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Register a new userCorrelation function of weakly interacting bosons in a disordered lattice
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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 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 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.
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Disorder can profoundly affect the transport properties of a wide range of quantum materials. Presently, there is significant disagreement regarding the effect of disorder on transport in the disordered Bose-Hubbard (DBH) model, which is the paradigm used to theoretically study disorder in strongly correlated bosonic systems. We experimentally realize the DBH model by using optical speckle to introduce precisely known, controllable, and fine-grained disorder to an optical lattice5. Here, by measuring the dissipation strength for transport, we discover a disorder-induced SF-to-insulator (IN) transition in this system, but we find no evidence for an IN-to-SF transition. Emergence of the IN at disorder strengths several hundred times the tunnelling energy agrees with a predicted SF--Bose glass (BG) transition from recent quantum Monte Carlo (QMC) work. Both the SF--IN transition and correlated changes in the atomic quasimomentum distribution--which verify a simple model for the interplay of disorder and interactions in this system--are phenomena new to the unit filling regime explored in this work, compared with the high filling limit probed previously. We find that increasing disorder strength generically leads to greater dissipation in the regime of mixed SF and Mott-insulator (MI) phases, excluding predictions of a disorder-induced, or re-entrant, SF (RSF). While the absence of an RSF may be explained by the effect of finite temperature, we strongly constrain theories by measuring bounds on the entropy per particle in the disordered lattice.
Disorder, prevalent in nature, is intimately involved in such spectacular effects as the fractional quantum Hall effect and vortex pinning in type-II superconductors. Understanding the role of disorder is therefore of fundamental interest to materials research and condensed matter physics. Universal behavior, such as Anderson localization, in disordered non-interacting systems is well understood. But, the effects of disorder combined with strong interactions remains an outstanding challenge to theory. Here, we experimentally probe a paradigm for disordered, strongly-correlated bosonic systems-the disordered Bose-Hubbard (DBH) model-using a Bose-Einstein condensate (BEC) of ultra-cold atoms trapped in a completely characterized disordered optical lattice. We determine that disorder suppresses condensate fraction for superfluid (SF) or coexisting SF and Mott insulator (MI) phases by independently varying the disorder strength and the ratio of tunneling to interaction energy. In the future, these results can constrain theories of the DBH model and be extended to study disorder for strongly-correlated fermionic particles.
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting fermionic atoms in a disordered optical lattice. We find that the topological Anderson and Mott insulators in the noninteracting and clean limits can be adiabatically connected without gap closing in the phase diagram of our model. Lying between the two phases, we uncover a disordered correlated topological insulator, which is induced from a trivial band insulator by the combination of disorder and interaction, as the generalization of topological Anderson insulators to the many-body interacting regime. The phase diagram is determined by computing various topological properties and confirmed by unsupervised and automated machine learning. We develop an approach to provide a unified and clear description of topological phase transitions driven by interaction and disorder. The topological phases can be detected from disorder/interaction induced edge excitations and charge pumping in optical lattices.
We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap, and focus on states at the Lowest Landau Level (LLL). At linear order in the coupling parameter $g$, we exploit the rich algebraic structure of the problem to give an explicit construction of a large family of quantum states with energies of the form $E_0+gE_1/4+O(g^2)$, where $E_0$ and $E_1$ are integers. As a result, any superposition of these states evolves periodically with a period of at most $8pi/g$ until, at much longer time scales of order $1/g^2$, corrections to the energies of order $g^2$ become important and may upset this perfectly periodic behavior. We further construct coherent-like combinations of these states that naturally connect to classical dynamics in an appropriate regime, and explain how our findings relate to the known time-periodic features of the corresponding weakly nonlinear classical theory. We briefly comment on possible generalizations of our analysis to other numbers of spatial dimensions and other analogous physical systems.
We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap. When the interactions are turned off, the energy levels are equidistant and highly degenerate. At linear order in the coupling parameter, these degenerate levels split, and we study the patterns of this splitting. It turns out that the problem is mathematically identical to diagonalizing the quantum resonant system of the two-dimensional Gross-Pitaevskii equation, whose classical counterpart has been previously studied in the mathematical literature on turbulence. Our purpose is to explore the implications of the symmetries and energy bounds of this resonant system, previously studied for the classical case, for the quantum level splitting. Simplifications in computing the splitting spectrum numerically result from exploiting the symmetries. The highest energy state emanating from each unperturbed level is explicitly described by our analytics. We furthermore discuss the energy level spacing distributions in the spirit of quantum chaos theory. After separating the eigenvalues into blocks with respect to the known conservation laws, we observe the Wigner-Dyson statistics within specific large blocks, which leaves little room for further integrable structures in the problem beyond the symmetries that are already explicitly known.
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