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New Journal of Physics

Inhomogeneous broadening of a Mott insulator spectrum

Vera Guarrera, L. Fallani, Jessica Lye, C. Fort, M. Inguscio

Published Apr 27, 2007• 39 citations
Publisher

Abstract

We report an analysis of the inhomogeneous broadening of the excitation spectrum of a three-dimensional (3D) Mott insulator (MI) due to the presence of weak disorder. We present a theoretical model predicting the modification in the spectrum and compare the results to the experimental data obtained for a system of ultracold 87 Rb atoms in a 3D optical lattice, where quasi-disorder is added by means of an auxiliary 1D optical lattice with non-commensurate wavelength. The model shows good agreement with the measured points, confirming a significant broadening of the MI spectrum resonances even for a very small height of the disordering potential.

DOI
10.1088/1367-2630/9/4/107

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We report an analysis of the inhomogeneous broadening of the excitation spectrum of a three-dimensional (3D) Mott insulator (MI) due to the presence of weak disorder. We present a theoretical model predicting the modification in the spectrum and compare the results to the experimental data obtained for a system of ultracold 87 Rb atoms in a 3D optical lattice, where quasi-disorder is added by means of an auxiliary 1D optical lattice with non-commensurate wavelength. The model shows good agreement with the measured points, confirming a significant broadening of the MI spectrum resonances even for a very small height of the disordering potential.
In recent years ultracold atoms in optical lattices have been extensively employed as quantum simulators to study the physics of conventional solid state systems. Due to the possibility of introducing controlled disorder, it appears now a straightforward progression to use ultracold atoms in optical potentials to also study the physics of complex systems. We experimentally study a system of bosonic 87Rb atoms in a 3D optical lattice, where disorder is introduced on the length scale of the lattice sites by using an auxiliary optical lattice with a non‐commensurate wavelength. Increasing the amount of disorder, we observe the transition from a Mott Insulator state to a novel gapless insulating phase induced by the cooperation of interactions and disorder, which could be identified with a Bose Glass phase. We discuss the experimental results as well as possible additional techniques for a better diagnostic of the system and future implementations of the two‐color lattices in the study of different disorder‐induced phenomena.
We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasiperiodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the noncommensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly, we find that a perturbative treatment in both cases, weak and strong disorders, gives a good description at all frequencies. In particular, we find that the infrared-absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected since for other quantities, like the conductivity in one-dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems and, in particular, the effect of the harmonic trap.
We use a bichromatic optical lattice to experimentally realize a disordered system of ultracold strongly interacting 87Rb bosons. In the absence of disorder, the atoms are pinned by repulsive interactions in the sites of an ideal optical crystal, forming one-dimensional Mott-insulator states. We measure the excitation spectrum of the system as a function of disorder strength and characterize its phase-coherence properties with a time-of-flight technique. Increasing disorder, we observe a broadening of the Mott-insulator resonances and the transition to a state with vanishing long-range phase coherence and a flat density of excitations, which suggest the formation of a Bose-glass phase.
We prepare and study a metastable attractive Mott-insulator state formed with bosonic atoms in a three-dimensional optical lattice. Starting from a Mott insulator with Cs atoms at weak repulsive interactions, we use a magnetic Feshbach resonance to tune the interactions to large attractive values and produce a metastable state pinned by attractive interactions with a lifetime on the order of 10 s. We probe the (de)excitation spectrum via lattice modulation spectroscopy, measuring the interaction dependence of two- and three-body bound-state energies. As a result of increased on-site three-body loss we observe resonance broadening and suppression of tunneling processes that produce three-body occupation.
We present a detailed analysis of the dynamical response of ultracold bosonic atoms in a one-dimensional optical lattice subjected to a periodic modulation of the lattice depth. Following the experimental realization by Stöferle et al (2004 Phys. Rev. Lett. 92 130403), we study the excitation spectrum of the system as revealed by the response of the total energy as a function of the modulation frequency Ω. By using the Time Evolving Block Decimation algorithm, we are able to simulate one-dimensional systems comparable in size to those in the experiment, with harmonic trapping and across many lattice depths ranging from the Mott-insulator (MI) to the superfluid (SF) regime. Our results produce many of the features seen in the experiment, namely a broad response in the SF regime, and narrow discrete resonances in the MI regime. We identify several signatures of the SF–MI transition that are manifested in the spectrum as it evolves from one limit to the other.