arXiv subjects

Sandor Varro

Publications and source records attributed to Sandor Varro.

At least 19 recordsLinked to original sources

arXiv2021

Coherent and incoherent superposition of transition matrix elements of the squeezing operator

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 oscillators. They expressed the matrix elements in terms of transcendental functions, the associated Legendre functions. In the present paper we will show that these matrix elements can also be expressed by the classical Gegenbauer polynomials. This new expression makes it possible to determine coherent and incoherent superpositions of these matrix elements in closed analytic forms. As an application, we describe multiphoton transitions in the system "charged particle + electromagnetic radiation", induced by a (strong) coherent field or by a black-body radiation component (with a Planck-Bose photon number distribution). The exact results are compared with the semi-classical ones. We will show that in case of interaction with a thermal field, the semi-classical result (with a Gaussian stochastic field amplitude) yields an acceptable approximation only in the Rayleigh-Jeans limit, however, in the Wien limit it completely fails.

quant-ph↗

arXiv2014

Regular phase operator and SU(1,1) coherent states of the harmonic oscillator

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 is shown that the eigenstates of the new 'exponential operators are SU(1,1) coherent states in the Holstein-Primakoff realization. In terms of these eigenstates, the diagonal representation of phase densities and a generalized spectal resolution of the regular phase operator are derived, which suit very well to our intuitive pictures on classical phase-related quantities

quant-ph↗

arXiv2013

Surface plasmon assisted electron pair formation in strong electromagnetic field

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 fields were created by femtosecond Ti:Sa lasers, used to excite surface plasmons in gold films at room temperature, in the Kretschmann geometry. Experimental investigations were carried out using a surface plasmon near-field scanning tunneling microscope, by measuring its response to the excitation at hot spots on the gold surface. Furthermore, the spectra of photoelectrons, liberated by multi-plasmon absorption, have also been measured by a time-of-flight spectrometer. In both cases new type of anomalies in the electon signal have been measured in the same intensity range, whose existence may be qualitatively understood, by using the intensity-dependent expression for the effective electon-electron scattering potential, derived earlier in a different context.

cond-mat.mes-hall↗

arXiv2013

A comparison of the new exact solutions of the relativistic wave equations of a charged particle propagating in a strong laser field in an underdense plasma

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 term of Ince polynomials [arXiv:1306.0097]. In each case these solutions form a doubly infinite discrete set, parametrized by quantized momentum components of the charged particle along the polarization vector and along the propagation direction of the electromagnetic radiation (which may be considered as a plasmon wave of arbitrary high amplitude, propagating in an underdense plasma). These solutions describe a high-contrast periodic structure of the particle density on the plasma length scale, and they may have relevance in the study of novel acceleration mechanisms.

quant-ph↗

arXiv2013

A new class of exact solutions of the Klein-Gordon equation of a charged particle interacting with an electromagnetic plane wave in a medium

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 quantized spectra of the momentum components of the charged particle along the polarization vector and along the propagation direction of the applied electromagnetic plane wave field. Since this field may represent a laser radiation of arbitrary high intensity propagating in an underdense plasma, the solutions obtained may have relevance, for instance, in describing possible quantum features of laser acceleration of electrons.

quant-ph↗

arXiv2013

New exact solutions of the Dirac equation of a charged particle interacting with an electromagnetic plane wave in a medium

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 numbers represent quantized spectra of the energy-momentum components of the charged particle along the polarization vector and along the propagation direction of the applied electromagnetic plane wave field (which is considered as a laser field of arbitrary high intensity, propagating in an underdense plasma). These new solutions may serve as a basis for the description of possible quantum features of mechanisms of acceleration of electrons by high-intensity laser fields.

quant-ph↗

arXiv2013

Hysteresis phenomena in electron tunneling, induced by surface plasmons

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 and the SPO excited tunnel current was used as the detector. When scanning the STM from negative to positive bias and reversed, hysteresis in the tunnel signal was found, excluding (or rather minimizing) the role of the presence of a Casimir effect in the process. It was found, however, that a multiple image charge induced double well potential may explain our experimental findings. The stepwise behaviour of the area of the observed hysteresis loops is a new, additional indication of the non-classical properties of the SPOs.

physics.optics↗

arXiv2013

Generation of rectangular optical waves by relativistic clipping

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 radiation contains rectangular trains, which are approximate realizations of Rademacher functions in the optical or terahertz regime.

physics.optics↗

arXiv2013

Nonlinear photoemission from metal surfaces induced by short laser pulses: the effect of field enhancement by surface plasmons

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 spectra with the known fast fall - plateau - cutoff envelope shape, even when taking the large field enhancement into account. The theoretical analysis of our data, based on the concept of plasmon-induced near-field effects, gives reasonably good explanation and qualitative agreement in the whole intensity range.

physics.optics↗

arXiv2013

Hanbury Brown - Twiss type correlations with surface plasmon light

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.

quant-ph↗

arXiv2013

The digital randomness of black-body radiation

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 'round-off errors') has been represented by binary sequences, like z = 0.001011000010.... It has been shown that the binary variables realized by the 0-s and 1-s at different positions are independent. From the condition of independence the original distribution of the fractional part z can be recovered. If these binary variables have the same distribution, then they describe a temperature-independent random energy, whose expectation value is just the zero-point energy. Thus, the zero-point fluctuation can be considered as a physical representative of an ideal random number generator.

quant-ph↗

arXiv2011

Synchrotron radiation in the presence of a cylindrical mirror. Note on the interference of the direct radiation and the high-order whispering-gallery modes

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 field amplitudes diverge as functions of time. The physical reason for this resonance is the constructive interference between the radiation emitted earlier and fed back by reflection to the actual position of the radiating electron.

physics.acc-ph↗

arXiv2010

The role of self-coherence in correlations of bosons and fermions in linear counting experiments. Notes on the wave-particle duality

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 from quantum theory which uses quantized field amplitudes. By applying both the particle and the wave picture at the same time, the phenomena of photon bunching and antibunching, photon anticorrelation and fermion antibunching, measured in beam experiments, are interpreted in the frame of an intuitively clear description.

quant-ph↗

arXiv2009

Spontaneous emission of radiation by metallic electrons in the presence of electromagnetic fields of surface plasmon oscillations

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 found in the intensity dependence of the emitted fundamental and the second harmonic signals, even at moderate incoming laser intensities. The theoretical predictions deduced from the formalism are in good qualitative agreement with the experimental results.

physics.optics↗

arXiv2009

Entangled States and Entropy Remnants of a Photon-Electron System

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 Schroedinger equation is solved non-perturbatively for the system of a free electron interacting with a quantized mode of the electromagnetic radiation. Wave packets of the dressed states so obtained are constructed in order to describe the spatio-temporal separation of the subsystems before and after the interaction. The joint probability amplitudes are calculated for the detection of the electron at some space-time location and the detection of a definite number of photons. The analytical study of the time evolution of entanglement between the initially separated electron wave packet and the radiation mode leads to the conclusion that in general there are non-vanishing entropy remnants in the subsystems after the interaction. On the basis of the simple model to be presented here, the calculated values of the entropy remnants crucially depend on the character of the switching-on and off of the interaction.

quant-ph↗

arXiv2008

Entangled Photon-Electron States and the Number-Phase Minimum Uncertainty States of the Photon Field

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 Susskind and Glogower (1964) cosine operator have been obtained by Jackiw (1968). However, these states have so far been remained mere mathematical constructions without any physical significance. It is proved that the most fundamental interaction in quantum electrodynamics - namely the interaction of a free electron with a mode of the quantized radiation field - leads quite naturally to the generation of the mentioned minimum uncertainty states. It is shown that from the entangled photon-electron states developing from a highly excited number state, due to the interaction with a Gaussian electronic wave packet, the minimum uncertainty states of Jackiw's type can be constructed. In the electron's coordinate representation the physical meaning of the expansion coefficients of these states are the joint probability amplitudes of simultaneous detection of an electron and of a definite number of photons. The joint occupation probabilities in these states preserve their functional form as time elapses, but they vary from point to point in space-time, depending on the location of the detected electron. An analysis of the entanglement entropies derived from the photon number distribution and from the electron's density operator is given.

quant-ph↗

arXiv2007

Correlation in single-photon experiments

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 in one elementary experiment, because the photon cannot excite both of the detectors at the same time. It is explicitely shown in several examples that the bunching or anti-bunching of the counts in serieses of elementary single-photon experiments are governed by the statistical properties of grouping the sequences of the elementary measurements.

quant-ph↗

arXiv2007

Attosecond electron pulses from interference of above-threshold de Broglie waves

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 kinematic dispersion, the propagation of attosecond de Broglie waves in vacuum is very different from that of attosecond light pulses, which propagate without changing shape. Above the metal surface there are "collaps bands" and "revival layers" of the electron current even at macroscopic distances. In the range of parameters considered, the maximum value of the current densities of such ultrashort electron pulses has been estimated to be of order of couple of tenths of milliamps per square centimeters.

physics.plasm-ph↗