Symplectic tomographic probability distribution of crystallized Schrödinger cat states
arXiv:2203.07783 · doi:10.1016/j.physleta.2022.128044
Abstract
Within the framework of the probability representation of quantum mechanics, we study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides; in other words, the cyclic groups (containing the rotational symmetries) and dihedral groups (containing the rotational and inversion symmetries). We obtain the Wigner functions and tomographic probability distributions (symplectic and optical tomograms) determining the density matrices of the states explicitly as the sums of Gaussian terms. The obtained Wigner functions demonstrate nonclassical behavior, i.e., contain negative values, while the tomograms show a series of maxima and minima different for each state, where the number of the critical points reflects the order of the group defining the states. We discuss general properties of such a generalization of normal probability distributions.
References in corpus (15)
- Generation of a superposition of odd photon number states for quantum information networks
- Symplectic tomography as classical approach to quantum systems
- Generation of Optical Coherent State Superpositions by Number-Resolved Photon Subtraction from Squeezed Vacuum
- Generation of large-amplitude coherent-state superposition via ancilla-assisted photon-subtraction
- Review of Entangled Coherent States
- Deterministic creation of entangled atom-light Schrödinger-cat states
- Coherent states on the circle
- Quantum Phase and Quantum Phase Operators: Some Physics and Some History
- Quantum Tomography twenty years later
- The sinh-Gordon defect matrix generalized for n defects
- Sampling Theorem and Discrete Fourier Transform on the Hyperboloid
- Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere
- Evolution and entanglement of Gaussian states in the parametric amplifier
- General superposition states associated to the rotational and inversion symmetries in the phase space
- Dynamic Generation of Light States with Discrete Symmetries