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Lucjan Jacak

Publications and source records attributed to Lucjan Jacak.

17 recordsLinked to original sources
arXiv2020

Effective information processing with pure braid group formalism in view of 2D holographic principle for information

The so-called holographic principle, originally addressed to the high energy physics, suggests more generally that the information inseparatly bounded with a physical carrier (measured by its entropy) scales as the event horizon surface---a two-dimensional object. In this paper we present an idea of representing classical information in formalism of pure braid groups, characterized by an exceptionally rich structure for two-dimensional spaces. This leads to some interesting properties, e.g. information geometrization, multi-character alphabets energetic efficiency for information coding characteristic or a group structure decoding scheme. We also proved that proposed pure braid group approach meets all the conditions for storing and processing of information.

math.GM↗
arXiv2015

Hierarchy of fillings for FQHE in monolayer and in bilayer graphene: Explanation of $ν=-\frac{1}{2}$ fractional quantum Hall state in bilayer graphene

The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and bilayer graphene. The filling rates for FQHE in graphene are found and illustrated in the first three Landau levels. The good agreement with the experimental data is achieved. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained.

physics.gen-ph↗
arXiv2014

Explanation of fractional hierarchy observed experimentally in higher Landau levels

The puzzle of an odd structure of fractional fillings for FQHE in higher Landau levels not repeating the hierarchy from the lowest Landau level is solved. The fractional filling rates for correlated states in higher Landau levels including spin subbands are systematically derived for the first time. Using topology-type commensurability arguments the hierarchy in higher Landau level fillings is determined in perfect agreement with the experimental observations. The relative paucity of fractional structure in higher Landau levels is explained and the criterion for pairing in states at half fillings and for other even-denominator rates of consecutive Landau levels is formulated.

physics.gen-ph↗
arXiv2014

Explanation of the odd structure of fractional Hall states in higher Landau levels and filling ratios with even denominators

The structure of fractional fillings of higher Landau levels including spin subbands is systematically derived for the first time. Using topology-type commensurability arguments for 2D charged system in the presence of strong quantizing magnetic field, a hierarchy of fillings in the higher Landau levels for FQHE and for other correlated states is determined in perfect agreement with the experimental observations. The relative paucity of fractional structure in the higher Landau levels in contrast to the plethora of filling factors for FQHE in the zeroth Landau level is explained. The filling fractions with even denominators in consecutive LLs were also identified together with the criterion for particle pairing.

physics.gen-ph↗
arXiv2012

Confirmation in graphene of wave packet multilooped dynamics related to fractional quantum Hall state

Cyclotron braid subgroups are defined in order to identify the topological origin of Laughlin correlations in 2D Hall systems. Flux-tubes and vortices for composite fermion constructions are explained in terms of unavoidably multilooped cyclotron braids. A link of braid picture with quasiclassical quantum dynamics is conjectured in order to support the phenomenological model of composite fermions with auxiliary fluxtubes, for Landau level fillings out of 1/p, p odd. The even denominator fractional lowest Landau level fillings, including Hall metal at n = 1/2, are also discussed in cyclotron braid terms. The topological arguments are utilized to explain novel experimentally observed features of the fractional quantum Hall state in graphene including the triggering role of carriers mobility for this collective state.

cond-mat.mes-hall↗
arXiv2012

The triggering role of carrier mobility in the fractional quantum Hall effect-evidence in graphene

Recent experiments on suspended graphene layers have indicated the crucial role of carrier mobility in the competition between Laughlin collective state and insulating state, probably of Wigner-crystal-type. Moreover, the fractional quantum Hall effect (FQHE) in graphene has been observed at a low carrier density where the interaction is reduced as a result of particles dilution. This suggests that the interaction may not be as important in the triggering of FQHE as expected based on the standard formulation of the composite fermions model. Here, the topological arguments are presented to explain these novel features of the FQHE in graphene and, the triggering role of carriers mobility in particular.

cond-mat.mes-hall↗
arXiv2011

On two-dimensional exciton bound by distant ionized-donor in a narrow quantum well

The ground state energy of exciton bound by distant ionized donor impurity in two-dimensional semiconductor quantum well (QW) is studied theoretically within the Hartree approach in the effective mass approximation. The influence of the distance between QW plane and ionized donor, as well as of the electron-hole mass ratio, the magnetic field aligned across the QW plane and dielectric constant of the barrier material on the stability of exciton bound by ionized donor impurity is analyzed and discussed.

cond-mat.mes-hall↗
arXiv2011

Exciton bound by distant ionized donor in two-dimensional GaAs/AlGaAs quantum well

The ground state energy of exciton bound by distant ionized donor impurity in quasi-two-dimensional GaAs/AlGaAs semiconductor quantum well (QW) is studied theoretically within the Hartree approach in the effective mass approximation. The influence of the distance between QW plane and ionized donor, as well as of the magnetic field aligned across the QW plane and varying dielectric constant of the barrier material on the stability of exciton bound by ionized donor impurity is analyzed and discussed.

cond-mat.mes-hall↗
arXiv2005

Exciton-LO-phonon dynamics in InAs/GaAs quantum dots: Effects of zone-edge phonon damping

The dynamics of an exciton-LO-phonon system after an ultrafast optical excitation in an InAs/GaAs quantum dot is studied theoretically. Influence of anharmonic phonon damping and its interplay with the phonon dispersion is analyzed. The signatures of the zone-edge decay process in the absorption spectrum and time evolution are highlighted, providing a possible way of experimental investigation on phonon anharmonicity effects.

cond-mat.mes-hall↗
arXiv2005

Optimal strategy for a single-qubit gate and trade-off between opposite types of decoherence

We study reliable quantum information processing (QIP) under two different types of environment. First type is Markovian exponential decay, and the appropriate elementary strategy of protection of qubit is to apply fast gates. The second one is strongly non-Markovian and occurs solely during operations on the qubit. The best strategy is then to work with slow gates. If the two types are both present, one has to optimize the speed of gate. We show that such a trade-off is present for a single-qubit operation in a semiconductor quantum dot implementation of QIP, where recombination of exciton (qubit) is Markovian, while phonon dressing gives rise to the non-Markovian contribution.

quant-ph↗
arXiv2004

Resonant nature of phonon-induced damping of Rabi oscillations in quantum dots

Optically controlled coherent dynamics of charge (excitonic) degrees of freedom in a semiconductor quantum dot under the influence of lattice dynamics (phonons) is discussed theoretically. We show that the dynamics of the lattice response in the strongly non-linear regime is governed by a semiclassical resonance between the phonon modes and the optically driven dynamics. We stress on the importance of the stability of intermediate states for the truly coherent control.

cond-mat.mes-hall↗
arXiv2004

Phonon impact on the coherent control of quantum states in semiconductor quantum dots

This chapter is devoted to the recent theoretical results on the optical quantum control over charges confined in quantum dots under influence of phonons. We show that lattice relaxation processes lead to decoherence of the confined carrier states. The theoretical approach leading to a uniform, compact description of the phonon impact on carrier dynamics, perturbative in phonon couplings but applicable to arbitrary unperturbed evolution, is described in detail. Next, some applications are presented: phonon damping of Rabi oscillations in quantum dots and phonon-induced error of a single-qubit gate for an excitonic quantum dot qubit as well as for a semiconductor quantum dot spin qubit operated via a STIRAP transfer.

cond-mat.mes-hall↗
arXiv2004

Damping of Rabi oscillations in quantum dots due to lattice dynamics

We show that the interaction between carriers confined in a quantum dot and the surrounding lattice under external driving of carrier dynamics has a dynamical, resonant character. The quality of Rabi oscillations in such a system depends on the relation between nonlinear spectral characteristics of the driven dynamics and the spectral density of effectively coupled lattice modes (phonon frequencies and density of states). For a large number of Rabi oscillations within a fixed time (allowed by e.g. exciton recombination) the spectrum of the dynamics extends towards high frequencies, coming into resonance with acoustical and optical phonons. Thus, this resonant lattice response strongly restricts the possibility of fully coherent control over the charge state in a quantum dot.

cond-mat.mes-hall↗
arXiv2003

Quantum Hall Systems: Braid groups, composite fermions, and fractional charge

The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding braid group formalism. The braid group formalism of anyons (previously known) is developed for composite fermions. The main formalism used in many-body quantum Hall theories -- the Chern-Simons theory is also presented. The Chern-Simons theory of anyons (particles obeying fractional statistics) and composite fermions (related to Hall systems) is given, in detail. Numerical studies, which play the important role in quantum Hall theories, are presented for spherical systems (Haldane sphere). The composite fermion theory is tested in numerical studies. The concept of the hierarchy of condensed states of composite fermion excitations is introduced (in analogy to the Haldane hierarchy)1). The hierarchies of odd-denominator states and even-denominator states are presented. The BCS paired Hall state is also discussed. The introduction into multi-component quantum Hall systems and spin quantum Hall systems is sketched. 1)First condensed states of composite fermion excitations have been very recently confirmed in the experiment (Pan et al. Phys. Rev. Lett. 90 (2003) 016801). a sample of this book is available at http://www.oup.co.uk/isbn/0-19-852870-1

cond-mat.mes-hall↗
arXiv2003

Justification for the composite fermion picture

The mean field (MF) composite Fermion (CF) picture successfully predicts the low-lying bands of states of fractional quantum Hall systems. This success cannot be attributed to the originally proposed cancellation between Coulomb and Chern--Simons interactions beyond the mean field and solely depends on the short range of the repulsive Coulomb pseudopotential in the lowest Landau level (LL). The class of pseudopotentials is defined for which the MFCF picture can be applied. The success or failure of the MFCF picture in various systems (electrons in the lowest and excited LL's, Laughlin quasiparticles) is explained.

cond-mat.mes-hall↗
arXiv2001

Mechanical effects in quantum dots in magnetic and electric fields

The mechanical effects in finite two-dimensional electron systems (quantum dots or droplets) in a strong perpendicular magnetic field are studied. It is shown that, due to asymmetry of the cyclotron dynamics, an additional in-plane electric field causes a ground state transition accompanied by a change in the average total angular momentum of the system, unless the lateral confining potential is exactly parabolic. A precise mechanical experiment is proposed in which a macroscopic angular momentum of a dense matrix of quantum dots could be measured and used to detect and estimate anharmonicity of the confinement.

cond-mat.mes-hall↗