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Polarons and bipolarons in the Rydberg-dressed extended Bose-Hubbard model
G. A. Domínguez-Castro, L. Santos, and L. A. Ardila
Impurities immersed in hard-core Bose gases offer exciting opportunities to explore polaron and bipolaron physics. We investigate the ground-state properties of a single and a pair of impurities throughout the superfluid and insulating (charge density wave) phases of the bosonic environment. In the superfluid phase, the impurity exhibits polaron-like behavior, forming a dressed quasiparticle. In contrast, in the insulating phase, the impurity regains its particle-like character, moving through a potential landscape shaped by the charge density wave order. Moreover, we show that two impurities can form a bound state even in the absence of an explicit impurity-impurity coupling. We establish the stability of this bound state within both the superfluid and insulating phases. Our results offer valuable insights for ongoing lattice polaron experiments with ultracold gases.
Henning Korbmacher, G. A. Domínguez-Castro, Mateusz Łacki, Jakub Zakrzewski, and Luis Santos.
Henning Korbmacher, G. A. Domínguez-Castro, Mateusz Łacki, Jakub Zakrzewski, and Luis Santos.
Ultracold dipolar hard-core bosons in optical ladders provide exciting possibilities for the quantum simulation of anisotropic spin ladders. We show that introducing a tilt along the rungs results in a rich phase diagram at unit rung filling. In particular, for a sufficiently strong dipolar strength, the interplay between the long-range tail of the dipolar interactions and the tilting leads to the emergence of a quantum floating phase, a critical phase with incommensurate density-density correlations. Interestingly, the floating phase is topological, constituting an intermediate gapless stage in the melting of a crystal into a gapped topological Haldane phase. This novel scenario for topological floating phases in dipolar spin ladders can be investigated in ongoing experiments.
Localized and extended phases in square moiré patterns
Random defects do not constitute the unique source of electron localization in two dimensions. Lattice quasidisorder generated from two inplane superimposed rotated, main and secondary, square lattices, namely monolayers where moiré patterns are formed, leads to a sharp localized to delocalized single-particle transition. This is demonstrated here for both, discrete and continuum models of moiré patterns that arise as the twisting angle between the main and the secondary lattices is varied in the interval . Localized to delocalized transition is recognized as the moiré patterns depart from being perfect square crystals to non-crystalline structures. Extended single-particle states are found for rotation angles associated with Pythagorean triples that produce perfectly periodic structures. Conversely, angles not arising from such Pythagorean triples lead to non-commensurate or quasidisordered structures, thus originating localized states. These conclusions are drawn from a stationary analysis where the standard inverse participation ratio (IPR) parameter measuring localization allowed to detect the transition. While both, ground state and excited states are analyzed for the discrete model, where the secondary lattice is considered as a perturbation of the main one, the sharp transition is tracked back for the fundamental state in the continuous scenario where the secondary lattice is not a perturbation any more.
Emergent interaction-induced topology in Bose-Hubbard ladders
David Wellnitz, G. A. Domínguez-Castro, Thomas Bilitewski, Monika Aidelsburger, Ana Maria Rey, Luis Santos
We investigate the quantum many-body dynamics of bosonic atoms hopping in a two-leg ladder with strong on-site contact interactions. We observe that when the atoms are prepared in a staggered pattern with pairs of atoms on every other rung, singlon defects, i.e., rungs with only one atom, can localize due to an emergent topological model, even though the underlying model in the absence of interactions admits only topologically trivial states. This emergent topological localization results from the formation of a zero-energy edge mode in an effective lattice formed by two adjacent chains with alternating strong and weak hoping links (Su-Schrieffer-Heeger chains) and opposite staggering which interface at the defect position. Our findings open the opportunity to dynamically generate nontrivial topological behaviors without the need for complex Hamiltonian engineering.
Relaxation in dipolar spin ladders: From pair production to false-vacuum decay
G. A. Domínguez-Castro, Thomas Bilitewski, David Wellnitz, Ana Maria Rey, Luis Santos.
Ultracold dipolar particles pinned in optical lattices or tweezers provide an excellent platform for the study of the intriguing equilibration dynamics of spin models with dipolar exchange. Starting with an initial state in which spins of opposite orientation are prepared in each of the legs of a ladder lattice, we show that spin relaxation displays an unexpected dependence on interleg distance and dipole orientation. This dependence, stemming from the interplay between intra- and interleg interactions, results in three distinct relaxation regimes: (i) ergodic, characterized by the fast relaxation towards equilibrium of correlated pairs of excitations generated at exponentially fast rates from the initial state; (ii) metastable, in which the state is quasilocalized in the initial state and only decays in exceedingly long timescales, resembling false-vacuum decay; and, surprisingly, (iii) partially relaxed, with coexisting fast partial relaxation and partial quasilocalization. The realization of this intriguing dynamics is at hand in current state-of-the-art experiments in dipolar gases.
Ground states of one-dimensional dipolar lattice bosons at unit filling
Mateusz Łącki, Henning Korbmacher, G. A. Domínguez-Castro, Jakub Zakrzewski, Luis Santos.
Recent experiments on ultracold dipoles in optical lattices open exciting possibilities for the quantum simulation of extended Hubbard models. When considered in one dimension, these models present at unit filling a particularly interesting ground-state physics, including a symmetry-protected topological phase known as Haldane insulator. We show that the tail of the dipolar interaction beyond nearest-neighbors, which may be tailored by means of the transversal confinement, does not only modify quantitatively the Haldane insulator regime and lead to density waves of larger periods, but results as well in unexpected insulating phases. These insulating phases may be topological or topologically trivial, and are characterized by peculiar correlations of the site occupations. These phases may be realized and observed in state-of-the-art experiments.
Universal correlations along the BEC-BCS crossover
J. C. Obeso-Jureidini, G. A. Domínguez-Castro, E. Neri, R. Paredes, V. Romero-Rochín.
Universality of the long-distance behavior across the Bardeen–Cooper–Schrieffer (BEC)-Bose–Einstein condensate (BCS) smooth transition for two-body density correlation functions and the Cooper-pair probability density is demonstrated in a balanced mixture of a two-component Fermi gas at T = 0. It is numerically shown at the mean-field level that these two-body quantities exhibit an exponential decay in terms of the chemical potential and the low-energy behavior of the gap. A general expression is found for the two-body distributions holding for different features of finite-range potentials, such as divergences at the origin, discontinuities at a finite radius, power-law decay, and exponential decay. The correlation length characterizing the long-distance behavior unravels the dependence on the energy needed to break pairs along the BEC-BCS crossover, a quantity meaningful to the stability of the many-body state.
Bose polaron in a one-dimensional lattice with power-law hopping
G. A. Domínguez-Castro
Polarons, quasiparticles resulting from the interaction between an impurity and the collective excitations of a medium, play a fundamental role in physics, mainly because they represent an essential building block for understanding more complex many-body phenomena. In this manuscript, we study the spectral properties of a single impurity mixed with identical bosons in a one-dimensional lattice with power-law hopping. In particular, based on the so-called T-matrix approximation, we show the existence of well-defined quasiparticle branches for several tunneling ranges and for both repulsive and attractive impurity-boson interactions. Furthermore, we demonstrate the persistence of the attractive polaron branch when the impurity-boson bound state is absorbed into the two-body continuum and that the attractive polaron becomes more robust as the range of the hopping increases. The results discussed here are relevant for the understanding of the equilibrium properties of quantum systems with power-law interactions.
Tunable momentum pair creation of spin excitations in dipolar bilayers
Thomas Bilitewski, G. A. Domínguez-Castro, David Wellnitz, Ana Maria Rey, Luis Santos
We study the temporal growth and spatial propagation of quantum correlations in a two-dimensional bilayer realizing a spin-1/2 quantum XXZ model with couplings mediated by long-range and anisotropic dipolar interactions. Starting with an initial state consisting of spins with opposite magnetization in each of the layers, we predict a dynamic instability that results, at short times, in the creation of correlated pairs of excitations at specific momenta at exponentially fast rates and entanglement between spatially separated modes. The momentum structure of the created pairs can be controlled via the dipolar orientation, the layer separation, or the dipolar couplings. The predicted behavior remains observable at very low filling fractions, making it accessible in state-of-the-art experiments with Rydberg atoms, magnetic atoms, and polar molecule arrays.
Polarons and bipolarons in a two-dimensional square lattice
Shanshan Ding, G. A. Domínguez-Castro, Aleksi Julku, Arturo Camacho Guardian, Georg M Bruun
Quasiparticles and their interactions are a key part of our understanding of quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced our understanding of isolated quasiparticles, but so far they have provided limited information regarding their interactions and possible bound states. Here, we show how exploring mobile impurities immersed in a Bose-Einstein condensate (BEC) in a two-dimensional lattice can address this problem. First, the spectral properties of individual impurities are examined, and in addition to the attractive and repulsive polarons known from continuum gases, we identify a new kind of quasiparticle stable for repulsive boson-impurity interactions. The spatial properties of polarons are calculated showing that there is an increased density of bosons at the site of the impurity both for repulsive and attractive interactions. We then derive an effective Schrödinger equation describing two polarons interacting via the exchange of density oscillations in the BEC, which takes into account strong impurity-boson two-body correlations. Using this, we show that the attractive nature of the effective interaction between two polarons combined with the two-dimensionality of the lattice leads to the formation of bound states - i.e. bipolarons. The wave functions of the bipolarons are examined showing that the ground state is symmetric under particle exchange and therefore relevant for bosonic impurities, whereas the first excited state is doubly degenerate and odd under particle exchange making it relevant for fermionic impurities. Our results show that quantum gas microscopy in optical lattices is a promising platform to explore the spatial properties of polarons as well as to finally observe the elusive bipolarons.
Hening Korbmacher, G. A. Domínguez-Castro, Wei-Han Li, Jakub Zakrzewski, Luis Santos
Polar lattice gases are usually assumed to have an intersite interaction that decays with the interparticle distance 𝑟 as 1/𝑟3. However, a loose-enough transversal confinement may strongly modify the dipolar decay in one-dimensional lattices. We show that this modification alters significantly the ground-state properties of hard-core dipolar bosons. For repulsive intersite interactions, the corrected decay alters the conditions for devil's staircase insulators, affecting significantly the particle distribution in the presence of an overall harmonic confinement. For attractive interactions, it results in a reduction of the critical dipole interaction for the formation of self-bound clusters, and for a marked enhancement of the region of liquefied lattice droplets.
G. A. Domínguez-Castro, R. Paredes
The use of machine learning algorithms to address classification problems in several scientific branches has increased over the past years. In particular, the supervised learning technique with artificial neural networks has been successfully employed in classifying phases of matter. In this article, we use a fully connected feed-forward neural network to classify extended and localized single-particle states that arise from quasiperiodic one-dimensional lattices. We demonstrate that our neural network achieves to correctly uncover the nature of the single-particle states even when the wave functions come from a more complex Hamiltonian than the one used to train the network.
Localization of pairs in one-dimensional quasicrystals with power-law hopping
G. A. Domínguez-Castro and R. Paredes
Pair localization in one-dimensional quasicrystals with nearest-neighbor hopping is independent of whether short-range interactions are repulsive or attractive. We numerically demonstrate that this symmetry is broken when the hopping follows a power law. In particular, for repulsively bound states, we find that the critical quasiperiodicity that signals the transition to localization is always bounded by the standard Aubry-André critical point, whereas attractively bound dimers get localized at larger quasiperiodic modulations as the range of the hopping increases. Extensive numerical calculations establish the contrasting nature of the pair energy gap for repulsive and attractive interactions, as well as the behavior of the algebraic localization of the pairs as a function of quasiperiodicity, interaction strength, and power-law hops. The results here discussed are of direct relevance to the study of the quantum dynamics of systems with power-law couplings.
G. A. Domínguez-Castro and R. Paredes
We report a robust delocalization transition of a pair of hard-core bosons moving in a one-dimensional quasicrystal with power-law hopping. We find that in the regime of strong interactions quasiperiodicity first suppresses the transport, as in the usual Anderson picture, and then, transport is enhanced when the quasiperiodic modulation is increased. By introducing an effective Hamiltonian, valid for strong interactions, we unveil the mechanism behind the delocalization transition. Stationary single-particle properties, as well as two-particle correlations, confirm all of our findings. Extensive numerical calculations lead us to establish the values of quasiperiodic modulation, interparticle interactions, and power hops for which the delocalization takes place. Our results are of direct relevance to current experiments of systems with long-range interactions.
Persistence of ferromagnetic domains in a disordered two-dimensional lattice
C. Madroñero, G. A. Domínguez-Castro, L. A. González-García, R. Paredes
We investigate the persistence, in time and space, of ferromagnetic domains in two dimensions subjected to the influence of both the static disorder of variable strength and weak interactions. The domains are represented by a two-species bosonic mixture of 87Rb ultracold atoms in different hyperfine states, such that initially one lies on the left half and the other on the right half of a square lattice. The dynamics of the double domain is followed by describing the two-component superfluid through the time-dependent Gross-Pitaevskii coupled equations, with values of the intra- and interspecies interaction that guarantee miscibility of the components. A robust analysis of the magnetization dynamics for several values of the interspecies interaction, reachable in current experimental setups, and the investigation of the density-weighted magnetization correlator lead us to conclude that the presence of structural disorder yields a slowdown the process of destruction of the initial ferromagnetic order. As shown by our numerical calculations, magnetization is maintained up to 50% of its initial value for the largest disorder amplitude considered.
Unconventional Superfluidity in Ultracold Dipolar Gases
G. A. Domínguez-Castro, R. Paredes
In this manuscript, we discuss the emergence of p-wave superfluidity in a dipolar Fermi gas confined in a double layer array of parallel optical lattices in two dimensions. The dipole moments of the molecules placed at the sites of the optical lattices, separated a distance L and pointing in opposite directions produce an effective attractive interaction among them, except between those dipoles situated one on top of the other. Such interaction between dipoles is precisely the origin of the non-conventional superfluid state. We present the analysis for the ground state of the many-body system within the mean-field scheme. In particular, we study the stable regions, as a function of the system parameters, namely the effective interaction between dipoles and the filling factor n, for which the superfluid state can exist. Following the BKT scheme, we estimate the critical temperature of the superfluid state.
Validity of Gross–Pitaevskii solutions of harmonically confined BEC gases in reduced dimensions
R. Zamora-Zamora, G. A. Domínguez-Castro, C. Trallero-Giner, R. Paredes, V. Romero-Rochín
By exact numerical solutions of the Gross–Pitaevskii (GP) equation in 3D, we assess the validity of 1D and 2D approximations in the study of Bose–Einstein condensates confined in harmonic trap potentials. Typically, these approximations are performed when one or more of the harmonic frequencies are much greater than the remaining ones, using arguments based on the adiabatic evolution of the initial approximated state. Deviations from the 3D solution are evaluated as a function of both the effective interaction strength and the ratio between the trap frequencies that define the reduced dimension where the condensate is confined. The observables analyzed are both of stationary and dynamical character, namely, the chemical potential, the wave function profiles, and the time evolution of the approximated 1D and 2D stationary states, considered as initial states in the 3D GP equation. Our study, besides setting quantitative limits on approximations previously developed, should be useful in actual experimental studies where quasi-1D and quasi-2D conditions are assumed. From a qualitative perspective, 1D and 2D approximations certainly become valid when the anisotropy is large, but in addition the interaction strength needs to be above a certain threshold.
The Aubry–André model as a hobbyhorse for understanding the localization phenomenon
G. A. Domínguez-Castro and R. Paredes
We present a thorough pedagogical analysis of the single particle localization phenomenon in a quasiperiodic lattice in one dimension. Beginning with a detailed derivation of the Aubry–André Hamiltonian we describe the localization transition through the analysis of stationary and dynamical observables. Emphasis is placed on both the properties of the model and technical aspects of the performed calculations. In particular, the stationary properties investigated are the inverse participation ratio, the normalized participation ratio and the energy spectrum as a function of the disorder strength. Two dynamical quantities allow us to discern the localization phenomenon, being the spreading of an initially localized state and the evolution of population imbalance in even and odd sites across the lattice. The present manuscript could be useful in bringing advanced undergraduate and graduate students closer to the comprehension of localization phenomena, a topic of current interest in fields of condensed matter, ultracold atoms and complex systems.
Dynamics of vortex propagation in wave fields: from order to disorder and beyond
Karen Volke-Sepúlveda, Argelia Balbuena Ortega, Sebastián Bucio-Pacheco, Santiago López-Huidobro, Laura Pérez-García, Alejandro V Arzola, Adrián Huerta-Hernández, Jorge A Seman, Alexis Domínguez-Castro, Rosario Paredes
It is well known that speckle fields exhibit a multitude of vortex-type phase dislocations with unitary topological charge and opposite helicities, such that the average angular momentum is null. We tackle this problem the other way around: What is the minimum vortex number embedded in a carrier beam to produce a disordered pattern and what are the necessary conditions in terms of their initial distribution and topological charges? When studying this problem, we found interesting dynamical behavior of vortices in propagation through a focal region where they are forced to interact, depending on the initial conditions, that in some cases resemble the behavior of a system of particles with an effective repulsive interaction.
p‐Wave Superfluid Phases of Fermi Molecules in a Bilayer Lattice Array
G. A. Domínguez‐Castro, Rosario Paredes
The superfluid p=px+ipy phases in an ultracold gas of dipolar Fermi molecules lying in two parallel square lattices in 2D are investigated. As shown by a two-body study, dipole moments oriented in opposite directions in each layer are the key ingredients in our mean-field analysis from which unconventional superfluidity is predicted. The phase diagram summarizes our findings: stable and metastable superfluid phases appear as a function of both, the dipole–dipole interaction coupling parameter and filling factor. A first-order phase transition, and thus a mixture of superfluid phases at different densities, is revealed from the coexistence curves in the metastable region. The model predicts that these superfluid phases can be observed experimentally at 10 nK in molecules of NaK confined in optical lattices of size 532 nm. Other routes to reach higher temperatures require the use of subwavelength confinement technique.
Bound states and Cooper pairs of molecules in 2D optical lattices bilayer
A. Camacho‐Guardian, G. A. Domínguez‐Castro, R. Paredes
We investigate the formation of Cooper pairs, bound dimers and the dimer-dimer elastic scattering of ultracold dipolar Fermi molecules confined in a 2D optical lattice bilayer configuration. While the energy and their associated bound states are determined in a variational way, the correlated two-molecule pair is addressed as in the original Cooper formulation. We demonstrate that the 2D lattice confinement favors the formation of zero center mass momentum bound states. Regarding the Cooper pairs binding energy, this depends on the molecule populations in each layer. Maximum binding energies occur for non-zero (zero) pair momentum when the Fermi system is polarized (unpolarized). We find an analytic expression for the dimer-dimer effective interaction in the deep BEC regime. The present analysis represents a route for addressing the BCS-BEC crossover in dipolar Fermi gases confined in 2D optical lattices within the current experimental panorama.
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