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ACS Photonics

Squeezed Coherent States of Geometric Beams

Zhaoyang Wang, Zijian Shi, Yijie Shen, Qiang Liu, Xing Fu

Published Sep 26, 2024• 2 citations
Publisher

Abstract

Quantum-classical analogy refers to the fact that quantum and classical phenomena share a similar mathematical description and exhibit analogous behaviors, which has advanced optical frontiers. In this work, the mechanism of the squeezed state is incorporated into classical structured light, constructing a novel kind of structured light, termed the squeezed geometric beam, that is, the squeezed coherent state of geometric beams, and revealing a novel quantum-classical analogy between the noise of quantum squeezed state and the beam size of squeezed geometric beams, both evolving with the same squeezing parameter. The presented method provides an inspirational extensible framework to reveal more structured light analogies of quantum states. In addition, it is demonstrated in theory and experiment that thanks to the unveiled squeezing mechanism, the squeezed geometric beam as an information carrier can effectively lower the modal crosstalk, thus boosting the communication capacity of spatial mode multiplexing.

DOI
10.1021/acsphotonics.4c01366

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Quantum-classical analogy refers to the fact that quantum and classical phenomena share a similar mathematical description and exhibit analogous behaviors, which has advanced optical frontiers. In this work, the mechanism of the squeezed state is incorporated into classical structured light, constructing a novel kind of structured light, termed the squeezed geometric beam, that is, the squeezed coherent state of geometric beams, and revealing a novel quantum-classical analogy between the noise of quantum squeezed state and the beam size of squeezed geometric beams, both evolving with the same squeezing parameter. The presented method provides an inspirational extensible framework to reveal more structured light analogies of quantum states. In addition, it is demonstrated in theory and experiment that thanks to the unveiled squeezing mechanism, the squeezed geometric beam as an information carrier can effectively lower the modal crosstalk, thus boosting the communication capacity of spatial mode multiplexing.
Much of the richness in nature arises due to the connection between classical and quantum mechanics. In advanced science, the tools of quantum mechanics was not only applied in microscopic description but also found its efficacy in classical phenomena, broadening the fundamental scientific frontier. A pioneering inspiration is substituting Fock state with structured spatial modes to reconstruct a novel Hilbert space. Based on this idea, here we propose the classical analogy of squeezed coherent state for the first time, deriving classical wave-packets by applying squeezed and displacement operators on free space structured modes. Such a generalized structured light not only creates new degrees of freedom into structured light, including tunable squeezed degree and displacement degree but also exhibits direct correlation between quadrature operator space and real space. Versatile generalized classical squeezed states could be experimentally generated by a simple large-aperture off-axis-pumped solid-state laser. On account of its tunablity, we initially put forward a blueprint using classical structured light, an analogy of squeezed states to realize super-resolution imaging, providing an alternative way to beat diffraction limit as well as opening an original page for subsequent applications of high-dimensional structured light, such as high-sensitive measurement and ultra-precise optical manipulation.
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Control of structured light is of great importance to explore fundamental physical effects and extend practical scientific applications, which has been advanced by accepting methods of quantum optics - many classical analogies of exotic quantum states were designed using structured modes. However, the prevailing quantum-like structured modes are limited by discrete states where the mode index is analog to the photon number state. Yet, beyond discrete states, there is a broad range of quantum states to be explored in the field of structured light -- continuous-variable (CV) states. As a typical example of CV states, squeezed state plays a prominent role in high-sensitivity interferometry and gravitational wave detection. In this work, we bring together two seemingly disparate branches of physics, namely, classical structured light and quantum squeezed state. We propose the structured light analogy of squeezed state (SLASS), which can break the spatial limit following the process of surpassing the standard quantum limit (SQL) with quantum squeezed states. This work paves the way for adopting methods from CV quantum states into structured light, opening new research directions of CV entanglement, teleportation, classical and quantum informatics of structured light in the future.
Quantum enhanced measurements depend on generation of squeezed light with quantum fluctuations below standard quantum limit. Precise spatial information about squeezed modes is crucial to reach maximum quantum advantage in sensing applications. Yet the mixed mode squeezed vacuum (the extreme case of squeezed light) is particularly elusive for such characterization. We will present our method, based on the structured light homodyning, to extract squeezing levels and mode shapes from a multimode quantum squeezed vacuum beam.
We use the spatial degree of freedom of light modes to construct optical analogs of generalized quantum coherent states for Hermite- and Laguerre--Gauss modes. Our optical analogs preserve the statistical properties of their quantum counterparts, encoded in their amplitude and phase distributions. We explore three basic symmetries that provide generalized displaced, rotated, and squeezed coherent states. Given the substantial interest in squeezed states for probing matter, we believe that the optical analogs introduced here have significant implications for optical sensing. Specifically, the single-particle nature of our spatial modes makes them robust candidates for sensing photosensitive materials. Overall, our approach opens the door to optical metrology and sensing protocols that mimic those already existing in the quantum realm, and facilitates further exploration of the quantum state zoo through classical optical analogs.
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