arXiv subjects

Sándor Varró

Publications and source records attributed to Sándor Varró.

16 recordsLinked to original sources

arXiv2026

A quantum optical concept of attosecond pulses: the attoquants

High-harmonic generation (HHG) is conventionally understood to produce attosecond pulse trains only when the emitted harmonics are mutually phase-locked, in accordance with the classical theory of mode-locking. Such locking is necessary for pulse synthesis when the harmonic field is in a separable multimode quantum state. This requirement, however, can be circumvented entirely for harmonic combs exhibiting intermodal entanglement. We introduce a novel family of multimode quantum states, termed attoquants: states associated with highly structured pulse trains that are inherently insensitive to relative phases. As a concrete example, we analyse the coherent permanent state, constructed as a completely symmetric superposition of products of coherent states over all permutations of a fixed parameter set. It is shown analytically that its electric-field expectation value is a locked Fourier superposition of the driving-field harmonics, yielding an attosecond pulse train without requiring mode-locking. We further calculate the photon statistics, the Wigner function, and the logarithmic negativity of this state, confirming it to be genuinely nonclassical and entangled. Finally, we offer a phenomenological interpretation for the generation of such entangled states during HHG, as a consequence of multi-atom effects. Since the coherence volume of the driving field greatly exceeds that of its harmonics, a collectively-driven cluster of atoms can radiate the individual harmonics as spatially resolved, but fundamentally indistinguishable sources. This can generate the permutation-symmetric entanglement structure of an attoquant.

quant-ph↗

arXiv2026

Wave packet motion in a quantized electromagnetic field: Analytic results

We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position expectation values and uncertainties for arbitrary wave packets and field states, allowing us to identify quantum corrections to the corresponding classical motion. While the corrections to the position expectation value are weak and largely insensitive to the quantum state of the field, the wave packet broadening exhibits a pronounced dependence on the field state. In particular, the quantum uncertainty of the radiation is directly imprinted onto the spatial uncertainty of the particle. We illustrate these effects for Gaussian wave packets interacting with coherent, Fock, and squeezed states, including bright squeezed vacuum. The interaction with a finite-duration laser pulse is also analyzed as a multimode example. Our results provide a transparent analytic route toward understanding how quantum fluctuations of light influence electron dynamics in strong-field settings.

quant-ph↗

arXiv2025

Hidden facts in Landau-Zener transitions revealed by the Riccati Equation

We express the dynamics of the two probability amplitudes in the elementary Landau-Zener problem in terms of the solution of the corresponding Riccati differential equation and identify three key features: (i) The solution of the Riccati equation provides the bridge between the two probability amplitudes. (ii) Neglecting the non-linearity in the Riccati equation is equivalent to the Markov approximation which yields the exact asymptotic expression for one of the probability amplitudes, and (iii) the Riccati equation identifies the origin of the failure of the Markov approximation not being able to provide us in general with the correct asymptotic expression of the other probability amplitude. Our approach relies on approximate yet analytical solutions of the Riccati equation in different time regimes, highlighting the impact of its non-linear nature on the time evolution of the system.

quant-ph↗

arXiv2024

Quantum Optical Aspects of High-Harmonic Generation

The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.

quant-ph↗

arXiv2024

A different perspective on the Landau-Zener dynamics

We present two different approaches towards the Landau-Zener problem: (i) The Markov approximation in the integro-differential equation for one of the two probability amplitudes, and (ii) an amplitude-and-phase analysis of the linear second order differential equation for same probability amplitude. Our treatment shows that the Markov approximation neglects the non-linearity of the equation but still provides us with the exact asymptotic result.

quant-ph↗

arXiv2023

Parametric model for high-order harmonic generation with quantized fields

A quantum optical model for the high-order harmonic generation is presented, in which both the exciting field and the high harmonic modes are quantized, while the target material appears via parameters only. As a consequence, the model is independent from the excited material system to a large extent, and allows us to focus on the properties of the electromagnetic fields. Technically, the Hamiltonian known for parametric down-conversion is adopted, where photons in the $n$th harmonic mode are created in exchange of annihilating $n$ photons from the fundamental mode. In our treatment, initially the fundamental mode is in a coherent state corresponding to large photon numbers, while the high harmonic modes are in vacuum state. Due to the interaction, the latter modes get populated while the fundamental one loses photons. Analytical approximations are presented for the time evolution that are verified by numerically exact calculations. For multimode, finite bandwith excitation, the time dependence of the high-order harmonic radiation is also given.

quant-ph↗

arXiv2023

Diatomic molecule in a strong infrared laser field: level-shifts and bond-length change due to laser-dressed Morse potential

We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment function, and we derive analytic formulae for the bond-length change and for the shifted energy eigenvalues of the vibrations, by using the Kramers-Henneberger frame. We apply these results to the important cases of $\mathrm{H}_{2}$ and $\mathrm{LiH}$, driven by a near- or mid-infrared laser in the $10^{13}$ $\mathrm{ W/cm^2}$ intensity range.

physics.atom-ph↗

arXiv2021

Quantum interference in strong-field ionization by a linearly polarized laser pulse, and its relevance to tunnel exit time and momentum

We investigate the liberation of an atomic electron by a linearly polarized single-cycle near-infrared laser pulse having a peak intensity that ensures tunneling. Based on phase space analysis and energy distribution in the instantaneous potential, we reveal the importance of quantum interference between tunneling and over-the-barrier pathways of escape. Tunneling is blurred both in space and time, and the contribution of tunneling at the mean energy is almost negligible. We suggest and justify improved initial conditions for a classical particle approximation of strong-field ionization, based on the quantum momentum function, and we show how to reconstruct them from the detected momentum of an escaped electron.

quant-ph↗

arXiv2021

A quantum optical description of photon statistics and cross-correlations in high harmonic generation

We present a study of photon statistics associated with high-order harmonic generation (HHG) involving one-mode and intermodal correlations of the high harmonic photons. The aim of the paper is to give insight into the nonclassical properties of high-order harmonic modes. To this end, we use a simplified model describing an elementary quantum emitter: the model of a two-level atom. While the material system is extremely simplified in this description, the conclusions and the methods may be generalized for more complex cases. Our primary interest is an effective model of HHG in which the exciting pulse is classical, and the harmonics are quantized, although we touch upon the more generalized, fully quantized model as well. Evolution of the Mandel-parameter, photon antibunching, squeezing and cross-correlations are calculated. Results imply that with respect to a single quantized emitter, nonclassicality of the harmonics is present: sub-Poissonian photon statistic and squeezing can characterize certain optical modes, while strong anticorrelation can also be present.

quant-ph↗

arXiv2020

High-order harmonics as induced by a quantized field:a phase-space picture

The interaction of matter with a quantized electromagnetic mode is considered. Representing a strong exciting field, the mode is assumed to contain a large number of photons. As a result, the material response is highly nonlinear: the completely quantized description results in generation of high harmonics. In order to understand the essence of the physical processes that are involved, we consider a finite dimensional model for the material system. Using an appropriate description in phase space, this approach leads to a transparent picture showing that the interaction splits the initial, exciting coherent state into parts, and the rapid change of the populations of these parts (that are coherent states themselves) results in the generation of high-order harmonics as secondary radiation. The method we use is an application of the discrete lattice of coherent states that was introduced by J. von Neumann.

quant-ph↗

arXiv2018

Laser induced distortion of band structure in solids: an analytic model

We consider a spatially periodic (cosine) potential as a model for a crystalline solid that interacts with a harmonically oscillating external electric field. This problem is periodic both in space and time and can be solved analytically using the Kramers-Henneberger co-moving frame. By analyzing the stability of the closely related Mathieu-type differential equation, the electronic band structure can be obtained. We demonstrate that by changing the field intensity, the width of the zero-field band gaps can be drastically modified, including the special case when the external field causes the band gaps to disappear

cond-mat.mes-hall↗

arXiv2017

Carrier-envelope phase controlled isolated attosecond pulses in the nm wavelength range, based on superradiant nonlinear Thomson-backscattering

A proposal for a novel source of isolated attosecond XUV -- soft X-ray pulses with a well controlled carrier-envelope phase difference (CEP) is presented in the framework of nonlinear Thomson-backscattering. Based on the analytic solution of the Newton-Lorentz equations, the motion of a relativistic electron is calculated explicitly, for head-on collision with an intense fs laser pulse. By using the received formulae, the collective spectrum and the corresponding temporal shape of the radiation emitted by a mono-energetic electron bunch can be easily computed. For certain suitable and realistic parameters, single-cycle isolated pulses of ca. 20 as length are predicted in the XUV -- soft X-ray spectral range, including the 2.33-4.37 nm water window. According to our analysis, the generated almost linearly polarized beam is extremely well collimated around the initial velocity of the electron bunch, with considerable intensity and with its CEP locked to that of the fs laser pulse.

physics.atom-ph↗

arXiv2016

A quantum optical model for the dynamics of high harmonic generation

We investigate a two-level atom in the field of a strong laser pulse. The resulting time-dependent polarization is the source of a radiation the frequency components of which are essentially harmonics of the driving field's carrier frequency. The time evolution of this secondary radiation is analyzed in terms of the expectation values of the photon number operators for a large number of electromagnetic modes that are initially in the vacuum state. Our method is based on a multimode version of the Jaynes-Cummings-Paul model and can be generalized to different radiating systems as well. We show, that after the exciting pulse, the final distribution of the photon numbers is close to the conventional (Fourier transform-based) power spectrum of the secondary radiation. The details of the high harmonic spectra are also analyzed, for many-cycle excitations a clear physical interpretation can be given in terms of the Floquet quasi-energies. A first step towards the determination of the photon statistics of the HHG modes reveals states with slightly super-Poissonian distribution.

quant-ph↗

arXiv2015

Electron Acceleration by a Bichromatic Chirped Laser Pulse in Underdense Plasmas

A theoretical study of laser and plasma based electron acceleration is presented. An effective model has been used, in which the presence of an underdense plasma has been taken account via its index of refraction $n_{m}$. In the confines of this model, the basic phenomena can be studied by numerically solving the classical relativistic equations of motion. The key idea of this paper is the application of chirped, bichromatic laser fields. We investigated the advantages and disadvantages of mixing the second harmonic to the original $λ= 800 \, \mathrm{nm}$ wavelength pulse. We performed calculations both for plane wave and Gaussian pulses.

physics.plasm-ph↗

arXiv2015

Electron Acceleration in Underdense Plasmas Described with a Classical Effective Theory

An effective theory of laser--plasma based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction $n_{m}$ in which a single electron propagates. Because of the simplicity of this model, we did not need to perform PIC simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analysed. We compared our results to PIC simulations and experimental data. Keywords: Underdense plasma; Electron acceleration; Classical electrodynamics; Relativistic equation of motion; Ultrashort laser pulses

physics.plasm-ph↗

arXiv2013

Pair production at the edge of the QED flux tube

We investigate the process of Abelian pair production in the presence of strong inhomogeneous and time-dependent external electric fields. The spatial dependence of the external field is motivated by a non-Abelian color flux tube in heavy-ion collisions. We show that the inhomogeneity significantly increase the particle yield compared to that in the commonly used models with a constant and homogeneous field. Moreover our results indicate that in contrast to the latter, most of the particles are produced at the interface of the field profile in accordance with Heisenberg's prediction.

hep-ph↗