One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of Anderson localization and the realization of the disordered Bose–Hubbard model. There are, however, still questions as to how to differentiate the complex insulating phases resulting from this interplay, and how to measure the size of the superfluid fragments that these phases entail. It has been suggested that the correlation function of such a system can give new insights, but so far very little experimental investigation has been performed. Here, we show the first experimental analysis of the correlation function for a weakly interacting, bosonic system in a quasiperiodic lattice. We observe an increase in the correlation length as well as a change in the shape of the correlation function in the delocalization crossover from Anderson glass to coherent, extended state. In between, the experiment indicates the formation of progressively larger coherent fragments, consistent with a fragmented BEC, or Bose glass.One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of Anderson localization and the realization of the disordered Bose–Hubbard model. There are, however, still questions as to how to differentiate the complex insulating phases resulting from this interplay, and how to measure the size of the superfluid fragments that these phases entail. It has been suggested that the correlation function of such a system can give new insights, but so far very little experimental investigation has been performed. Here, we show the first experimental analysis of the correlation function for a weakly interacting, bosonic system in a quasiperiodic lattice. We observe an increase in the correlation length as well as a change in the shape of the correlation function in the delocalization crossover from Anderson glass to coherent, extended state. In between, the experiment indicates the formation of progressively larger coherent fragments, consistent with a fragmented BEC, or Bose glass.

Jan 1, 201127 citations

Finite-temperature effects on interacting bosonic one-dimensional systems in disordered lattices

Lorenzo Gori, Thomas Barthel, Avinash Kumar +7 more

We analyze the finite-temperature effects on the phase diagram describing the insulating properties of interacting one-dimensional bosons in a quasiperiodic lattice. We examine thermal effects by comparing experimental results to exact diagonalization for small-sized systems and to density-matrix renormalization group (DMRG) computations. At weak interactions, we find short thermal correlation lengths, indicating a substantial impact of temperature on the system coherence. Conversely, at strong interactions, the obtained thermal correlation lengths are significantly larger than the localization length, and the quantum nature of the $T=0$ Bose-glass phase is preserved up to a crossover temperature that depends on the disorder strength. Furthermore, in the absence of disorder, we show how quasiexact finite- $T$ DMRG computations, compared to experimental results, can be employed to estimate the temperature, which is not directly accessible in the experiment.We analyze the finite-temperature effects on the phase diagram describing the insulating properties of interacting one-dimensional bosons in a quasiperiodic lattice. We examine thermal effects by comparing experimental results to exact diagonalization for small-sized systems and to density-matrix renormalization group (DMRG) computations. At weak interactions, we find short thermal correlation lengths, indicating a substantial impact of temperature on the system coherence. Conversely, at strong interactions, the obtained thermal correlation lengths are significantly larger than the localization length, and the quantum nature of the $T=0$ Bose-glass phase is preserved up to a crossover temperature that depends on the disorder strength. Furthermore, in the absence of disorder, we show how quasiexact finite-$T$ DMRG computations, compared to experimental results, can be employed to estimate the temperature, which is not directly accessible in the experiment.

arXiv:1512.04238Physical Review AMar 29, 201620 citations

Weakly interacting Bose gas in quasiperiodic disorder

Mohit Pandey

In a recent experiment, Anderson localization was observed directly for non-interacting Bose-Einstein Condensate in one dimension. The experiment was performed using quasiperiodic optical lattice. Their system can be described by the one-dimensional noninteracting Aubry-Andr�e model. This model which simulates disorder with its quasiperiodic potential shows transition from extended to localised states at a critical disorder strength. The ground state gets localised around a single point for disorder larger than the critical value. We find that while inverse participation ratio increases as we increase disorder and rises to one in insulator phase, super uid fraction decreases as we increase disorder and goes to zero sharply in the insulator phase . When we introduce weak repulsive interaction for Bose gas in the model at the mean field level, we see that the ground-state shows multiple-site localization for certain disorder range, which lies above the critical value. For given interaction strength, we find that the inverse participation ratio increases slowly and super uid fraction decreases slowly as we increase disorder. Moreover, by representing our model as a classical two-dimensional nonlinear Hamiltonian map, we distinguish between localised and extended states by studying the trajectories in phase-space. Using this, we find out the localization length of eigenstates as a function of disorder for non-interacting model. Further, we study the time-evolution of a wave-packet in different regimes of disorder and see the effect of interaction on it.In a recent experiment, Anderson localization was observed directly for non-interacting Bose-Einstein Condensate in one dimension. The experiment was performed using quasiperiodic optical lattice. Their system can be described by the one-dimensional noninteracting Aubry-Andr�e model. This model which simulates disorder with its quasiperiodic potential shows transition from extended to localised states at a critical disorder strength. The ground state gets localised around a single point for disorder larger than the critical value. We find that while inverse participation ratio increases as we increase disorder and rises to one in insulator phase, super uid fraction decreases as we increase disorder and goes to zero sharply in the insulator phase . When we introduce weak repulsive interaction for Bose gas in the model at the mean field level, we see that the ground-state shows multiple-site localization for certain disorder range, which lies above the critical value. For given interaction strength, we find that the inverse participation ratio increases slowly and super uid fraction decreases slowly as we increase disorder. Moreover, by representing our model as a classical two-dimensional nonlinear Hamiltonian map, we distinguish between localised and extended states by studying the trajectories in phase-space. Using this, we find out the localization length of eigenstates as a function of disorder for non-interacting model. Further, we study the time-evolution of a wave-packet in different regimes of disorder and see the effect of interaction on it.

Apr 1, 20150 citations

Observing the two-dimensional Bose glass in an optical quasicrystal

Jr-Chiun Yu, Shaurya Bhave, Lee Reeve +2 more

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.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.

NatureSep 11, 202438 citations

Noise correlation scalings: Revisiting the quantum phase transition in incommensurate lattices with hard-core bosons

Kai He, Indubala I. Satija, Charles W. Clark +2 more

Finite size scalings of the momentum distribution and noise correlations are performed to study Mott insulator, Bose glass, and superfluid quantum phases in hard-core bosons (HCBs) subjected to quasiperiodic disorder. The exponents of the correlation functions at the superfluid to Bose-glass (SF-BG) transition are found to be approximately one half of the ones that characterize the superfluid phase. The derivatives of the peak intensities of the correlation functions with respect to quasiperiodic disorder are shown to diverge at the SF-BG critical point. This behavior does not occur in the corresponding free fermion system, which also exhibits an Anderson-like transition at the same critical point and thus provides a unique experimental tool to locate the phase transition in interacting bosonic systems. We also report on the absence of primary sublattice peaks in the momentum distribution of the superfluid phase for special fillings.Finite size scalings of the momentum distribution and noise correlations are performed to study Mott insulator, Bose glass, and superfluid quantum phases in hard-core bosons (HCBs) subjected to quasiperiodic disorder. The exponents of the correlation functions at the superfluid to Bose-glass (SF-BG) transition are found to be approximately one half of the ones that characterize the superfluid phase. The derivatives of the peak intensities of the correlation functions with respect to quasiperiodic disorder are shown to diverge at the SF-BG critical point. This behavior does not occur in the corresponding free fermion system, which also exhibits an Anderson-like transition at the same critical point and thus provides a unique experimental tool to locate the phase transition in interacting bosonic systems. We also report on the absence of primary sublattice peaks in the momentum distribution of the superfluid phase for special fillings.

arXiv:1201.2740Physical Review AJan 11, 201217 citations

Localization versus incommemsurability for finite boson system in one-dimensional disordered lattice

Barnali Chakrabarti, A. Gammal

We explore the effect of disorder on a few-boson system in a finite one-dimensional quasiperiodic potential covering the full interaction ranging from uncorrelated to strongly correlated particles. We apply numerically exact multiconfigurational time-dependent Hartree for bosons to obtain the few-body emergent states in a finite lattice for both commensurate and incommensurate filling factors. The detailed characterization is done by the measures of one- and two-body correlations, fragmentation, order parameter. For commensurate filling, we trace the conventional fingerprints of disorder induced localization in the weakly interacting limit, however we observe robustness of fragmented and strongly correlated Mott in the disordered lattice. For filling factor smaller than one, we observe existing delocalization fraction of particles interplay in a complex way. For strongly interacting limit, the introduced disorder drags the fragmented superfluid of primary lattice to Mott localization. For filling factor larger than one in the primary lattice, the extra delocalization always resides on commensurate background of Mott-insulator. We observe beyond Bose-Hubbard physics in the fermionization limit when the pairing bosons fragment into two orbitals -- Mott dimerization happens. The introduced disorder first relocates the dimers, then strong disorder starts to interfere with the background Mott correlation. These findings unlock a rich landscape of unexplored localization process in the quasiperiodic potentials and pave the way for engineering exotic quantum many-body states with ultracold atoms.We explore the effect of disorder on a few-boson system in a finite one-dimensional quasiperiodic potential covering the full interaction ranging from uncorrelated to strongly correlated particles. We apply numerically exact multiconfigurational time-dependent Hartree for bosons to obtain the few-body emergent states in a finite lattice for both commensurate and incommensurate filling factors. The detailed characterization is done by the measures of one- and two-body correlations, fragmentation, order parameter. For commensurate filling, we trace the conventional fingerprints of disorder induced localization in the weakly interacting limit, however we observe robustness of fragmented and strongly correlated Mott in the disordered lattice. For filling factor smaller than one, we observe existing delocalization fraction of particles interplay in a complex way. For strongly interacting limit, the introduced disorder drags the fragmented superfluid of primary lattice to Mott localization. For filling factor larger than one in the primary lattice, the extra delocalization always resides on commensurate background of Mott-insulator. We observe beyond Bose-Hubbard physics in the fermionization limit when the pairing bosons fragment into two orbitals -- Mott dimerization happens. The introduced disorder first relocates the dimers, then strong disorder starts to interfere with the background Mott correlation. These findings unlock a rich landscape of unexplored localization process in the quasiperiodic potentials and pave the way for engineering exotic quantum many-body states with ultracold atoms.

arXiv:2502.14440Feb 20, 20251 citation

T=0

Bose-glass phase is preserved up to a crossover temperature that depends on the disorder strength. Furthermore, in the absence of disorder, we show how quasiexact finite-

T

DMRG computations, compared to experimental results, can be employed to estimate the temperature, which is not directly accessible in the experiment.