Quantum carpets from Gaussian sum theory

Abstract

In many closed quantum systems, an interesting phenomenon, called quantum carpet, can be observed, where the evolution of wave function exhibits a carpet-like pattern. The mechanism of quantum carpet is similar to the classical interference pattern of light. Although the origin of quantum carpets has been studied previously, there are still many interesting details worth exploring. Here, we presented a unified framework for a simultaneous analyzing on three features of quantum carpets, namely full revival, fractional revival and diagonal canal. For fractional revival, a complete formula is presented to explain its generation through "Gaussian sum theory", in which all the essential features, including the phases and amplitudes, of this phenomenon could be captured analytically. Moreover, we also revealed the relations between the interference terms of the diagonal canals and their geometric interpretations, providing a better understanding in the formation of diagonal canals.

arXiv comment8 pages, 8 figures

References in corpus (26)

• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Shortcut to adiabatic passage in two and three level atoms
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Quantum wave packet revivals
• Colloquium: Quantum interference of clusters and molecules
• Self-adjoint extensions of operators and the teaching of quantum mechanics
• Deep learning and the Schrödinger equation
• Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics
• Auger Recombination in Semiconductor Quantum Wells
• Shortcuts to adiabaticity in a time-dependent box
• Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm
• Blind quantum computation with noise environment
• Visualizing revivals and fractional revivals in a Kerr medium using optical tomogram
• Analytic next-to-nearest neighbour XX models with perfect state transfer and fractional revival
• Perfect wave-packet splitting and reconstruction in a one-dimensional lattice
• A graph with fractional revival
• Thermodynamic Entanglement of Magnonic Condensates
• Fractional Revivals, Multiple-Cat States and Quantum Carpets in the Interaction of a Qubit with $N$ Qubits
• Free-Space Entangled Quantum Carpets
• A novel analytic spin chain model with fractional revival
• Fractional revivals of superposed coherent states
• Strong entanglement of spins inside a quantum domain wall
• Quantum revivals and magnetization tunneling in effective spin systems
• Magneto-spatial dispersion of quantum wells
• Off-resonant many-body quantum carpets in strongly tilted optical lattices
• Interference Energy Spectrum of the Infinite Square Well