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AIP conference proceedings

Quantum States of ultracold bosons in optical lattices interacting via long-range interaction

Rohit Panda, B. Chatterjee

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We simulate a one-dimensional system of a few ultracold bosons trapped in an optical lattice with long-range interactions from an ab initio perspective using the MCTDH-B method. We emphasise the distinct influence of the long-range interactions and the effects not observed by systems with contact interactions. We consider both the nearest-neighbour and the next-nearest neighbour interactions in addition to the usual contact interactions. We observe and analyse the ground state that arises due to the intricate interplay between the interaction potentials and the non-trivial influence of the particle number. By systematically tuning the coupling between different interaction types and varying particle numbers across different regimes, we uncover a diverse set of novel ground-state configurations whose emergence is governed by the delicate interplay of competing energetic factors.

DOI
10.1063/5.0225056

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We simulate a one-dimensional system of a few ultracold bosons trapped in an optical lattice with long-range interactions from an ab initio perspective using the MCTDH-B method. We emphasise the distinct influence of the long-range interactions and the effects not observed by systems with contact interactions. We consider both the nearest-neighbour and the next-nearest neighbour interactions in addition to the usual contact interactions. We observe and analyse the ground state that arises due to the intricate interplay between the interaction potentials and the non-trivial influence of the particle number. By systematically tuning the coupling between different interaction types and varying particle numbers across different regimes, we uncover a diverse set of novel ground-state configurations whose emergence is governed by the delicate interplay of competing energetic factors.
We investigate the dynamical instabilities of a one-dimensional ultracold Bose-Bose mixture with long-range dipole-dipole interactions, trapped in deep optical lattices and subject to periodically varying contact interaction. The effect of beyond-mean-field corrections due to quantum fluctuations is considered. In the tight-binding regime, we employ Wannier functions to derive a discrete nonlinear Schrödinger equation that captures the dynamics of the system. Using linear stability analysis coupled to multiple scale expansion, we systematically study the modulational and parametric instabilities of the system in the miscible regime, identifying the conditions under which these instabilities emerge. The corresponding instability domains are found and examined. The roles of long-range interactions and quantum fluctuations are highlighted, demonstrating their significant impact on the stability and dynamics of the lattice system. Our analytical predictions are validated through direct numerical simulations, which confirm the instability diagrams through the effective onset of instabilities and reveal the intricate interplay between interaction strength, quantum fluctuation, and the long-range nature of the dipole-dipole forces. This work provides insights into the control and manipulation of ultracold quantum gases in optical lattices, which have potential applications in quantum simulation and condensed-matter physics.
Abstract The out-of-equilibrium dynamics of finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. Our study reveals that the driving enforces the bosons in different wells to oscillate in-phase and to exhibit a dipole-like mode. A wide range from weak-to-strong driving frequencies is covered and a resonance-like behavior of the intra-well dynamics is discussed. In the proximity of the resonance a rich intraband excitation spectrum is observed. The single particle excitation mechanisms are studied in the framework of Floquet theory elucidating the role of the driving frequency. The impact of the interatomic repulsive interactions is examined in detail yielding a strong influence on the tunneling period and the excitation probabilities. Finally, the dependence of the resonance upon a variation of the tunable parameters of the optical lattice is examined. Our analysis is based on the ab initio multi-configuration time-dependent Hartree method for bosons.
We investigate the ground state properties and tunneling dynamics of ultracold dipolar bosons in a one dimensional triple well trap from a few-body ab-initio perspective. Our focus is primarily on the distinctive features of dipolar bosons compared to the contact interacting bosons. Formation of intra-well localization is observed for very strong dipolar interaction. General population rearangement as well as fragmentation and localization effects have been found, depending strongly on the particle number. The energy spectrum for two particles exhibits avoided crossings that lead to several distinct resonances involving different bands, i.e. to an inter-band resonant tunneling dynamics. The corresponding mechanisms are investigated by studying among others the pair-probability and performing an eigenstate analysis.
We show that coupling ultracold atoms in optical lattices to quantized modes of an optical cavity leads to quantum phases of matter, which at the same time possess properties of systems with both short- and long-range interactions. This opens perspectives for novel quantum simulators of finite-range interacting systems, even though the light-induced interaction is global (i.e., infinitely long range). This is achieved by spatial structuring of the global light-matter coupling at a microscopic scale. Such simulators can directly benefit from the collective enhancement of the global light-matter interaction and constitute an alternative to standard approaches using Rydberg atoms or polar molecules. The system in the steady state of light induces effective many-body interactions that change the landscape of the phase diagram of the typical Bose-Hubbard model. Therefore, the system can support nontrivial superfluid states, bosonic dimer, trimer, etc., states, and supersolid phases depending on the choice of the wavelength and pattern of the light with respect to the classical optical lattice potential. We find that by carefully choosing the system parameters one can investigate diverse strongly correlated physics with the same setup, i.e., modifying the geometry of light beams. In particular, we present the interplay between the density and bond (or matter-wave coherence) interactions. We show how to tune the effective interaction length in such a hybrid system with both short-range and global interactions.
Disorder is ubiquitous in condensed matter systems, but a thorough understanding of these systems is hindered by poor control over the nature of disorder and competing interactions. Ultracold gases trapped in optical lattices, on the other hand, offer an unprecedented level of control over interactions and disorder, and are ideal candidates to test theoretical predictions and study fascinating phenomena resulting from the interplay between disorder, interaction, and quantum degeneracy. In this dissertation, I present my research on strongly correlated many-body lattice bosons in the presence of disordered potentials. My results are based on quantum Monte Carlo simulations by the Worm algorithm. Experimentally, lattice bosons can be realized by ultracold gases in optical lattices. I studied the ground state phase diagram of the above systems in the presence of diagonal (quasi-periodic disordered potential or random disordered potential) and off-diagonal disorder (in the form of site dilution). First, I will discuss the ground state phase diagram of two-dimensional bosons in quasi-periodic lattices. Then, I will discuss the phase diagram as well as finite temperature thermodynamic properties of two-dimensional dipolar lattice bosons in the presence of random diagonal disordered potentials. Finally, I will discuss the phase diagram of two-dimensional hard-core lattice bosons system in the presence of long-range hopping and long-range two-body interactions both in the absence of disorder and in the presence of site dilution (equivalent to off-diagonal disorder). This system is equivalent to the long-range XXZ model as realized by polar molecules trapped in a deep optical lattice. These results provide theoretical guidance for experimentalists to find quantum phase transitions as well as exotic quantum phases in strongly correlated bosonic lattice systems.
We study the expansion dynamics of harmonically trapped bosons in a two-dimensional lattice within the extended Bose-Hubbard model. We evaluate the dynamics of the system following a sudden removal of the confining potential, starting with a cloud mostly in n = 1 Mott state. We show that the nearest neighbour interactions have a strong influence on the dynamics of ultracold bosons on an optical lattice. Also we conclude that validity of the widely used contact potential approximation is questionable in the presence of Feschbach resonances.