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.
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.
Abstract The presence of disorder substantially influences the behaviour of physical systems. It can give rise to slow or glassy dynamics, or to a complete suppression of transport as in Anderson insulators1, where normally extended wavefunctions such as light fields or electronic Bloch waves become exponentially localized. The combined effect of disorder and interactions is central to the richness of condensed-matter physics2. In bosonic systems, it can also lead to additional quantum states such as the Bose glass3,4—an insulating but compressible state without long-range phase coherence that emerges in disordered bosonic systems and is distinct from the well-known superfluid and Mott insulating ground states of interacting bosons. Here we report the experimental realization of the two-dimensional Bose glass using ultracold atoms in an eight-fold symmetric quasicrystalline optical lattice5. 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. We furthermore demonstrate that it is not possible to adiabatically traverse the Bose glass on typical experimental timescales by examining the capability to restore coherence and discuss the connection to the expected non-ergodicity of the Bose glass. Our observations are in good agreement with recent quantum Monte Carlo predictions6 and pave the way for experimentally testing the connection between the Bose glass, many-body localization and glassy dynamics more generally7,8.
Quasicrystals exhibit exotic properties inherited from the self-similarity of their long-range ordered, yet aperiodic, structure. The recent realization of optical quasicrystal lattices paves the way to the study of correlated Bose fluids in such structures, but the regime of strong interactions remains largely unexplored, both theoretically and experimentally. Here, we determine the quantum phase diagram of two-dimensional correlated bosons in an eightfold quasicrystal potential. Using large-scale quantum Monte Carlo calculations, we demonstrate a superfluid-to-Bose glass transition and determine the critical line. Moreover, we show that strong interactions stabilize Mott insulator phases, some of which have spontaneously broken eightfold symmetry. Our results are directly relevant to current generation experiments and, in particular, drive prospects to the observation of the still elusive Bose glass phase in two dimensions and exotic Mott phases.
Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as self-similarity, the inheritance of topological properties from higher dimensions, and the presence of non-trivial structure on all lengthscales. However, quasicrystalline materials are notoriously hard to synthesise, as defects and impurities may greatly alter their final microscopic composition. The field of quantum simulation with ultracold atoms offers a solution to this problem, namely the use of optical lattices – standing waves of light. Optical lattices are free of impurities and therefore ideally suited to study quasicrystals, enabling unprecedented access to observables that are unattainable in condensed matter systems. This study presents the first experimental realisation of a two-dimensional quasicrystalline potential for ultracold atoms, based on an eightfold symmetric optical lattice. Features pertaining to both ordered and disordered phases are observed, from sharp diffraction peaks in the matter-wave interference pattern, to a disorder-induced localised phase emerging at a critical lattice depth V_loc ~ 1.78 E_rec. The localised phase seems to be resilient against moderate interactions, which would make this the first experimental realisation of a 2D Bose glass.
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.
We study the low-temperature phases of interacting bosons on a two-dimensional quasicrystalline lattice. By means of numerically exact path integral Monte Carlo simulations, we show that for sufficiently weak interactions the system is a homogeneous Bose-Einstein condensate that develops density modulations for increasing filling factor. The simultaneous occurrence of sizeable condensate fraction and density modulation can be interpreted as the analogous, in a quasicrystalline lattice, of supersolid phases occurring in conventional periodic lattices. For sufficiently large interaction strength and particle density, global condensation is lost and quantum exchanges are restricted to specific spatial regions. The emerging quantum phase is therefore a Bose glass, which here is stabilized in the absence of any source of disorder or quasidisorder, purely as a result of the interplay between quantum effects, particle interactions and quasicrystalline substrate. This finding clearly indicates that (quasi)disorder is not essential to observe Bose glass physics. Our results are of interest for ongoing experiments on (quasi)disorder-free quasicrystalline lattices.