General solution for multi-dimensional time-dependent coupled quantum oscillator

Diego Ximenes Macedo, Ilde Guedes

Xin Chen, Yaoxiong Wang, Yunjian Ge +3 more

The quantum dynamics of a pulse-driven finite-dimensional quantum chain with only nearest-neighbor coupling is studied. We extend the concept of Rabi oscillations from two-level quantum systems to the multi-level quantum chains. The time-dependent quantum dynamics and solutions producing perfect population transfer are obtained for up to five-level quantum chains. The Gröbner basis analysis technique is used to generalize the results and get all analytical solutions for perfect population transfer. Explicit formulas for the solutions up to nine levels are presented. These results could be used to design control strategies for general finite-dimensional quantum systems.

Chi‐Fai Lo

Xu Xiu-Wei, Ren Ting-Qi, Shuyan Liu +3 more

Utilizing the general linear quantum transformation theory, we give the exact expressions of evolutionary operator's matrix elements, wave function, expectation value of an observable and partition function, for multi-dimensional coupled and forced quantum oscillator.

Alejandro R. Urzúa, I. Ramos-Prieto, M. Fernández‐Guasti +1 more

We show that by using the quantum orthogonal functions invariant, we found a solution to coupled time-dependent harmonic oscillators where all the time-dependent frequencies are arbitrary. This system may be found in many applications such as nonlinear and quantum physics, biophysics, molecular chemistry, and cosmology. We solve the time-dependent coupled harmonic oscillators by transforming the Hamiltonian of the interaction using a set of unitary operators. In passing, we show that N time-dependent and coupled oscillators have a generalized orthogonal functions invariant from which we can write a Ermakov–Lewis invariant.

Sara Hassoul, Salah Menouar, Hamid Benseridi +1 more