arXiv subjects

Jakub Zakrzewski

Publications and source records attributed to Jakub Zakrzewski.

At least 109 records · Page 6Linked to original sources

arXiv2019

Energy level dynamics across the many-body localization transition

The level dynamics across the many body localization transition is examined for XXZ-spin model with a random magnetic field. We compare different scenaria of parameter dependent motion in the system and consider measures such as level velocities, curvatures as well as their fidelity susceptibilities. Studying the ergodic phase of the model we find that the level dynamics does not reveal the commonly believed universal behavior after rescaling the curvatures by the level velocity variance. At the same time, distributions of level curvatures and fidelity susceptibilities coincide with properly rescaled distributions for Gaussian Orthogonal Ensemble of random matrices. Profound differences exists depending on way the level dynamics is imposed in the many-body localized phase of the model in which the level dynamics can be understood with the help of local integrals of motion.

cond-mat.dis-nn↗

arXiv2019

Many-body localization in presence of cavity mediated long-range interactions

We show that a one-dimensional Hubbard model with all-to-all coupling may exhibit many-body localization in the presence of local disorder. We numerically identify the parameter space where many-body localization occurs using exact diagonalization and finite-size scaling. The time evolution from a random initial state exhibits features consistent with the localization picture. The dynamics can be observed with quantum gases in optical cavities, localization can be revealed through the time-dependent dynamics of the light emitted by the resonator.

cond-mat.dis-nn↗

arXiv2019

Route to chaos in a coupled microresonator system with gain and loss

We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates, optical waveguides or atomic Bose-Einstein condensates of ultra-cold atoms placed in a circular-shaped trap. From the theoretical point of view this system is attractive due to its modulational instability and rich structure, including various types of spontaneous symmetry breaking, period doubling bifurcations, eventually leading to chaotic regime. It is described by set of partial differential equations but we show that the so called Galerkin approximation can explain most of the system characteristics mapping it on the dynamics of few coupled oscillator modes. The main goal of present study is to investigate various routes to chaos in our non-hermitian system and to show the correspondence between the continuous operator problem and its discrete representation.

physics.optics↗

arXiv2019

Intermediate spectral statistics in the many--body localization transition

Spectral statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between transitions in random and quasi-random disorder, showing the effects due to Griffiths rare events for the former case. It is argued that the transition for a random disorder exhibits universal features that are identified by constructing an appropriate model of intermediate spectral statistics which is a generalization of the family of short-range plasma models. The model incorporates the inter- and intra-sample fluctuations and faithfully reproduces level spacing distributions as well as number variance during the transition from ergodic to many--body localized phase. In particular, it grasps the critical level statistics which arise at disorder strength for which the fluctuations are the strongest.

cond-mat.dis-nn↗

arXiv2019

Level statistics across the many--body localization transition

Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between transitions in random and quasi-random disorder, showing the effects due to Griffiths rare events for the former case. It is argued that the transition in the case of random disorder exhibits universal features that are identified by constructing an appropriate model of intermediate spectral statistics which is a generalization of the family of short-range plasma models. The considered weighted short-range plasma model yields a very good agreement both for level spacing distribution including its exponential tail and the number variance up to tens of level spacings outperforming previously proposed models. In particular, our model grasps the critical level statistics which arise at disorder strength for which the inter-sample fluctuations are the strongest. Going beyond the paradigmatic examples of many-body localization in spin systems, we show that the considered model also grasps the level statistics of disordered Bose- and Fermi-Hubbard models. The remaining deviations for long-range spectral correlations are discussed and attributed mainly to the intricacies of level unfolding.

cond-mat.dis-nn↗

arXiv2018

Single-particle localization in dynamical potentials

Single particle localization of an ultra-cold atom is studied in one dimension when the atom is confined by an optical lattice and by the incommensurate potential of a high-finesse optical cavity. In the strong coupling regime the atom is a dynamical refractive medium, the cavity resonance depends on the atomic position within the standing-wave mode and nonlinearly determines the depth and form of the incommensurate potential. We show that the particular form of the quasi-random cavity potential leads to the appearance of mobility edges, even in presence of nearest-neighbour hopping. We provide a detailed characterization of the system as a function of its parameters and in particular of the strength of the atom-cavity coupling, which controls the functional form of the cavity potential. For strong atom-photon coupling the properties of the mobility edges significantly depend on the ratio between the periodicities of the confining optical lattice and of the cavity field.

cond-mat.dis-nn↗

arXiv2018

Impact of geometry on many-body localization

The impact of geometry on many body localization is studied on simple, exemplary systems amenable to exact diagonalization treatment. The crossover between ergodic and MBL phase for uniform as well as quasi-random disorder is analyzed using statistics of energy levels. It is observed that the transition to many-body localized phase is correlated with the number of nearest coupled neighbors. The crossover from extended to localized systems is approximately described by the so called plasma model.

cond-mat.dis-nn↗

arXiv2018

Spin-charge separation and many-body localization

We study many-body localization for a disordered chain of spin 1/2 fermions. In [Phys. Rev. B \textbf{94}, 241104 (2016)], when both down and up components are exposed to the same strong disorder, the authors observe a power law growth of the entanglement entropy that suggests that many-body localization is not complete; the density (charge) degree of freedom is localized, while the spin degree of freedom is apparently delocalized. We show that this power-like behavior is only a transient effect and that, for longer times, the growth is logarithmic in time suggesting that the spin degree of freedom is also localized, so that the system follows the standard many-body localization scenario. We also study the experimentally relevant case of quasiperiodic disorder.

cond-mat.dis-nn↗

arXiv2018

Restricted space ab initio models for double ionization by strong laser pulses

Double electron ionisation process occurs when an intense laser pulse interacts with atoms or molecules. Exact {\it ab initio} numerical simulation of such a situation is extremely computer resources demanding, thus often one is forced to apply reduced dimensionality models to get insight into the physics of the process. The performance of several algorithms for simulating double electron ionization by strong femtosecond laser pulses are studied. The obtained ionization yields and the momentum distributions of the released electrons are compared, and the effects of the model dimensionality on the ionization dynamics discussed.

physics.atom-ph↗

arXiv2018

Extended Bose-Hubbard Model with dipolar and contact interactions

We study the phase diagram of the one-dimensional boson gas trapped inside an optical lattice with contact and dipolar interaction taking into account next-nearest terms for both tunneling and interaction. Using the density matrix renormalization group, we calculate how the locations of phase transitions change with increasing dipolar interaction strength for average density $ρ= 1$. Furthermore, we show an emergence of pair-correlated phases for a large dipolar interaction strength and $ρ\geq 2$, including a supersolid phase with an incommensurate density wave ordering manifesting the corresponding spontaneous breaking of the translational symmetry.

cond-mat.quant-gas↗

arXiv2018

Discrete disorder models for many-body localization

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time non-ergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.

cond-mat.dis-nn↗

arXiv2018

Many-body localization of bosons in optical lattices

Many-body localization for a system of bosons trapped in a one dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose-Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.

cond-mat.dis-nn↗

arXiv2018

At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited

We address the question whether the super-Heisenberg scaling for quantum estimation is realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter dependent dynamics. If the parameter is coupled to the one-body part of the Hamiltonian the precision of its estimation is known to scale at most as $N^{-1}$ (Heisenberg scaling) in terms of the number of elementary subsystems used, $N$. The second approach considers fidelity at criticality often leading to an apparent super-Heisenberg scaling. However, scaling of time needed to ensure adiabaticity of the evolution brings back the the Heisenberg limit. We illustrate the general theory on a ferromagnetic Heisenberg spin chain which exhibits such super-Heisenberg scaling of fidelity around the critical value of the magnetic field. Even an elementary estimator represented by a single-site magnetization already outperforms the Heisenberg behavior providing the $N^{-1.5}$ scaling. In this case Fisher information sets the ultimate scaling as $N^{-1.75}$ which can be saturated by measuring magnetization on all sites simultaneously. We discuss universal scaling predictions of the estimation precision offered by such observables, both at zero and finite temperatures, and support them with numerical simulations in the model. We provide an experimental proposal of realization of the considered model via mapping the system to ultra-cold bosons in periodically shaken optical lattice. We explicitly derive that the Heisenberg limit is recovered when time needed for preparation of quantum states involved is taken into acocunt.

quant-ph↗

arXiv2018

Time crystals: a review

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals -- the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek's idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.

quant-ph↗

arXiv2017

Time crystal behavior of excited eigenstates

In analogy to spontaneous breaking of continuous space translation symmetry in the process of space crystal formation, it was proposed that spontaneous breaking of continuous time translation symmetry could lead to time crystal formation. In other words, a time-independent system prepared in the energy ground state is expected to reveal periodic motion under infinitely weak perturbation. In the case of the system proposed originally by Frank Wilczek, spontaneous breaking of time translation symmetry can not be observed if one starts with the ground state. We point out that the symmetry breaking can take place if the system is prepared in an excited eigenstate. The latter can be realized experimentally in ultra-cold atomic gases. We simulate the process of the spontaneous symmetry breaking due to measurements of particle positions and analyze the lifetime of the resulting symmetry broken state.

quant-ph↗

arXiv2017

Synthetic Random Flux Model in a periodically-driven optical lattice

We propose a realization of a synthetic Random Flux Model in a two-dimensional optical lattice. Starting from Bose-Hubbard Hamiltonian for two atom species we show how to use fast-periodic modulation of the system parameters to construct random gauge field. We investigate the transport properties of such a system and describe the impact of time-reversal symmetry breaking and correlations in disorder on Anderson localization length.

cond-mat.quant-gas↗

arXiv2017

Many-body localization for randomly interacting bosons

We study many-body localization in a one dimensional optical lattice filled with bosons. The interaction between bosons is assumed to be random, which can be realized for atoms close to a microchip exposed to a spatially fluctuating magnetic field. Close to a Feshbach resonance, such controlled fluctuations can be transfered to the interaction strength. We show that the system reveals an inverted mobility edge, with mobile particles at the lower edge of the spectrum. A statistical analysis of level spacings allows us to characterize the transition between localized and excited states. The existence of the mobility edge is confirmed in large systems, by time dependent numerical simulations using tDMRG. A simple analytical model predicts the long time behavior of the system.

cond-mat.quant-gas↗

arXiv2017

Two bosonic quantum walkers in one-dimensional optical lattices

Dynamical properties of two bosonic quantum walkers in a one-dimensional lattice are studied theoretically. Depending on the initial state, interactions, lattice tilting, and lattice disorder, whole plethora of different behaviors are observed. Particularly, it is shown that two bosons system manifests the many-body localization like behavior in the presence of a quenched disorder. The whole analysis is based on a specific decomposition of the temporal density profile into different contributions from singly and doubly occupied sites. In this way, the role of interactions is extracted. Since the contributions can be directly measured in experiments with ultra-cold atoms in optical lattices, the predictions presented may have some importance for upcoming experiment.

quant-ph↗