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.

High-resolution Infrared Spectroscopy of ^15N2^16O in 1650-3450 cm-1

High-resolution ro-vibrational spectroscopy of ^15N2^16O in 1650-3450 cm-1 region is studied using highly enriched isotopologue sample. The positions of more than 7300 lines of ^15N2^16O isotopologue were measured with a typical accuracy of 5.0×10-4 cm-1. The transitions were rovibrationally assigned on the basis of the global effective Hamiltonian model. The band by band analysis allowed for the determination of the rovibrational parameters of a total of 73 bands. 29 of them are newly reported and more rotational transitions have been observed for the others. The maximum deviation of the preidictions of the effective Hamiltonian model is up to 0.70 cm-1 for the ^15N2^16O species.

Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology

The alternative dynamics of loop quantum cosmology is examined by the path integral formulation.We consider the spatially flat FRW models with a massless scalar field,where the alternative quantizations inherit more features from full loop quantum gravity.The path integrals can be formulated in both timeless and deparameterized frameworks.It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other.Moreover,the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe,which coincide with those obtained in canonical theory.

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.

Theoretical methods for excited state dynamics of molecules and molecular aggregates

This contribution provides a summary of proposed theoretical and computational studies on excited state dynamics in molecular aggregates, as an important part of the National Natural Science Foundation (NNSF) Major Project entitled "Theoretical study of the low-lying electronic excited state for molecular aggregates". This study will focus on developments of novel methods to simulate excited state dynamics of molecular aggregates, with the aim of understanding several important chemical physics processes, and providing a solid foundation for predicting the opto-electronic properties of organic functional materials and devices. The contents of this study include: (1) The quantum chemical methods for electronic excited state and electronic couplings targeted for dynamics in molecular aggregates; (2) Methods to construct effective Hamiltonian models, and to solve their dynamics using system-bath approaches; (3) Non-adiabatic mixed quantum-classic methods targeted for molecular aggregates; (4) Theoretical studies of charge and energy transfer, and related spectroscopic phenomena in molecular aggregates.

B^0-B^0 Mixing in Local Gauged Baryon and Lepton Numbers

Using the effective Hamiltonian method, we analyze the B0-B0 mixing in the extension of the standard model （SM） where baryon number and lepton number are local gauge symmetries. The numerical results indicate the correction from the extra particles to the mass difference ArnB is significant. There is a 60% enhancement compared to the SM prediction for AraB at most, which agrees with the current experimental result.

Large Detuning Limit for the Multipartite Systems Interacting with Electromagnetic Fields

We study the dynamics of the multipartite systems nonresonantly interacting with electromagnetic fields, focusing on the large detuning limit for the effective Hamiltonian. Due to the many-particle interference effects, the more rigorous large detuning condition for neglecting the rapidly oscillating terms for the effective Plamiltonian should be △ 〉〉 N^1/2 g, instead of △ 〉〉 g usually used in the literature even in the case of multipartite systems, with N the number of microparticles involved, g the coupling strength, A the detuning. This result is significant since merely the satisfaction of the original condition will result in the invalidity of the effective Hamiltonian and the errors of the parameters associated with the detuning in the multipartite case.

Decay Process of Quantum Open System at Finite Temperatures

Starting from the formal solution to the Heisenberg equation, we revisit an universal model for a quantum open system with a harmonic oscillator linearly coupled to a boson bath. The analysis of the decay process for a Fock state and a coherent state demonstrate that this method is very useful in dealing with the problems in decay process of the open system. For finite temperatures, the calculations of the reduced density matrix and the mean excitation number for the open system show that an initiaJ coherent state will evolve into a temperature-dependant coherent state after tracing over the bath variables. Also in short-time limit, a temperature-dependant effective Hamiltonian for the open system characterizes the decay process of the open system.

Theory and algorithms for the excited states of large molecules and molecular aggregates

This project aims to attack the frontiers of electronic structure calculations on the excited states of large molecules and molecular aggregates by developing novel theoretical and computational methods. The methodology development is especially based on the time-dependent density functional theory (TDDFT) and valence bond (VB) theory, and is expected to be computationally effective and accurate as well. Research works on the following related subjects will be performed: (1) The analytical energy-derivative approaches for electronically excited state within TDDFT will be developed to reduce bypass the computational costs in the calculation of molecular excited-state properties. (2) The ab initio methods for electronically excited state based on VB theory and hybrid TDDFT-VB method will be developed to overcome the limitations of current TDDFT in simulating photophysics and photochemistry. (3) For larger aggregates, neither ab initio methods nor TDDFT is applicable. We intend to build the effective model Hamiltonian by developing novel theoretical and computational methods to calculate the involved microscopic physical parameters from the first-principles methods. The constructed effective Hamiltonian is then used to describe the excitonic states and excitonic dynamics of the natural or artificial photosynthesized systems, organic or inorganic photovoltaic cell. (4) The condensed phase environment is taken into account by combining the developed theories and algorithms based on TDDFT and VB with the polarizable continuum solvent models (PCM), molecular mechanism (MM), classical electrodynamics (ED) or molecular dynamics (MD) theory. (5) Highly efficient software packages will be designed and developed.