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arXiv:1409.1983 · Physica A Statistical Mechanics and its Applications

Lattice bosons in a quasi-disordered environment: The effects of a superlattice potential on single particle and many particle properties

R. Ramakumar, A. N. Das, S. Sil

Published May 21, 2015• 1 citation
arXivHTMLPDF
DOI
10.1016/j.physa.2015.05.079

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•Jan 1, 2008•0 citations
Abstract We uncover the interaction-induced stable self-localization of few bosons in finite-size disorder-free superlattices. In these nonthermalized multi-particle states, one of the particles forms a superposition of multiple standing waves, so that it provides a quasi-random potential to localize the other particles. We derive effective Hamiltonians for self-localized states and find their energy level spacings obeying the Poisson statistics. The spatial distribution of the localized particles decays exponentially, which is refered to Anderson-like localization (ALL). Surprisingly, we find that the correlated self-localization can be solely induced by interaction in the well-studied Bose–Hubbard models, which has been overlooked for a long time. We propose a dynamical scheme to detect self-localization, where long-time quantum walks of a single particle form a superposition of multiple standing waves for trapping the subsequently loaded particles. Our work provides an experimentally feasible way to realize stable ALL in translation-invariant disorder-free few-body systems.
We analyze the phase diagram of ultracold bosons in a one-dimensional superlattice potential with disorder, using the time-evolving block decimation algorithm for infinite-sized systems. For degenerate potential energies within the unit cell of the superlattice, loophole-shaped insulating phases with noninteger filling emerge with a particle-hole gap proportional to the boson hopping. Addition of a small amount of disorder destroys this gap. For not too large disorder, the loophole Mott regions detach from the axis of vanishing hopping, giving rise to insulating islands. Thus the system shows a transition from a compressible Bose glass to a Mott-insulating phase with increasing hopping amplitude. We present a straightforward effective model for the dynamics within a unit cell which provides a simple explanation for the emergence of Mott-insulating islands. In particular, it gives rather accurate predictions for the inner critical point of the Bose glass to Mott insulator transition.
In this thesis we investigate strongly-correlated states of ultracold bosonic atoms in rotating ring lattices and arrays of double-well potentials. In the first part of the thesis, we study the tunneling dynamics of ultracold bosons in double-well potentials. In the non-interacting limit single-particle transitions dominate, while in the interaction-dominated regime correlated tunneling of all particles prevails. At intermediate times of the many-particle flopping process correlated states occur, but the timescales of these processes increase dramatically with the number of particles. Using an array of double-well potentials, a large number of such few-particle superposition states can be produced in parallel. In the second part of the thesis, we study the effects of rotation on ultracold bosons confined to one-dimensional ring lattices. We find that at commensurate filling there exists a critical rotation frequency, at which the ground state of the weakly-interacting gas is fragmented into a macroscopic superposition of different quasi-momentum states. We demonstrate that the generation of such superposition states using slightly non-uniform ring lattices has several practical advantages. Moreover, we show that different quasi-momentum states can be distinguished in time-of-flight absorption imaging and propose to probe correlations via the many-body oscillations induced by a sudden change in the rotation frequency. Finally, we compare these macroscopic superposition states to those occurring in superconducting quantum interference devices. In the third part of the thesis, we demonstrate the creation of entangled states with ultracold bosonic atoms by dynamical manipulation of the shape of the lattice potential. To this end, we consider an optical superlattice that allows both the splitting of each site into a double-well potential and the variation of the height of the potential barrier between the sites. We show how to use this array of double-well potentials to perform entangling operations between neighboring qubits encoded on the Zeeman levels of the atoms. As one possible application, we present a method of realizing a resource state for measurement-based quantum computation via Bell-pair measurements. In the final part of the thesis, we study ultracold bosons on a two-dimensional square lattice in the presence of an effective magnetic field and point out a couple of features this system has in common with ultracold bosons in one-dimensional rotating ring lattices.