Work

Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling

Year: 2024

Type: article

Abstract: We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) from the Hamiltonian for two, coupled QHOs and provide a physical picture for the Kravchuk function eigenstates of the oscillator. The familiar su ( 2 ) structure of the coupled QHO Hamiltonian divides its spectrum into sets corresponding to the DQHO at different resolutions. In addition to energy ladder operators, the formulation allows for the introduction of resolution ladder operators connecting all DQHOs with different resolutions, thus enabling the dynamic scaling of the resolution of finite degree-of-freedom quantum simulations. The coherent state of the DQHO is constructed, and its expected position is proven to oscillate as a classical harmonic oscillator. The DQHO coherent state recovers that of the quantum harmonic oscillator at large resolution.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ad7ae5

Authors: Michael Q May, Hong Qin

Institutions: Princeton University, Princeton Plasma Physics Laboratory

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,165

Funder: U.S. Department of Energy