arXiv subjects

Alexandre V. Dodonov

Publications and source records attributed to Alexandre V. Dodonov.

4 recordsLinked to original sources

arXiv2025

One- and multiphoton resonances in the light-atom interaction

The interaction between atomic systems and electromagnetic fields is central to modern physics and emerging quantum technologies. The Rabi models, in their semiclassical and quantum versions, provide the simplest and most fundamental description of this interaction. In this work, we present a concise derivation of both models and show how one- and multiphoton resonances arise in the semiclassical regime. We then analyze how these resonances manifest in the quantum Rabi model, discussing similarities and differences in relation to the classical description. Special attention is given to the three-photon resonance, a phenomenon usually neglected in textbooks due to its relative weakness, but which is intrinsic to the radiation-matter interaction. Our goal is to offer an accessible pedagogical reference for students and researchers interested in Quantum Optics and Quantum Information, with an emphasis on the fundamentals of the Rabi models.

quant-ph↗

arXiv2024

Adiabatic versus instantaneous transitions from a harmonic oscillator to an inverted oscillator

We have obtained explicit analytical formulas for the mean energy and its variance (characterizing the energy fluctuations) of a quantum harmonic oscillator with time-dependent frequency in the adiabatic regimes after the frequency passes through zero. The behavior of energy turns out to be quite different in two cases: when the frequency remains real and when it becomes imaginary. In the first case, the mean energy always increases when the frequency returns to its initial value, and the increment coefficient is determined by the exponent in the power law of the frequency crossing zero. On the other hand, if the frequency becomes imaginary, the absolute value of mean energy increases exponentially, even in the adiabatic regime, unless the Hamiltonian becomes time independent. Small corrections to the leading terms of simple adiabatic approximate formulas are crucial in this case, due to the unstable nature of the motion.

quant-ph↗

arXiv2023

Adiabatic amplification of energy and magnetic moment of a charged particle after the magnetic field inversion

We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field, when this field changes adiabatically its sign. We show that after a single magnetic field passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again, but with the proportionality coefficient higher than in the initial state. The concrete value of this proportionality coefficient depends on the power index of the frequency dependence on time near zero point. In particular, the adiabatic ratio of the initial ground state (with zero radial and angular quantum numbers) triplicates if the frequency tends to zero linearly as function of time. If the Larmor frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on the lengths of the time intervals between zero points, so that the mean energy behavior can be quasi-stochastic after many passages through zero value. The original Born-Fock adiabatic theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many instantaneous Fock states, whose weights do not depend on time in the new adiabatic regime.

quant-ph↗

arXiv2023

Adiabatic amplification of the harmonic oscillator energy when the frequency passes through zero

We study the evolution of the energy of a harmonic oscillator when its frequency slowly varies with time and passes through zero value. We consider both the classical and quantum descriptions of the system. We show that after a single frequency passage through zero value, the famous adiabatic invariant ratio of energy to frequency (which does not hold for zero frequency) is reestablished again, but with the proportionality coefficient dependent on the initial state. The dependence on the initial state disappears after averaging over phases of initial states with the same energy (in particular, for the initial vacuum, Fock and thermal quantum states). In this case, the mean proportionality coefficient is always greater than unity. The concrete value of the mean proportionality coefficient depends on the power index of the frequency dependence on time near zero point. In particular, the mean energy triplicates if the frequency tends to zero linearly. If the frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on lengths of time intervals between zero points, so that the mean energy behavior turns out quasi-stochastic after many passages through zero value. The original Born-Fock theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many Fock states, whose weights do not depend on time in the new adiabatic regime. When the mean energy triplicates, the initial Nth Fock state becomes a superposition of, roughly speaking, 6N states, distributed non-uniformly. The initial vacuum and low-order Fock states become squeezed, as well as initial thermal states with low values of the mean energy.

quant-ph↗