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arXiv:2304.08545 · Physical Review A

Cascaded multiparameter quantum metrology

Gregory Krueper, Lior Cohen, Juliet T. Gopinath

Published Jan 15, 2025• 1 citation
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Abstract

We present an innovative, platform-independent concept for multiparameter sensing where the measurable parameters are in series, or cascaded, enabling measurements as a function of position. With temporally resolved detection, we show that squeezing can give a quantum enhancement in sensitivity over that of classical states by a factor of ${e}^{2r}$, where $r\ensuremath{\approx}1$ is the squeezing parameter. As an example, we have modeled an interferometer that senses multiple phase shifts along the same path, demonstrating a maximal quantum advantage by combining a coherent state with squeezed vacuum. Further classical modeling with up to 100 phases shows linear scaling potential for adding nodes to the sensor. The approach can be applied to remote sensing, geophysical surveying, and infrastructure monitoring.

DOI
10.1103/physreva.111.012618

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We present an innovative, platform-independent concept for multiparameter sensing where the measurable parameters are in series, or cascaded, enabling measurements as a function of position. With temporally resolved detection, we show that squeezing can give a quantum enhancement in sensitivity over that of classical states by a factor of e2r{e}^{2r}e2r, where r\ensuremath≈1r\ensuremath{\approx}1r\ensuremath≈1 is the squeezing parameter. As an example, we have modeled an interferometer that senses multiple phase shifts along the same path, demonstrating a maximal quantum advantage by combining a coherent state with squeezed vacuum. Further classical modeling with up to 100 phases shows linear scaling potential for adding nodes to the sensor. The approach can be applied to remote sensing, geophysical surveying, and infrastructure monitoring.
Squeezing currently represents the leading strategy to obtain quantum enhancements for precision measurements of single parameters in a variety of continuous- and discrete-variable settings. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. Here, we derive a general, operational concept of multiparameter squeezing from the sensitivity matrix of quantum metrology. Our formalism identifies metrologically useful multiparameter squeezing of arbitrary observables and systems. We provide an analytical solution to the optimization over the measurement observables and the phase-imprinting Hamiltonians to maximize sensitivity. When applied to spin- or continuous-variable systems, our results generalize widely-used concepts of spin- or quadrature squeezing parameters. The squeezing matrix provides a practical and versatile tool for the development of quantum-enhanced multiparameter measurements and the efficient characterization of multimode quantum states.
Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin- or continuous-variable systems, our results generalize widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.
Quantum-enhanced interferometers have been widely used in single-parameter precision measurement, and multiparameter precision measurement is the building block of numerous sensing and imaging applications. However, it remains challenging to realize high-sensitivity multiparameter sensing without increasing power, which is crucial for biological science. Here, we propose and demonstrate a deterministic quantum-enhanced interferometer, where high-sensitivity multiparameter sensing is realized by effectively squeezing noises and amplifying signals. Key technologies are essential to the results, including the parallel and sequential use of squeezed states inside the interferometer. Notably, in the quantum-enhanced three-arm interferometer, not only joint but also individual values of three signals are simultaneously measured with a signal-to-noise ratio of more than 10.37±0.13 dB compared with that of the conventional interferometer under the same phase-sensing power. These advances constitute a critical step toward observing multiple elusive signals and give rise to a wide range of sensing and imaging applications.
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Achieving the ultimate quantum precision in the estimation of multiple physical parameters simultaneously is a challenge in quantum metrology due to fundamental limitations and experimental challenges in harnessing the necessary quantum resources. We propose an experimentally feasible scheme to reach Heisenberg-scaling precision in the simultaneous estimation of two unknown phase parameters in a Mach-Zehnder interferometer by using squeezed and coherent states of light as input and homodyne detections at the outputs. Our results open a new research paradigm in harnessing the full quantum advantage of multiparameter estimation in distributed quantum sensing and quantum information processing, as enabled by multiphoton quantum interference with scalable experimental resources.
In quantum metrology, entangled states of many-particle systems are investigated to enhance measurement precision of the most precise clocks and field sensors. Whereas single-parameter quantum metrology is well established, joint multiparameter estimation poses conceptual challenges and has been explored only theoretically. We experimentally demonstrated multiparameter quantum metrology with an array of entangled atomic ensembles. By splitting a spin-squeezed ensemble, we created an atomic sensor array featuring intersensor entanglement that can be flexibly configured to enhance measurement precision of multiple parameters jointly. Using an optimal estimation protocol, we achieved substantial gains over the standard quantum limit in key multiparameter estimation tasks, thus grounding the concept of quantum enhancement of field sensor arrays and imaging devices.