Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

A study of the effective Hamiltonian method for decay dynamics

The decay dynamic of an excited quantum emitter(QE)is one of the most important contents in quantum optics.It has been widely applied in the field of quantum computing and quantum state manipulation.When the electromagnetic environment is described by several pseudomodes,the effective Hamiltonian method based on the multi-mode Jaynes-Cummings model provides a clear physical picture and a simple and convenient way to solve the decay dynamics.However,in previous studies,only the resonant modes are taken into account,while the non-resonant contributions are ignored.In this work,we study the applicability and accuracy of the effective Hamiltonian method for the decay dynamics.We consider different coupling strengths between a two-level QE and a gold nanosphere.The results for dynamics by the resolvent operator technique are used as a reference.Numerical results show that the effective Hamiltonian method provides accurate results when the two-level QE is resonant with the plasmon.However,when the detuning is large,the effective Hamiltonian method is not accurate.In addition,the effective Hamiltonian method cannot be applied when there is a bound state between the QE and the plasmon.These results are of great significance to the study of the decay dynamics in micro-nano structures described by quasi-normal modes.

Effective dynamics for a spin-1/2 particle constrained to a curved layer with inhomogeneous thickness

We derive an effective Hamiltonian for a spin-1/2 particle confined within a curved thin layer with non-uniform thickness using the confining potential approach.Our analysis reveals the presence of a pseudo-magnetic field and effective spin–orbit interaction(SOI)arising from the curvature,as well as an effective scalar potential resulting from variations in thickness.Importantly,we demonstrate that the physical effect of additional SOI from thickness fluctuations vanishes in low-dimensional systems,thus guaranteeing the robustness of spin interference measurements to thickness imperfection.Furthermore,we establish the applicability of the effective Hamiltonian in both symmetric and asymmetric confinement scenarios,which is crucial for its utilization in one-side etching systems.

High-order Hamiltonian obtained by Foldy-Wouthuysen transformation up to the order of mα^(8)

Complete relativistic corrections of an effective Hamiltonian for a single-particle system in an external electromagnetic field and their unitary equivalent form up to the order of mα^(8) are obtained.The derivation is based on two approaches applying Foldy-Wouthuysen(FW)transformation to the Dirac Hamiltonian for a particle in an external electromagnetic field.The results are consistent with the previous work at the mα^(6) and mα^(8) order correction[Phys.Rev.A 71012503(2005);Phys.Rev.A 100012513(2019)].We also further consider the effect of anomalous magnetic moments,namely,the Dirac-Pauli equation,and obtain FW-Hamiltonians at the same order.The results obtained can be used for the subsequent calculation of relativistic and radiation effects in simple atomic and molecular systems.

A review on different theoretical models of electrocaloric effect for refrigeration

The performance parameters for characterizing the electrocaloric effect are isothermal entropy change and the adiabatic temperature change,respectively.This paper reviews the electrocaloric effect of ferroelectric materials based on different theoretical models.First,it provides four different calculation scales(the first-principle-based effective Hamiltonian,the Landau-Devonshire thermodynamic theory,phase-field simulation,and finite element analysis)to explain the basic theory of calculating the electrocaloric effect.Then,it comprehensively reviews the recent progress of these methods in regulating the electrocaloric effect and the generation mechanism of the electrocaloric effect.Finally,it summarizes and anticipates the exploration of more novel electrocaloric materials based on the framework constructed by the different computational methods.