Superposed photon-added and photon-subtracted squeezed-vacuum states exhibit sub-Planck phase-space structures and metrological potential similar to the original compass states (superposition of four coherent states), but are more closely tied to modern experiments. Here, we observe that these compasslike states are highly susceptible to loss of quantum coherence when placed in contact with a thermal reservoir; that is, the interaction with the thermal reservoir causes decoherence, which progressively suppresses the capacity of these states to exhibit interference traits. We focus on the sub-Planck structures of these states and find that decoherence effects on these features are stronger with increasing the average thermal photon number of the reservoir, the squeezing parameter, or the quantity of added (or subtracted) photons to the squeezed-vacuum states. Furthermore, we observe that the sub-Planck structures of the photon-subtracted case survive comparatively longer in the thermal reservoir than their counterparts in the photon-added case, and prolonged contact with the thermal reservoir converts these compasslike states into a classical state.
We propose the cavity quantum electrodynamics method, using dispersive interaction between atoms and a high-quality cavity to realize the mesoscopic superposition of coherent states that would exhibit sub-Planck structures in phase space, i.e., the structures at a scale smaller than the Plank's constant $(\ensuremath{\hbar})$. These structures are direct signatures of quantum coherence and are formed as a result of interference between the two superposed cat states. In particular we focus on a superposition involving four coherent states. We show interferences in the conditional measurements involving two atoms.
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≥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
N2π. 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.