Egidijus Anisimovas

High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective

We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the extended Floquet Hilbert space by means of degenerate perturbation theory. The final results are equivalent to those obtained within a different approach [Phys.\ Rev.\ A {\bf 68}, 013820 (2003), Phys.\ Rev.\ X {\bf 4}, 031027 (2014)] and can also be related to the Floquet-Magnus expansion [J.\ Phys.\ A {\bf 34}, 3379 (2000)]. We discuss that the dependence on the driving phase, which plagues the latter, can lead to artifactual symmetry breaking. The high-frequency approach is illustrated using the example of a periodically driven Hubbard model. Moreover, we discuss the nature of the approximation and its limitations for systems of many interacting particles.

Measuring topology in a laser-coupled honeycomb lattice: from Chern insulators to topological semi-metals

Ultracold fermions trapped in a honeycomb optical lattice constitute a versatile setup to experimentally realize the Haldane model (1988 Phys. Rev. Lett. 61 2015). In this system, a non-uniform synthetic magnetic flux can be engineered through laser-induced methods, explicitly breaking time-reversal symmetry. This potentially opens a bulk gap in the energy spectrum, which is associated with a non-trivial topological order, i.e. a non-zero Chern number. In this paper, we consider the possibility of producing and identifying such a robust Chern insulator in the laser-coupled honeycomb lattice. We explore a large parameter space spanned by experimentally controllable parameters and obtain a variety of phase diagrams, clearly identifying the accessible topologically non-trivial regimes. We discuss the signatures of Chern insulators in cold-atom systems, considering available detection methods. We also highlight the existence of topological semi-metals in this system, which are gapless phases characterized by non-zero winding numbers, not present in Haldanes original model.

Energy spectra of few-electron quantum dots

We present the renormalized perturbation series for the energy spectra of parabolic quantum dots with two to five electrons, taking into consideration the ground and the lowest excited states. A complete classification of asymptotic energy levels is performed and the behaviour of energy levels from the quantum to the semiclassical regime is traced. Comparison between the present results and those from exact numerical Hamiltonian diagonalization indicates a fair accuracy of the proposed method over the whole range of the electron-electron coupling constant and magnetic field values. The results obtained indicate that increasing the number of electrons in a dot leads to more classical behaviour of the system.

Role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators

Fractional Chern insulators are the proposed phases of matter mimicking the physics of fractional quantum Hall states on a lattice without an overall magnetic field. The notion of Floquet fractional Chern insulators refers to the potential possibilities to generate the underlying topological bandstructure by means of Floquet engineering. In these schemes, a highly controllable and strongly interacting system is periodically driven by an external force at a frequency such that double tunneling events during one forcing period become important and contribute to shaping the required effective energy bands. We show that in the described circumstances it is necessary to take into account also third order processes combining two tunneling events with interactions. Referring to the obtained contributions as micromotion-induced interactions, we find that those interactions tend to have a negative impact on the stability of of fractional Chern insulating phases and discuss implications for future experiments.

Power-law dependence of the angular momentum transition fields in few-electron quantum dots

(Dated: 15 February 2004)We show that the critical magnetic fields at which a few-electron quantum dot undergoes tran-sitions between successive values of its angular momentum (M), for large M values follow a verysimple power-law dependence on the effective inter-electron interaction strength. We obtain thispower law analytically from a quasi-classical treatment and demonstrate its nearly-universal valid-ity by comparison with the results of exact diagonalization.

Accuracy of the Hartree-Fock method for Wigner molecules at high magnetic fields

Abstract.Few-electron systems confined in two-dimensional parabolic quantum dots at high magnetic fields are studied by the Hartree-Fock (HF) and exact diagonalization methods. A generalized multicenter Gaussian basis is proposed in the HF method. A comparison of the HF and exact results allows us to discuss the relevance of the symmetry of the charge density distribution for the accuracy of the HF method. It is shown that the energy estimates obtained with the broken-symmetry HF wave functions become exact in the infinite magnetic-field limit. In this limit the charge density of the broken-symmetry solution can be identified with the classical charge distribution.

Correlation between electrons and vortices in quantum dots

Exact many-body wave functions for quantum dots containing up to four interacting electrons are computed and we investigated the distribution of the wave function nodes, also called vortices. For this purpose, we evaluate the reduced wave function by fixing the positions of all but one electron and determine the locations of its zeros. We find that the zeros are strongly correlated with respect to each other and with respect to the position of the electrons and formulate rules describing their distribution. No multiple zeros are found, i.e. vortices with vorticity larger than one. Our exact calculations are compared to results extracted from the recently proposed rotating electron molecule (REM) wave functions.

Correlated few-particle states in artificial bipolar molecule

We investigate the ground and excited states of a bipolar artificial molecule composed of two vertically coupled quantum dots containing different type of carriers- electrons and holes-in equilibrium. The approach based on exact diagonalization is used and reveals an intricate pattern of ground-state angular momentum switching and a rearrangement of approximate single-particle levels as a function of the interdot coupling strength.

Configurational entropy of Wigner clusters

We present a theoretical study of classical Wigner clusters in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable configurations. Strongly interacting systems of classical charged particles confined in traps are known to form regular structures. The number of distinct arrangements grows very rapidly with the number of particles; many of these arrangements have quite low occurrence probabilities and often the lowest-energy structure is not the most probable one. We perform numerical simulations on systems containing up to 100 particles interacting through Coulomb or Yukawa forces, and show that the total number of metastable configurations is not a well-defined and representative quantity. Instead, we propose to rely on the configurational entropy as a robust and objective measure of uncertainty. The configurational entropy can be understood as the logarithm of the effective number of states; it is insensitive to the presence of overlooked low-probability states and can be reliably determined even within the limited time of a simulation or an experiment.

Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields

Department of Theoretical Physics, University of Lund, S¨olvegatan 14 A, S-223 62 Lund, Sweden(June 24, 2011)We calculate the energy band structure for electrons in an external periodic potential combinedwith a perpendicular magnetic field. Electron-electron interactions are included within a Hartreeapproximation. The calculated energy spectra display a considerable degree of self-similarity, justas the “Hofstadter butterfly.” However, screening affects the butterfly, most importantly the band-widths oscillate with magnetic field in a characteristic way. We also investigate the dynamic responseof the electron system in the far-infrared (FIR) regime. Some of the peaks in the FIR absorptionspectra can be interpreted mainly in semiclassical terms, while others originate from inter(sub)bandtransitions.73.20.Dx, 73.20.Mf