Lissajous coherent states via projection

• URL: http://arxiv.org/abs/2603.00788v1
• Date: Sat, 28 Feb 2026 19:16:33 GMT
• Title: Lissajous coherent states via projection
• Authors: Errico J. Russo, James Schneeloch, Edwin E. Hach, Richard J. Birrittella, Wanda Vargas, Christopher C. Gerry,
• Abstract summary: We construct stationary coherent states concentrated on Lissajous figures of the isotropic and anisotropic harmonic oscillators.<n>We show that our stationary states are true coherent states as they can be used to resolve the relevant identity operators on their respective degenerate subspaces.
• Score: 0.01675245825272646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We construct stationary coherent states concentrated on Lissajous figures of the isotropic and anisotropic harmonic oscillators, the latter having coprime frequencies, by projecting products of ordinary coherent states (one coherent state for each degree of freedom) onto sets of degenerate states. By performing these projections, we are deriving our states from sets of coherent states that are known to follow the classical motion of a two-dimensional harmonic oscillator for arbitrary frequencies. We clarify the nature of any singularities present in the phase of the wavefunction for each of the states we derive, and we establish a rigorous connection between the laminar flow of probability current and the emergence of quantum interference. Through this analysis, we are able to provide a clear and quantifiable definition for a vortex state of the two-dimensional harmonic oscillator (2DHO). In an appendix, we show that our stationary states are true coherent states as they can be used to resolve the relevant identity operators (the above mentioned projection operators) on their respective degenerate subspaces. In the special case of the isotropic oscillator, the states obtained are the SU(2) coherent states, and we derive from our formalism the familiar resolution of unity for these states.

Related papers

• Multi-emitter oscillating bound states in Waveguide QED [0.0]
  We investigate the formation and dynamics of superpositions of bound states in a cavity array waveguide coupled to two spatially separated quantum emitters.<n>We show that spontaneous emission can drive the system into non-local equilibrium states in which both photonic and emitter populations exhibit persistent oscillations.
  arXiv  Detail & Related papers  (2026-02-17T21:37:22Z)
• Construction of the Jaynes-Cummings interaction over the finite two-dimensional oscillator [51.56484100374058]
  The construction of the coupling between the degenerate energy states of the finite oscillator and the two levels of the atom allows the identification of excitation-conserved eigenbasis.<n>A dynamical approach to the evolution of mean values of the fields mediated by the atom is shown in the interaction picture.
  arXiv  Detail & Related papers  (2025-09-08T20:49:16Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Non-equilibrium dynamics of charged dual-unitary circuits [44.99833362998488]
  interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the centre of an intense multidisciplinary research effort. We show that one can introduce a class of solvable states, which extends that of generic dual unitary circuits. In contrast to the known class of solvable states, which relax to the infinite temperature state, these states relax to a family of non-trivial generalised Gibbs ensembles.
  arXiv  Detail & Related papers  (2024-07-31T17:57:14Z)
• Quantum Lissajous Figures via Projection [0.0]
  We present a new category of quantum Lissajous states for a 2DHO having commensurate angular frequencies. The states result from the projection of ordinary coherent states onto a degenerate subspace of the 2DHO.
  arXiv  Detail & Related papers  (2024-05-20T18:00:24Z)
• Teleportation of a qubit using exotic entangled coherent states [0.0]
  We study the exotic Landau problem at the classical level where two conserved quantities are derived. We form entangled coherent states which are Bell-like states labeled quasi-Bell states. The effect of non-maximality of a quasi-Bell state based quantum channel is investigated in the context of a teleportation of a qubit.
  arXiv  Detail & Related papers  (2024-04-03T12:03:38Z)
• Bounding the rotating wave approximation for coupled harmonic oscillators [34.82692226532414]
  We study the validity of the rotating wave approximation of an ideal system composed of two harmonic oscillators evolving with a quadratic Hamiltonian and arbitrarily strong interaction.<n>We are able to fully quantify the deviation of arbitrary pure Gaussian states that evolve through different dynamics from a common quantum state.
  arXiv  Detail & Related papers  (2024-03-22T16:51:53Z)
• Entanglement entropy in conformal quantum mechanics [68.8204255655161]
  We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory.
  arXiv  Detail & Related papers  (2023-06-21T14:21:23Z)
• Coherent States for infinite homogeneous waveguide arrays: Cauchy coherent states for $E(2)$ [0.0]
  Perelomov coherent states for infinite homogeneous waveguide arrays with Euclidean E(2) symmetry are defined. It is shown that Perelomov coherent states for the Eucliean E(2) group have a simple and natural physical realization.
  arXiv  Detail & Related papers  (2021-12-01T22:51:53Z)
• Bose-Einstein condensate soliton qubit states for metrological applications [58.720142291102135]
  We propose novel quantum metrology applications with two soliton qubit states. Phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes.
  arXiv  Detail & Related papers  (2020-11-26T09:05:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.