arXiv subjects

Petra Ruth Kapralova-Zdanska

Publications and source records attributed to Petra Ruth Kapralova-Zdanska.

3 recordsLinked to original sources

arXiv2022

Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space

We revisit the complex time method for the application to quantum dynamics as an exceptional point is encircled in the parameter space of the Hamiltonian. The basic idea of the complex time method is using complex contour integration to perform the first-order adiabatic perturbation integral. In this way, the quantum dynamical problem is transformed to a study of singularities in the complex time plane -- transition points -- which represent complex degeneracies of the adiabatic Hamiltonian as the time-dependent parameters defining the encircling contour are analytically continued to complex plane. As an underlying illustration of the approach we discuss a switch between Rabi oscillations and rapid adiabatic passage which occurs upon the encircling of an exceptional point in a special time-symmetric case.

quant-ph↗

arXiv2021

Coalescence of two branch points in complex time marks the end of rapid adiabatic passage and the start of Rabi oscillations

We study theoretically the population transfer in two-level atoms driven by chirped lasers. It is known that in the Hermitian case, the rapid adiabatic passage (RAP) is stable for an above-critical chirp below which the final populations of states Rabi oscillate with varying laser power. We show that if the excited state is represented by a resonance, the separatrix marking this critical phenomenon in the space of the laser pulse parameters emanates from an exceptional point (EP) -- a non-Hermitian singularity formed in the atomic system by the fast laser field oscillations and encircled due to slow variations of the laser pulse envelope and instantaneous frequency. This critical phenomenon is neatly understood via extending the "slow" time variable into the complex plane, uncovering a set of branch points which encode non-adiabatic dynamics, where the switch between RAP and Rabi oscillations is triggered by a coalescence of two such branch points. We assert that the intriguing interrelation between the two different singularities -- the EP and the branch point coalescence in complex time plane -- can motivate feasible experiments involving laser driven atoms.

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arXiv2021

Complex scaling spectrum using multiple avoided crossings at stabilization graph

This study concerns finite basis set $\{χ_k\}$ calculations of resonances based on real scaling, $χ_k(x)\to χ_k(xe^{-η})$. I demonstrate that resonance width is generally influenced by several neighboring quasi-discrete continuum states. Based on this finding I propose a new method to calculate the complex resonance energy together with several states of complex rotated continuum. The theory is introduced for a one-dimensional model, then it is applied for helium doubly excited resonance $2s^2$. The new method requires the real spectrum ("stabilization graph") for a sufficiently large interval of the parameter $η$ on which the potential curve of the sought resonance gradually meets several different quasi-continuum states. Diabatic Hamiltonian which comprehends the resonance and the several quasi-continuum states participating at the avoided crossings is constructed. As $η$ is taken to complex plane, $η\to iθ$, the corresponding part of the complex scaled spectrum is obtained.

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