arXiv subjects

T. P. Polak

Publications and source records attributed to T. P. Polak.

15 recordsLinked to original sources

arXiv2021

Coexistence of two kinds of superfluidity in Bose-Hubbard model with density-induced tunneling at finite temperatures

With use of the U(1) quantum rotor method in the path integral effective action formulation, we have confirmed the mathematical similarity of the phase Hamiltonian and of the extended Bose-Hubbard model with density-induced tunneling (DIT). Moreover, we have shown that the latter model can be mapped to a pseudospin Hamiltonian that exhibits two coexisting (single-particle and pair) superfluid phases. Phase separation of the two has also been confirmed, determining that there exists a range of coefficients in which only pair condensation, and not single-particle superfluidity, is present. The DIT part supports the coherence in the system at high densities and low temperatures, but also has dissipative effects independent of the system's thermal properties.

cond-mat.quant-gas↗

arXiv2017

Finite size effects and Hofstadter butterfly in a bosonic Mott insulator with relativistic dispersion background

Gauge potentials with different configurations have been recently realized in the optical lattice experiments. It is remarkable that one of the simplest gauge can generate particle energy spectrum with the self-similar structure known as a Hofstadter butterfly. We investigate theoretically the impact of strong on-site interaction on such a spectrum. In particular, it is shown that the fractal structure is encoded in the quasi-particle and hole bosonic branches. A square lattice and other structures (brick-wall and staggered magnetic flux lattice) with relativistic energy dispersions which are currently accessible in the experiments are considered. Moreover, although in brick-wall and staggered flux lattices the quasi-particle densities of states looks qualitatively similar, the corresponding Hofstadter butterfly assumes different forms. In particular, we use a superposition of two different synthetic gauge fields which appears to be a generator of non-trivial phenomena in the optical lattice systems. The analysis is carried out within the strong coupling expansion method on the finite size lattices and also at finite temperatures which are relevant for the currently made experiments.

cond-mat.quant-gas↗

arXiv2015

Conductivity of strongly correlated bosons in optical lattices in an Abelian synthetic magnetic field

Topological phase engineering of neutral bosons loaded in an optical lattice opens a new window for manipulating of transport phenomena in such systems. Exploiting the Bose Hubbard model and using the magnetic Kubo formula proposed in this paper we show that the optical conductivity abruptly changes for different flux densities in the Mott phase. Especially, when the frequency of the applied field corresponds to the on-site boson interaction energy, we observe insulator or metallic behavior for a given Hofstadter spectrum. We also prove, that for different synthetic magnetic field configurations, the critical conductivity at the tip of the lobe is non-universal and depends on the energy minima of the spectrum. In the case of $1/2$ and $1/3$ flux per plaquette, our results are in good agreement with those of the previous Monte Carlo (MC) study. Moreover, we show that for half magnetic-flux through the cell the critical conductivity suddenly changes in the presence of a superlattice potential with uniaxial periodicity.

cond-mat.quant-gas↗

arXiv2013

Time-of-flight patterns of ultra-cold bosons in optical lattices in various Abelian artificial magnetic field gauges

We calculate the time-of-flight patterns of strongly interacting bosons confined in two-dimensional square lattice in the presence of an artificial magnetic field using quantum rotor model that is inherently combined with the Bogolyubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method let us to study cases of the artificial magnetic field being uniform, staggered or forming a checkerboard configuration. Effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The presented time-of-flight patterns may serve as a verification of chosen gauge in experiments, but also provide important hints on unconventional, non-zero momentum condensates, or possibility of observing graphene-like physics resulting from occurrence of Dirac cones in artificial magnetic fields in systems of ultra-cold bosons in optical lattices. Also, we elucidate on differences between effects of magnetic field in solids and the artificial magnetic field in optical lattices, which can be controlled on much higher level leading to effects not possible in condensed matter physics.

cond-mat.quant-gas↗

arXiv2011

Synthetic magnetic field effects on neutral bosonic condensates in quasi three-dimensional anisotropic layered structures

We discuss a system of dilute Bose gas confined in a layered structure of stacked square lattices (slab geometry). A derived phase diagram reveals a non-monotonic dependence of the ratio of tunneling to on-site repulsion on the artificial magnetic field applied to the system. The effect is reduced when more layers are added, which mimics a two- to quasi-three-dimensional geometry crossover. Furthermore, we establish a correspondence between anisotropic infinite (quasi three-dimensional) and isotropic finite (slab geometry) systems that share exactly the same critical values, which can be an important clue for choosing experimental setups that are less demanding, but still leading to the identical results. Finally, we show that the properties of the ideal Bose gas in a three-dimensional optical lattice can be closely mimicked by finite (slab) systems, when the number of two-dimensional layers is larger than ten for isotropic interactions or even less, when the layers are weakly coupled.

cond-mat.quant-gas↗

arXiv2011

Sign reversal of the boson-boson interaction potential in planar Bose-Fermi mixtures under a synthetic magnetic field

We study the mutually coupled, strongly interacting bosonic and non-interacting fermionic, species of unequal masses in the regime were the retardation effects are an important part of the physics. A cloud of neutral atoms experiences a synthetic magnetic field because of a vector potential that imposes a phase shift on the constituents. The magnetic field causes the oscillations of the magnitude and sign of the effective interaction between bosons from repulsive to attractive in contrast to the static case. We show that the dynamics for the gaseous Bose-Fermi mixtures when reaching the quantum-Hall regime becomes highly nontrivial.

cond-mat.quant-gas↗

arXiv2010

Finite-temperature effects on the superfluid Bose-Einstein condensation of confined ultracold atoms in three-dimensional optical lattices

We discuss the finite-temperature phase diagram in the three-dimensional Bose-Hubbard (BH) model in the strong correlation regime, relevant for Bose-Einstein condensates in optical lattices, by employing a quantum rotor approach. In systems with strong on site repulsive interactions, the rotor U(1) phase variable dual to the local boson density emerges as an important collective field. After establishing the connection between the rotor construction and the the on--site interaction in the BH model the robust effective action formalism is developed which allows us to study the superfluid phase transition in various temperature--interaction regimes.

cond-mat.quant-gas↗

arXiv2010

Frustration effects in rapidly rotating square and triangular optical lattices

We discuss the ground state of the two-dimensional Bose-Hubbard (BH) Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing \mathrm{U}\left(1\right) quantum rotor approach and the topologically constrained path integral that includes a summation over \mathrm{U}\left(1\right) topological charge. We derive an effective quantum action for the BH model, which enables a non-perturbative treatment of the zero-temperature phase transition. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f=0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice, which improves upon previous theoretical treatments. The ground state of the rotating Bose-Einstein condensates on a triangular lattice appears to be most stable against the effects of rotation. Performed calculations revealed strong dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.

cond-mat.quant-gas↗

arXiv2010

Zero-temperature phase diagram of Bose-Fermi gaseous mixtures in optical lattices

We study the ground state phase diagram of a mixture of bosonic and fermionic cold atoms confined on two- and three-dimensional optical lattices. The coupling between bosonic fluctuations and fermionic atoms can be attractive or repulsive and has similarities with electron-phonon coupling in crystals. We investigate behavior of the mixtures in the limit, where the Bogoliubov sound velocity that dictates bosonic dynamics is comparable to the Fermi velocity, hence the retardation effects are important part of the physics. The dynamic Lindhard response function of the fermionic density to changes in the bosonic number of particles above some critical frequency can alter the sign and in consequence the inter-species interaction between particles becomes repulsive in contrast to the static limit (instantaneous and always attractive). Considering the above we show that the structure of the phase diagrams crucially depends on the difference in masses of the bosons and fermions. We discuss the situations where integrating out fermionic field provides an additional interaction that can decrease or increase bosonic coherence.

cond-mat.quant-gas↗

arXiv2009

Superfluid to Mott-insulator transition in an anizotropic two--dimensional optical lattice

We study the superfluid to Mott-insulator transition of bosons in an optical anizotropic lattice by employing the Bose-Hubbard model living on a two-dimensional lattice with anizotropy parameter $κ$. The compressible superfluid state and incompressible Mott-insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing the evolution of the MI lobes is quantified for arbitrary values of $κ$, corresponding to various kind of lattices: from square, through rectangular to almost one-dimensional.

cond-mat.other↗

arXiv2007

Resonance phenomena in asymmetric superconducting quantum interference devices

Theory of self induced resonances in asymmetric two-junction interferometer device is presented. In real devices it is impossible to have an ideal interferometer free of imperfections. Thus, we extended previous theoretical approaches introducing a model which contains several asymmetries: Josephson current $ε$, capacitances $χ$ and dissipation $ρ$ presented in an equivalent circuit. Moreover, non conventional symmetry of the order parameter in high temperature superconducting quantum interference devices forced us to include phase asymmetries. Therefore, the model has been extended to the case of $π$-shift interferometers, where a phase shift is present in one of the junctions.

cond-mat.supr-con↗

arXiv2007

Quantum rotor description of the Mott-insulator transition in the Bose-Hubbard model

We present the novel approach to the Bose-Hubbard model using the $\mathrm{U}(1)$ quantum rotor description. The effective action formalism allows us to formulate a problem in the phase only action and obtain an analytical formulas for the critical lines. We show that the nontrivial $\mathrm{U}(1)$ phase field configurations have an impact on the phase diagrams. The topological character of the quantum field is governed by terms of the integer charges - winding numbers. The comparison presented results to recently obtained quantum Monte Carlo numerical calculations suggests that the competition between quantum effects in strongly interacting boson systems is correctly captured by our model.

cond-mat.stat-mech↗

arXiv2007

Competition between local and nonlocal dissipation effects in two-dimensional quantum Josephson junction arrays

We discuss the local and nonlocal dissipation effects on the existence of the global phase coherence transitions in two dimensional Josephson-coupled junctions. The quantum phase transitions are also examined for various lattice geometries: square, triangular and honeycomb. The T=0 superconductor-insulator phase transition is analyzed as a function of several control parameters which include self-capacitance and junction capacitance and both local and nonlocal dissipation effects. We found the critical value of the nonlocal dissipation parameter α_{1} depends on a geometry of the lattice. The critical value of the normal state conductance seems to be difficult to obtain experimentally if we take into consideration different damping mechanisms which are presented in real physical systems.

cond-mat.supr-con↗

arXiv2005

Local dissipation effects in two-dimensional quantum Josephson junction arrays with magnetic field

We study the quantum phase transitions in two-dimensional arrays of Josephson-couples junctions with short range Josephson couplings (given by the Josephson energy) and the charging energy. We map the problem onto the solvable quantum generalization of the spherical model that improves over the mean-field theory method. The arrays are placed on the top of a two-dimensional electron gas separated by an insulator. We include effects of the local dissipation in the presence of an external magnetic flux f in square lattice for several rational fluxes f=0,1/2,1/3,1/4 and 1/6. We also have examined the T=0 superconducting-insulator phase boundary as function of a dissipation alpha for two different geometry of the lattice: square and triangular. We have found critical value of the dissipation parameter independent on geometry of the lattice and presence magnetic field.

cond-mat.supr-con↗

arXiv2003

Ground state properties of charge and magnetically frustrated two--dimensional quantum Josephson--junction arrays

We study a quantum Hamiltonian that models an two--dimensional array of Josephson junctions with short range Josephson couplings, (given by the Josephson energy E_J and charging energiey E_C due to the small capacitance of the junctions. We include the effects from both the self-C0 and the junction-C1 capacitances in the presence of external magnetic flux f=fi/fi0 as well as uniform background of charges q_{x}. We derive an effective quantum non--linear sigma-model for the array Hamiltonian which enables us a non mean--field treatment of the zero--temperature phase transition scenario. We calculate the ground--state phase diagram, analytically deriving E_J^{crit}(E_C,q_x,f) for several rational fluxes f=0,1/2,1/3,1/4 and 1/6 that improves upon previous theoretical treatments based on mean--field approximations.

cond-mat.supr-con↗