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arXiv:1309.3890 · Physical Review A

Single-site-resolved measurement of the current statistics in optical lattices

Stefan Keßler, Florian Marquardt

Published Jun 3, 2014• 37 citations
arXivHTMLPDF

Abstract

At present, great effort is spent on the experimental realization of gauge fields for quantum many-body systems in optical lattices. At the same time, the single-site-resolved detection of individual atoms has become a new powerful experimental tool. We discuss a protocol for the single-site-resolved measurement of the current statistics of quantum many-body systems, which makes use of a bichromatic optical superlattice and single-site detection. We illustrate the protocol by a numerical study of the current statistics for interacting bosons in one and two dimensions and discuss the role of the on-site interactions for the current pattern and the ground-state symmetry for small two-dimensional lattices with artificial magnetic fields.

DOI
10.1103/physreva.89.061601

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At present, great effort is spent on the experimental realization of gauge fields for quantum many-body systems in optical lattices. At the same time, the single-site-resolved detection of individual atoms has become a new powerful experimental tool. We discuss a protocol for the single-site-resolved measurement of the current statistics of quantum many-body systems, which makes use of a bichromatic optical superlattice and single-site detection. We illustrate the protocol by a numerical study of the current statistics for interacting bosons in one and two dimensions and discuss the role of the on-site interactions for the current pattern and the ground-state symmetry for small two-dimensional lattices with artificial magnetic fields.
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Ultracold quantum gases in optical lattices provide a rich experimental toolbox for simulating the physics of condensed matter systems. With atoms in the lattice playing the role of electrons or Cooper pairs in real materials, it is possible to experimentally realize condensed matter Hamiltonians in a controlled way. To realize the full potential of such quantum simulations, we leverage a quantum gas microscope which can spatially resolve the atoms in the optical lattice at the single site level and project arbitrary potential landscapes onto the atoms by combining the high resolution optics with static holographic masks or a spatial light modulator. The versatility of this system allows for a wide range of studies. In this thesis, we focus on three experiments that highlight the utility of a tunable platform and demonstrate the richness of physics that comes with interactions.\nIn the first, we observe on-site interparticle interactions introduce a non-linearity into the many-body energy spectrum of a harmonic oscillator. The excitation of a single atom into a higher band induces an energy shift in the excitation energy for the second atom, blockading the orbital excitation. We demonstrate a technique for deterministic number filtering based upon orbital excitation blockade. When applied to a high temperature Mott insulator, this number filtering realizes a form of algorithmic cooling, which can be used for initializing a large quantum register or creating low entropy initial states for many-body simulation.\nIn the second, we study the applicability of statistical physics in an isolated system governed by quantum mechanics. While the descriptive power of these two fields has been confirmed through repeated and varied empirical studies, their underlying axioms of entropy maximization and unitary evolution appear mutually exclusive. With our quantum gas microscope, we have the ability to probe local observables such as the on-site number statistics as well as measure the quantum mechanical purity through interference operations. With these capabilities, we are able to observe the local thermalization of a manifestly quantum mechanically pure many-body system.\nIn the last chapter, we report on the first cold atoms studies of an interacting system under an artificial gauge field. We consider the propagation of a pair of atoms in a 2timesN2\\times N2timesN ladder governed by the Harper-Hofstadter model. The eigenstates of this system include both scattering states, which can exhibit chiral propagation, and bound states. A superexchange energy shift in our initial state leads to imbalanced population in the two chiral scattering sectors, leading to chiral propagation dynamics. This effect is the result of both the presence of interactions and the artificial gauge fields. These two components are essential ingredients for fractional quantum Hall physics. Moreover, the dynamic tunable gauge field we develop and the control afforded by a quantum gas microscope make this platform well-suited for future studies in this regime.
This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice. We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism. In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing scheme leaves most atoms in the vibrational ground state. Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available. The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.
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The Mott-insulator--superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions.