We investigate the ground-state and dynamical properties of ultracold Bose gases in optical lattices with a quasicrystal structure, inspired by recent experiments on twisted bilayer and quasicrystalline optical lattices. The interplay between on-site repulsive interactions and the quasiperiodic potential leads to rich physics. At low filling factors, increasing the interaction strength induces a delocalization effect that transforms a Bose-glass (BG) phase-characterized by disconnected superfluid (SF) regions-into a robust SF phase with a percolated network of SF clusters. This transition is quantitatively identified via the percolation probability. At higher filling factors, we uncover a reentrant behavior: with increasing interaction, the system first changes from BG to SF, but further strengthening reverses the trend, restoring the BG phase. This reentrance originates from an interaction-driven rearrangement of particles, where a percolated SF network fragments into isolated SF islands as repulsion dominates. The quench dynamics show distinct transient features: intraphase quenches cause minor variations in the percolation probability and the inverse participation ratio (IPR), while interphase quenches produce strong responses. In particular, an SF-to-BG quench exhibits an abrupt loss of global SF connectivity, whereas a BG-to-SF quench shows oscillatory percolation and a gradual IPR decrease, stabilizing the SF phase. These results elucidate the competition between quasiperiodicity and interactions in ultracold Bose gases and offer insights relevant to current experiments with twisted bilayer and quasicrystal optical lattices.
We investigate the ground-state and dynamical properties of ultracold Bose gases in optical lattices with a quasicrystal structure, inspired by recent experiments on twisted bilayer and quasicrystalline optical lattices. The interplay between on-site repulsive interactions and the quasiperiodic potential leads to rich physics. At low filling factors, increasing the interaction strength induces a delocalization effect that transforms a Bose-glass (BG) phase-characterized by disconnected superfluid (SF) regions-into a robust SF phase with a percolated network of SF clusters. This transition is quantitatively identified via the percolation probability. At higher filling factors, we uncover a reentrant behavior: with increasing interaction, the system first changes from BG to SF, but further strengthening reverses the trend, restoring the BG phase. This reentrance originates from an interaction-driven rearrangement of particles, where a percolated SF network fragments into isolated SF islands as repulsion dominates. The quench dynamics show distinct transient features: intraphase quenches cause minor variations in the percolation probability and the inverse participation ratio (IPR), while interphase quenches produce strong responses. In particular, an SF-to-BG quench exhibits an abrupt loss of global SF connectivity, whereas a BG-to-SF quench shows oscillatory percolation and a gradual IPR decrease, stabilizing the SF phase. These results elucidate the competition between quasiperiodicity and interactions in ultracold Bose gases and offer insights relevant to current experiments with twisted bilayer and quasicrystal optical lattices.
Recent experiments have realized ultracold gases in twisted-bilayer optical lattices. We show that interacting bosons in these lattices present a highly nontrivial ground-state physics resulting from the interplay between inter- and intralayer hopping and interactions. This physics is crucially determined by site clusterization, which we properly take into account by developing a specifically tailored cluster Gutzwiller approach. Clusterization results in a large variety of different Mott-like phases characterized by typically different occupations of the clusters, and in the appearance of pockets of sites in between which particles can freely move, but which remain for any practical purposes disconnected from the rest of the sites. This peculiar phase, which resembles the well-known Bose glass phase, may occur even for commensurate twist angles and is further enhanced when the twisting is incommensurate. Moreover, in the incommensurate case, the formation of mobility islands may occur even without interlayer hopping solely due to interlayer interactions.
This thesis concerns the physics of ultracold bosons in quasicrystalline lattices, studied by means of quantum simulation using ultracold 39K atoms loaded to an eight-fold rotationally symmetric optical quasicrystal. Quasicrystalline and quasiperiodic systems, thanks to their long-range order and lack of periodicity, exhibit a wealth of interesting properties such as a dense and self-similar momentum space, and a localization transition to Anderson insulator or Bose glass states (in non-interacting or interacting cases respectively) reminiscent of that in disordered systems, whilst lacking the rare regions that typically exist in such systems. Here we will cover experiments into this system’s behaviour in both equilibrium and non-equilibrium settings. First, we focus on mapping out its phase diagram in both weakly and strongly interacting regimes. We observe consistency with numerical predictions for the superfluid-Bose glass phase transition using coherence measurements, as well as finding a region of roughly zero compressibility around where the numerics predicts the existence of a Mott insulator ground state. We also study which regimes of the phase diagram can be ramped through adiabatically, finding that entropy is created upon traversing the Bose glass phase irrespective of ramp duration, which we attribute to its localized nature. Next we look into the dynamics of the system after a quench of the lattice depth in the weakly interacting regime. Upon quenching from the superfluid regime to the Bose glass regime, we observe a quantum walk to higher order diffraction peaks in momentum space whose maximum order is unbounded by kinetic energy thanks to the dense, self-similar nature of the quasicrystal’s momentum space. Quenching in the opposite direction we observe instead a walk between sites in real space for short times by looking at the position (as opposed to momentum) space autocorrelation function of the cloud, finding an expansion rate in agreement with an intuitive estimate based on the Lieb-Robinson bounds of a periodic system. We also look into the timescales of these dynamics in the context of what we might expect from the underlying Hamiltonian, before finally investigating the loss of coherence exhibited by the system after a slower quench of the lattice depth from an initially superfluid cloud. We observe that coherence is lost sooner after the quench for deeper final lattices, with the loss becoming almost instantaneous for quenches that cross the localization transition across the whole cloud. After this we explore the system’s transport dynamics by means of a quench to an excited state at the same time as an additional confining potential is switched off. We observe that unlike in the case of a periodic square lattice, where ballistic expansion that scales with the tunnelling strength occurs in the non-interacting case before becoming slower upon the introduction of interactions thanks to diffusion, in the quasicrystal the transport rate no longer scales with tunnelling strength. Instead we observe a drop relative to the tunnelling rate by 2 − 3 orders of magnitude as the lattice depth is increased from 1Er to 5Er with little dependence on the interaction strength. We also note that the finite rate measured for the deeper lattices is potentially an overestimate since the finite loss rate of atoms makes mass transport indistinguishable from density-dependent losses at that point. Finally, we discuss use of a quantum gas magnification scheme with which to magnify the real space density distribution of our atoms such that it can be measured with single-site resolution. Some preliminary results are presented regarding how the density distribution changes with lattice depth in the weakly interacting regime, in which we observe that as lattice depth increases a higher proportion of atoms occupy deeper sites close to the centre of the quasicrystal’s configuration space, as we might expect.
Due to their intrinsic interplay between long-range order and quasi-disorder, quasicrystalline systems provide a rich platform for investigating novel quantum phenomena. Here we study the non-equilibrium dynamics following quantum quenches across the superfluid to Bose-glass transition using ultracold bosons in an optical quasicrystal. Fast quenches into the Bose glass regime induce a quantum walk in momentum space that spreads over increasingly higher momentum orders. Conversely, quenches into the superfluid regime initiate a real-space quantum walk of initially localized atoms, forming a light-cone-like structure bounded by Lieb-Robinson limits. Characteristic timescales reveal strong links to the underlying Hamiltonian and are governed primarily by quasi-disorder strength in the Bose glass phase, and by tunneling strength in the superfluid phase. Finally, we analyze slower quenches into deeper lattices and observe the decay of coherence across the phase transition.
Moiré related physics in twisted bilayer two-dimensional (2D) materials has attracted widespread interest in condensed matter physics. Simulation of moiré related physics in cold atom platform is expected to outperform the 2D materials thanks to its advantage of higher tunablility. Here, we demonstrate that, the cold atom platform enables a new mechanism of moiré lattice formation, induced by interlayer interaction with intrinsic "dynamical" character, in contrast to conventional moiré lattice induced by "static" ways such as single-particle interlayer tunneling. Specifically, we consider a twisted bilayer Bose-Hubbard model with vanishing interlayer tunneling, and the bilayer is solely coupled through interlayer interaction that originates from contact interaction of atoms. We find that this system hosts a plethora of novel phases unique to this dynamical lattice, including a variety of Mott insulator (MI) and superfluid (SF) phases either preserving or breaking moiré lattice symmetry, phases with one layer in SF and the other in MI, "interlocked" MI, and self-localized phases at commensurate twist angles, which exhibits the characteristics of Bose glass and quasi-many-body localization in the absence of (quasi)disorder or quasicrystalline lattices. Our prediction can be readily observed in current experimental setup of twisted bilayer optical lattices, opening up new avenues for exploring the rich physics of interaction induced moiré systems in cold atoms.
The combined effect of disorder and interactions is central to the richness of condensed matter physics and can lead to novel quantum states such as the Bose glass phase in disordered bosonic systems. Here, we report on the experimental realisation of the two-dimensional Bose glass using ultra-cold atoms in an eight-fold symmetric quasicrystalline optical lattice. By probing the coherence properties of the system, we observe a Bose glass to superfluid transition and map out the phase diagram in the weakly interacting regime. Moreover, we reveal the non-ergodic nature of the Bose glass by probing the capability to restore coherence. Our observations are in good agreement with recent quantum Monte Carlo predictions and pave the way for experimentally testing the connection between the Bose glass, many-body localisation, and glassy dynamics more generally.
We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz–Petrich type. By using a mean-field variational method designed in momentum space as well as Gross–Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases.