qubit-cavity-resonator system after applying this strategy. Entangled qubit-cavity states are created through squeezing, even though there is no direct interaction between them. We also analyze the effect of atomic, optical, and vibrational losses on the quantum entanglement. We finally discuss our schemes to be implemented in future experimental setups and promote further studies to generalize the concept of “monogamy of entanglement” in tripartite systems outside qubit-composite states, in particular, (2 ⊗ 2 ⊗ n)-dimensional systems.
Quantum measurement is physically realized through a finite dynamical interaction between a system and a measuring apparatus, giving rise to a continuous transition from weak to strong regimes. While this crossover is well understood under ideal conditions, the combined role of thermal instabilities and pre- and post-selection open dynamics has not been systematically addressed. Here, we develop a generalized open-system framework to analyze the weak-to-strong measurement transition in the simultaneous presence of environmental decoherence and thermal noise. We model the probe as a thermal Gaussian state, explicitly incorporating temperature-dependent fluctuations in the measuring device, and include open-system evolution of the measured system prior to post-selection. By deriving the apparatus's final state, we show that the measurement statistics are modified in a nontrivial, highly sensitive manner by the temperature regime of the system's thermal instabilities, the probe's thermal properties, and the particular choice of pre- and post-selection. This approach allows us to characterize how thermal effects reshape the weak-value condition, the anomalous amplification, and the resulting metrological sensitivity, demonstrating the protocol's practical utility for precision measurements across the full measurement crossover.
This paper delves into the crucial aspects of pointer-induced quantum decoherence and the transition between von Neumann's projective strong measurement and Aharonov's weak measurement. Both phenomena significantly impact the dynamical understanding of quantum measurement processes. Specifically, we focus on the interplay between quantum decoherence and the transition from weak to strong measurement by deducing and comparing the quantum decoherence and weak-to-strong measurement transition factors within a general model and using the well-known Stern-Gerlach experiment as an illustrative example. Our findings reveal that both phenomena can be effectively characterized by a universal factor intricately linked to the coupling between the measured system and the pointer. The analysis presented in our current work can clarify the mechanism behind the relations of pointer-induced quantum decoherence to the weak measurement and weak-to-strong measurement transition.
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.
How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. We developed a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions. We first analyze the transition from projective measurement to weak measurement in generic light-matter interactions, and show that any classical electron-laser-beam interaction can be represented as an outcome of a weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal decay factor exp⁡(−Γ2/2)\exp(-\Gamma^2/2)exp(−Γ2/2), quantifies the measurement regimes and their transition from quantum to classical, where Γ\GammaΓ corresponds to the ratio between the electron wavepacket size and the optical wavelength. This presentation of the measurement transition from projective to weak sheds new light on the transition from quantum-to-classical electrodynamics, enabling to employ the very essence of wave-particle duality in quantum measurement for exploring and applying a variety of quantum and classical types of electron-photon interactions.