Optical Tautochrone and Squeezing Dynamics in Nonuniform Lattices

Abstract

We present exact analogies between the tautochrone problem of classical mechanics and the squeezed states of quantum optics to optical lattices. Both phenomena emerge in the same physical system, that of waveguide arrays with nonuniform couplings. Extension to two dimensions yields Lissajous-type trajectories and multidirectional tautochrone focusing. Furthermore, we investigate the impact of Kerr nonlinearity and show that it determines the diffraction behavior, namely coherent-state-like or squeezed propagation. These quantum inspired classical lattices highlight the role of the coupling coefficients to beam engineering and light control in complex media.

13 pages, 11 figures

References in corpus (18)

• Photonic Floquet Topological Insulators
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light
• Perfect state transfer in quantum spin networks
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Shortcuts to adiabaticity: concepts, methods, and applications
• Quantum Brachistochrone
• Coherent Quantum Transport in Photonic Lattices
• Thermodynamic theory of highly multimoded nonlinear optical systems
• Experimental Perfect Quantum State Transfer
• Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices
• A Faithful Communication Hamiltonian in Photonic Lattices
• Periodic wave packet reconstruction in truncated tight-binding lattices
• Exact dynamics of finite Glauber-Fock photonic lattices
• Controlling Optical Beam Thermalization via Band-Gap Engineering
• Classical Simulation of Squeezed Vacuum in Optical Waveguide Arrays
• Dynamic localization in Glauber-Fock lattices
• Supersymmetric reshaping and higher-dimensional rearrangement of photonic lattices