Finer sub-Planck structures and displacement sensitivity of SU(1,1) circular states
State Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology, School of Physics, Anhui University（安徽大学物理学院光电信息获取与保护技术国家重点实验室）；School of Physics and Technology, Nantong University（南通大学物理与 technology 学院）；Department of Physics, Jiangsu University（江苏大学物理系）
Naeem Akhtar, Jia-Xin Peng, Tariq Aziz, Xiaosen Yang, Dong Wang
Quantum states with sub-Planck features exhibit sensitivity to phase-space displacements beyond the standard quantum limit, making them useful for quantum metrology. In the context of the SU(1,1) group, sub-Planck features have been constructed through the superposition of four Perelomov coherent states on the hyperbolic plane (the SU(1,1) compass state). However, these structures differ in scale along different phase-space directions (anisotropic features), resulting in nonuniform sensitivity enhancement to phase-space displacements. Here, we construct $N$-component compass states, which are obtained by superposing $N \geq 6$ SU(1,1) coherent states with an even total number, evenly arranged along a circular path on the hyperbolic plane; that is, all components lie at the same distance from the origin and have equal angular spacing of $\frac{2π}{N}$. We observe that these generalized SU(1,1) compass states exhibit isotropic sub-Planck structures, leading to an isotropic enhancement in sensitivity to phase-space displacements that progressively increases with larger $N$. These states are directly relevant to quantum platforms supporting Kerr-type interactions between two bosonic modes, where the underlying SU(1,1) dynamical symmetry enables the generation of multicomponent SU(1,1) compass states. Specifically, the compact evolution of SU(1,1) coherent states under the considered dynamics enables the generation of multicomponent SU(1,1) compass states at specific times. We also investigate the effects of thermal decoherence on these multicomponent compass states within a frequency-resolved Lindblad framework, demonstrating the evolution and degradation of their nonclassical signatures.
Reflection of a particle from a mirror pair that is fixed to a platform which falls freely in a gravitational field is shown to infer displacement of the center of mass of this platform of order the Planck length. This displacement and its relationship to the wave and particle nature of reflection in such an energy measurement is elucidated using harmonic motion of the mirror pair.
Coherent-state superpositions are of great importance for many quantum subjects, ranging from foundational to technological, e.g., from tests of collapse models to quantum metrology. Here we explore various aspects of these states, related to the connection between sub-Planck structures present in their Wigner function and their sensitivity to displacements (ultimately determining their metrological potential). We review this for the usual Heisenberg-Weyl algebra associated to a harmonic oscillator, and extend it to find analogous results for the $\mathfrak{su}(2)$ algebra, typically associate…
We investigate the sub-Planck-scale structures associated with the SU(1,1) group by establishing that the Planck scale on the hyperbolic plane can be considered as the inverse of the Bargmann index $k$. Our discussion involves SU(1,1) versions of Wigner functions, and the quantum-interference effect is easily visualized through plots of these Wigner functions. Specifically, the superpositions of four Perelomov SU(1,1) coherent states (compass state) yield nearly isotropic sub-Planck structures in phase space scaling as $\frac1{k}$ compared with $\frac1{\sqrt{k}}$ scaling for individual SU(1,1)…
A proposed experiment to test whether space is discretized [J. D. Bekenstein, Phys. Rev. D 86, 124040 (2012); Found. Phys. 44, 452 (2014)] is based on the supposed impossibility of an incident photon causing a displacement of a transparent block by less than the Planck length. An analysis of the quantum and thermal jitter of the block shows that it greatly diminishes the possibility that the experiment could reveal Planck-scale signals.
Decoherence across phase-space scales: From compass states to general quantum states
School of Physics, Anhui University（安徽大学物理学院）；School of Physics and Technology, Nantong University（南通大学物理与信息技术学院）；Department of Physics, Zhejiang Normal University（浙江师范大学物理系）；Department of Physics, Jiangsu University（江苏大学物理系）
We introduce quantum hypercube states, a class of continuous-variable quantum states that are generated as orthographic projections of hypercubes onto the quadrature phase-space of a bosonic mode. In addition to their interesting geometry, hypercube states display phase-space features much smaller than Planck's constant, and a large volume of Wigner-negativity. We theoretically show that these features make hypercube states sensitive to displacements at extremely small scales in a way that is surprisingly robust to initial thermal occupation and to small separation of the superposed state-comp…
