Sandor Varro

Wigner Research Centre for Physics of the Loránd Eötvös Research Network

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 o...

A quantum optical model for high-order harmonic generation is presented in which both the exciting field and the high-order harmonic modes are quantized, while the target material appears only via parameters. As a consequence, the model is independent of the excited material system to a large extent and allows us to focus on the properties of the e...

Recent observations of anomalous angular correlations of electron–positron pairs in several nuclear reactions have indicated the existence of a hypothetical neutral boson of rest mass ~17 MeV/c2, called the X17 particle. Similarly, one has interpreted an independent set of experiments on photon pair spectra around the invariant mass ~38 MeV/c2, by...

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 th...

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 th...

We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969 Zh. Eksp. Teor. Fiz. 56 1375–90) long ago, in their thorough analysis of the parame...

We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969) long ago, in their thorough analysis of the parametric excitation of harmonic osci...

Varró S, Coherent and incoherent superposition of the transition matrix elements of the squeezing operator. Abstract. We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been...

We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969) long ago, in their thorough analysis of the parametric excitation of harmonic osci...

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 e...

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 emitt...

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 emitt...

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 o...

Optical generation of high-order harmonics is a prototypical example of nonlinear light–matter interactions in the high-field regime. Quantum optical effects have recently been demonstrated to have a significant influence on this phenomenon. These findings underline the importance of understanding the dynamics of the quantized electromagnetic field...

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 e...

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...

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...

Electrodynamical processes induced in complex systems like semiconductors by strong electromagnetic fields have traditionally been described using semiclassical approaches. Although these approaches allowed the investigation of ultrafast dynamics in solids culminating in multipetahertz electronics, they do not provide any access to the quantum-opti...

The reflection and transmission of a few-cycle laser pulse impinging on two parallel thin metal layers have been analyzed. The two layers, with a thickness much smaller than the skin depth of the incoming radiation field, are represented by current sheets embedded in three dielectrics, all with different index of refraction. The dynamics of the sur...

New theoretical and numerical results are presented regarding isolated attosecond XUV – soft X-ray pulses, that can be generated by Thomson-backscattering of a high-intensity single-cycle near-infrared laser pulse on a suitable nanobunch of MeV electons. A simple approximate formula is derived for the cut-off frequency of the collective radiation s...

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 di...

This chapter includes a brief biography of Lajos Jánossy (1912–1978) presented by Sándor Varró (Sect. 18.1) and his translation into English from Hungarian of Jánossy’s group paper of 1954 year “Coincidences of photons traveling in coherent beams of light” (Sect. 18.2). Starting with cosmic rays research and the study of statistics of coincidences...

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 di...

The reflection and transmission of a few-cycle laser pulse impinging on two parallel thin metal layers have been analyzed. The two layers, with a thickness much smaller than the skin depth of the incoming radiation field, are represented by current sheets embedded in three dielectrics, all with different index of refraction. The dynamics of the sur...

This work presents an analytic angular differential cross section formula for the electromagnetic radiation field-assisted electron scattering on impurities in semiconductors. These impurities are approximated with various model potentials. The scattered electrons are described with the well-known Volkov wave function, which has been used to descri...

Electrodynamical processes induced in complex systems like semiconductors by strong electromagnetic fields, have traditionally/conventionally been described using semi-classical approaches. Although these approaches, allowed the investigation of ultrafast dynamics in solids culminating in multi-petahertz electronics, they do not provide any access...

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 co...

Electron scattering and conduction on various types of impurities in semiconductor can be calculated via the first order Born approximation when the electrons are considered as free particles described by plane waves. In the following we present analytic angular differential cross section formula for electromagnetic radiation field assisted electro...

Surface plasmon polaritons (SPPs) have several unique properties, including their strong-field enhancing effect in near field. This means, among other things, that nonlinear phenomena may be studied at much lower laser intensities. The present paper describes in detail the theory of basic properties of SPPs, and our model of a laser-induced oscilla...

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...

Surface plasmon polaritons (SPPs) have several unique properties, including their strong-field enhancing effect in near field. This means, among other things, that nonlinear phenomena may be studied at much lower laser intensities. The present paper describes in detail the theory of basic properties of SPPs, and our model of a laser-induced oscilla...

We investigate nonlinear Thomson scattering as a source of high-order harmonic radiation with the potential to enable attosecond light pulse generation. We present a new analytic solution of the electron’s relativistic equations of motion in the case of a short laser pulse with a sine-squared envelope. Based on the single electron emission, we comp...

We investigate the scattering of electrons on a hard sphere in the presence of a laser field of arbitrary intensity. We use spherical Gordon–Volkov states, and we present a novel method for the computation of a key quantity in this theory. We compute and analyze some additional results regarding the total differential scattering cross sections in t...

Supplementing our STM and electron emission studies, concluding in electron pairing in strong laser fields, further time-of-flight electron emission studies were carried out, changing the angle of polarization of incident light, exciting surface plasmon oscillations. It has been found, that those parts of the electron spectrum which have been attri...

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...

We present the general theory for proton nuclei scattering in a bichromatic laser field. As a physical example we consider proton collision on carbon twelve at 49 MeV/amu moderate energies in the field of a titan sapphire laser with its second harmonic.

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....

A new solution is proposed to the long-standing problem of describing the quantum phase of a harmonic oscillator. In terms of an'exponential phase operator', defined by a new 'polar decomposition' of the quantized amplitude of the oscillator, a regular phase operator is constructed in the Hilbert-Fock space as a strongly convergent power series. It...

The recent development of laser technology and the large number of extreme laser experiments under construction renewed the research related to pair production in strong fields. If the predicted threshold of nonlinear QED is reached, pair production may be observed and the measurements must be compared with appropriate theoretical predictions. Howe...

In this contribution we present results on pair production from vacuum in QED in case of inhomogeneous external electric fields. The central tool of our description is the relativistic one particle single-time Wigner-function, that describes the evolution of the e+e- densities in phase-space. We compare the influence of homogeneous and inhomogeneou...

We present a non-relativistic analytic quantum mechanical model to calculate angular differential cross-sections for laser-assisted proton nucleon scattering on a Woods–Saxon optical potential where the n th-order photon absorption is taken into account simultaneously. With this novel description we can integrate two well-established fields, namely...

The basis of low-temperature superconductivity has been set to be the pair formation of electrons, due to their effective attraction. The appearance of an effective attraction potential has also been predicted for electron-electron scattering in the presence of a strong, inhomogeneous radiation field. In the present work the strong electromagnetic...

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 th...

The relativistic wave equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave, in a medium of index of refraction n_m < 1, have been studied. In the Dirac case the found exact solutions [arXiv:1305.4370] are expressed in terms of new complex polynomials, and in the Klein-Gordon case they are expressed in...

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The...

The key element in the Proton-Driven-Plasma-Wake-Field-Accelerator (AWAKE) project is the generation of highly uniform plasma from Rubidium vapor. The standard way to achieve full ionization is to use high power laser which can assure the over-barrier-ionization (OBI) along the 10 meters long active region. The Wigner-team in Budapest is investigat...

Exact solutions are presented of the Klein-Gordon equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The solutions are expressed in terms of Ince polynomials, which form a doubly infinite set labeled by two integer quantum numbers. These integer numbers represent q...

Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n < 1. The found solutions are expressed in terms of new complex trigonometric polynomials, which form a doubly infinite set labeled by two integer quantum numbers. These quantum...

A high spatial resolution surface plasmon near field scanning tunneling microscope (STM) has been used to study the properties of localized surface plasmons (SPO) in so-called hot spots on a gold surface, where the local electromagnetic field is extremely high. A CW semiconductor laser and a femtosecond Ti:Sa laser were used to excite the plasmons...

Theoretical results are reported, concerning the reflection and transmission of few-cycle laser pulses on a very thin conducting layer, which may represent the surface current density of the massless charges of graphene. It is shown that the pulse may undergo violent distortions, even at moderate intensities, to that extent, that the scattered radi...

Nonlinear electron emission processes induced by surface plasmon oscillations have been studied both experimentally and theoretically. The measured above-threshold electron spectra extend up to energies whose appearance cannot be explained solely by standard non-perturbative methods, which predict photon energy separated discrete energy line spectr...

The statistical properties of the fractional part of the random energy of a spectral component of black-body radiation have been analysed in the frame of classical Kolmogorovian probability theory. Besides the integer part of the energy (which satisfies the well-known Planck-Bose distribution), the realizations of its fractional part (related to 'r...

Intensity-intensity correlations are studied for light signals stemming from the spontaneous decay of surface plasmon oscillations, generated in the Kretschmann geometry. Non-classical photon statistics and the the transition from antibunching to bunching of the electron counts have been found experimentally and analysed on a new theoretical basis.

In the present paper we report on our theoretical results concerning the reflection and transmission of a few-cycle laser pulse on a very thin conducting layer, which is ment to represent the surface current density of the massless relativistic electrons and holes of graphene. We show that the pulses may undergo violent phase-dependent distortions...

Intensity–intensity correlations are studied for light signals stemming from the spontaneous decay of surface plasmon oscillations, generated in the Kretschmann geometry. Non-classical photon statistics and the transition from antibunching to bunching of the electron counts have been found experimentally and analysed on a new theoretical basis.

Correlations of detection events in two detectors are studied in case of linear excitation of the measuring apparatus. On the basis of classical probability theory and fundamental conservation laws, a general formula is derived for the two-point correlation functions for both bosons and fermions. The results obtained coincide with that derivable fr...

We derive a new integral equation for the nonperturbative evaluation of transition matrix elements of multiphoton processes at high laser field intensities. Our approach to the problem is partly based on the use of the Kramers–Henneberger transformation. As a specific example, we apply our method to the generation of harmonics by an electron in a s...

Exact solutions are given for the Maxwell equations driven by a gyrating ultrarelativistic electron inside a reflecting cylindrical boundary. The axis of the electrons's trajectory and the axis of the surrounding cylinder are supposed to coincide. It is found that, at certain values of the ratio of the cylinder's and of the trajectory's radii, the...

In the present paper, an example of entanglement between two different kinds of interacting particles, photons and electrons is analysed. The initial-value problem of the Schrödinger equation is solved non-perturbatively for the system of a free electron interacting with a quantized mode of electromagnetic radiation. Wave packets of the dressed sta...

The familiar wave function for a free particle in two dimensions and in a state with definite values of energy and angular momentum shows some unusual effects. We identify the origin of these subtleties as interference in two-dimensional space where Huygens’ principle breaks down. Our arguments are based upon the corresponding Wigner function.

The spontaneous emission of radiation of metallic electrons embedded in a high-intensity enhanced surface plasmon field is considered analytically. The electrons are described by exact dressed quantum states which contain the interaction with the plasmon field non-perturbatively. Considerable deviations from the pertubative behaviour have been foun...

Evanescent fields of surface plasmon polaritons (SPP) above metal surfaces can reach 1-2 orders of magnitude higher, nearly atomic field strengths in comparison to the relatively weak exciting laser fields of a femtosecond Ti:sapphire laser oscillator. We used these high plasmonic fields to study the characteristic SPP phenomena of intense field op...

Theoretical and experimental results on laser light-excited nonlinear surface plasmon (SPO) phenomena are reported. Strongly directional light emission of SPOs was indicated and observed already at relatively low cw laser power. The width of this peaked directional distribution seems to depend on the laser power. Another manifestation of nonlineari...

The exact analytic solutions of the energy eigenvalue equation of the system consisting of a free electron and one mode of the quantized radiation field are used for studying the physical meaning of a class of number-phase minimum uncertainty states. The states of the mode which minimize the uncertainty product of the photon number and the Suskind...

Correlations of detection events in photodetectors placed at the opposite sides of a beam splitter are studied in the frame of classical probability theory. It is assumed that there is always one photon present during one elementary measurement (one measurement act). Due to the conservation of energy, thereis a strict anticorrelation in detections...

Experimental and theoretical studies of the statistical properties of surface plasmon polaritons (SPOs) are described. Both classical and non-classical properties of surface plasmons are analysed. The temporal statistical behaviour at low excitation level, as measured by detecting the SPO emitted photon statistics as expressed by the correlation fu...

We consider Wigner functions in two space dimensions. In particular, we focus on Wigner functions corresponding to energy eigenstates of a non-relativistic particle moving in two dimensions in the absence of a potential. With the help of the Weyl–Wigner correspondence we first transform the eigenvalue equations for energy and angular momentum into...

It has been shown that in the scattered radiation, generated by an ultrashort laser pulse impinging on a metal nano-layer, non-oscillatory wakefields appears with a definite sign. The magnitude of these wakefields is proportional to the incoming field strength, and the definite sign of them is governed by the cosine of the carrier-envelope phase di...

It is shown that the the interference of above-threshold electron de Broglie waves, generated by an intense laser pulse at a metal surface yields attosecond electron pulses. This inerference is an analogon of the superposition of high harmonics generated from rare gas atoms, resulting in trains of attosecond light pulses.Owing to the inherent kinem...

We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius—that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables: the absolute value of the D-dimensional position and momentum...

The reflection and transmission of a few-cycle femtosecond Ti:Sa laser pulse impinging on a thin plasma layer have been analysed on the basis of classical electrodynamics. The plasma electrons were represented by a surface current density along the layer. An approximate analytic solution has been given for the system of the coupled Maxwell-Lorentz...

The reflection and transmission of a few-cycle femtosecond Ti:Sa laser pulse impinging on a metal nano-layer have been analyzed. The thickness of the layer was assumed to be of the order of 2 – 10 nm, and the metallic free electrons were represented by a surface current density at the plane boundary of a dielectric substrate. The target studied thi...

A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications (from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up...

The present study gives a detailed analysis of the black-body radiation based on classical random variables. It is shown that the energy of a mode of a chaotic radiation field (Gauss variable) can be uniquely decomposed into a sum of a discrete variable (Planck variable having the Planck-Bose distribution) and a continuous dark variable (with a tru...

It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The integer part is a discrete random variable (we call it Planck variable) whose distribution is just the Bose di...

On the basis of classical electrodynamics the reflection and transmission of a few-cycle femtosecond Ti:Sa laser pulse impinging on a thin metal layer have been analysed. The thickness of the layer was assumed to be much smaller than the skin depth of the radiation field, and the metallic electrons were represented by a surface current density. The...

On the basis of the Hamiltonian form of the Klein-Gordon equation of a charged scalar particle field introduced by Feshbach and Villars, the gaugeinvariant 2×2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and the off-diagonal elements correspond to cross-densities in phase-space. The sys...

For some time now anomalous transparency induced by high intensity laser light interacting with thin solid foils has been found experimentally [1] and several theoretical models have been suggested to explain this phenomena [2, 3]. In our present study based mostly on classical electrodynamics the increase of the transmittivity is the consequence o...

On the basis of the Hamiltonian form of the Klein-Gordon equation for a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2 x 2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and whose off-diagonal elements correspond to cross-densities in phase space. T...

On the basis of the Hamiltonian form of the Klein-Gordon equation of a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2×2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and the off-diagonal elements correspond to cross-densities in phase-space. The sy...

We report on many-particle simulations of the quantum electron gas in thin metal films, irradiated with intense femtosecond laser pulses at grazing incidence. A gradual population of electron states is predicted, where subsequent steps of occupation probabilities are separated by the incident photon energy &plank;omega0. During the laser interactio...

A detailed study of the electromagnetic field's configuration inside plasmas generated on solid surfaces by ultrashort laser pulses is given in the present work. The radiation due to the nonrelativistic motion of the electrons in the overdense region is considered the main source of high harmonics, whose polarization dependence on the fundamental b...

Recent experiments have shown that second and third harmonics generated in laser plasmas on solid surfaces preserve the polarization of the incoming laser beam. This contradicts to most theories according to that the polarization of even harmonics should be p-polarized for p- and s-polarized laser beams as well. In the present work a theoretical mo...