Analytic calculation of nonadiabatic transition probabilities from monodromy of differential equations

The model of a level crossing with a Coulomb band: exact probabilities of nonadiabatic transitions

We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. Our model corresponds to the case of a single linear diabatic energy level interacting with a band of an arbitrary N states, for which the diabatic energies decay with time according to the Coulomb law. We show that the time-dependent Schroedingier equation for this system can be solved in terms of Meijer functions whose asymptotics at a large time can be compactly written in terms of elementary functions that depend on the roots of an Nth order characteristic polynomi…

Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory

We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-Stückelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that pr…

Exact results for models of multichannel quantum nonadiabatic transitions

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form $\hat{H}(t) = \hat{A} +\hat{B} t + \hat{C}/t$, where $t$ is time and $\hat{A}$, $\hat{B}$, $\hat{C}$ are Hermitian $N\times N$ matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at $t \rightarrow -\infty$. This allows one to continue such solutions analytically to $t \rightarrow +\infty$, and connect their asymptotic behavior at $t \right…

Exact transition probabilities in the three-state Landau-Zener-Coulomb model

We obtain the exact expression for the matrix of nonadiabatic transition probabilities in the model of three interacting states with a time-dependent Hamiltonian. Unlike other known solvable Landau-Zener-like problems, our solution is generally expressed in terms of hypergeometric functions that have relatively complex behavior, e.g. the obtained transition probabilities may show multiple oscillations as functions of parameters of the model Hamiltonian.

非绝热转变在非厄密itian PT 对称双能级系统中的研究

Nonadiabatic transitions in non-Hermitian $\mathcal{PT}$-symmetric two-level systems

研究PT对称双能级系统在非绝热驱动下的动态演化，揭示间隙闭合与能级反交叉对粒子分布的影响，通过解析解和数值模拟验证结果。

Investigation of robust population transfer using quadratically chirped laser interacting with two-level system

We have proposed and demonstrated a fast and robust method of population transfer between two quantum states using a quadratically chirped laser source. Incorporating the Jaynes-Cummings in a full quantum description of the interaction, and numerically solving the time-dependent Schrödinger equation, transition probabilities have been obtained and the condition of the adiabatic passage is investigated. In this scheme, a laser source has been swept quadratically in time for arbitrarily engineering the transition probabilities. The results show that complete and robust population transfer could …