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arXiv:2512.21229

Squeezed quantum multiplets: properties and phase space representation

Juan Pablo Paz, Corina Révora, Christian Tomás Schmiegelow

quant-phSubmitted Dec 24, 2025• Announced Dec 25, 2025• 0 citations
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Abstract

We define and study the properties of ``squeezed quantum multiplets''. Ordinary multiplets are sets of $D$-orthonormal quantum states formed by superpositions of states squeezed along $D$ equally spaced directions in quadrature space. More generally, we also discuss superpositions of ``higher-order squeezed states'', including tri-squeezed and quad-squeezed states. All these states involve superpositions of multiples of $p$ photons. We compare states in ordinary ($p=2$) multiplets and higher-order ones ($p>2$) in the most relevant cases, showing that ordinary squeezed multiplets and higher-order ones share some important similarities, as well as some differences. Finally, we present analytical expressions for phase-space distributions (Wigner and characteristic functions) representing ordinary squeezed multiplets. We use this to show that some squeezed multiplets are highly sensitive to perturbations in all phase-space directions, making them interesting for metrological applications.

Comments
10 pages, 5 figures

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This paper starts with the transition from classical physics to quantum mechanics which was greatly aided by the concept of phase space. The role of canonical transformations in quantum mechanics is addressed. The Wigner phase-space distribution function is then defined which arises from the formulation of the density matrix, followed by the harmonic oscillator in phase space. Coherent and one- and two-mode squeezed states of light as well as the squeezed vacuum are discussed in the phase-space picture. Attention is also drawn to the fact that squeezed states naturally generate entanglement between the two-modes. Coupled harmonic oscillators are also elucidated in connection with the Wigner phase space. It will be noted that the phase-space picture of quantum mechanics has become an important scientific language for the rapidly expanding field of quantum optics. Here, we mainly focus on the simplest form of the Wigner function, which finds application in many branches of quantum mechanics. We make use of several symmetry groups such as Lorentz groups, the symplectic group in two and four dimensions, and the Euclidean group. The decoherence problem of an optical field is examined through a reformulation of the Poincaré sphere as a further illustration of the density matrix.
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Abstract We present a theoretical study on the generation and nonclassical properties of hybrid squeezed states (HSS), a class of engineered quantum states with enhanced quantum features. Using a modified beam splitter-Kerr medium scheme, we construct superpositions of squeezed vacuum and two-photon-added squeezed states, providing a flexible framework to generate and control hybrid quantum states. Nonclassicality is analysed via Mandel's QQQ parameter, photon number distributions, probability distribution functions, and Wigner functions, revealing sub-Poissonian statistics, oscillatory photon distributions, and significant Wigner negativity. Phase-sensitivity analysis within a Mach-Zehnder interferometric framework demonstrates that HSS outperform conventional squeezed and photon-added squeezed states, achieving measurement precisions that exceed the standard quantum limit and approach the Heisenberg limit under optimal parameters. These results establish hybrid squeezed states as a powerful resource for quantum metrology, communication, and optical interferometry.
ABSTRACT Inspired by the superposition of coherent states, we investigate the superposition of squeezed states (pure Gaussian states) and propose a mathematical characterization under the Fock‐Bargmann representation, with the possibility to further generalize to the superposition of non‐Gaussian states. We introduce generalized circular states constructed by superposing squeezed coherent states symmetrically on a circle. We demonstrate their photon distributions as “trimmed and rescaled” versions of those of the initial squeezed states. We find that squeezing disappears while higher‐order squeezing might be strengthened for some specific generalized circular states. We derive analytic expressions of the Wigner functions, with negativity indicating nonclassicality. This work reveals that circular superpositions of squeezed states possess enhanced quantum features, which are relevant to quantum metrology and information processing.