Welcome to the Greiner group website! We study ultracold gases loaded into artificial crystals of light known as optical lattices. The behavior of ultracold atoms in optical lattices is similar to that of electrons in solids. Because of that, ultracold atoms can provide clean realizations of models from condensed matter which can be studied in a highly controlled environment.

We developed a novel microscopy technique that allows us to image atoms in optical lattices with submicron and single-site optical resolution. Our experiments with bosonic rubidium and fermionic lithium are at the interface of atomic physics, condensed matter physics and quantum information. Find out more about our current work by following the links below.

# News

## Microscopy of the interacting Harper-Hofstadter model in the few-body limit

Nature 546, 519-523 (2017) | arXiv:1612.05631 |

## Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms

Nature 545, 462-466 (2017) | arXiv:1612.08436 |

## Quantum thermalization through entanglement in an isolated many-body system

arXiv:1603.04409 | Science 353, 6301, 794-800 (2016) |

## Site-resolved observations of antiferromagnetic correlations in the Hubbard model

arXiv:1605.02704 | Science 353, 6305, 1253-1256 (2016) |

## Measuring entanglement entropy in a quantum many-body system

We directly measure entanglement entropy in a quantum many-body system, leveraging our single-site-resolved control over bosonic atoms in an optical lattice afforded by the quantum gas microscope. We observe the growth of spatial entanglement between subsystems as the atoms, initially localized in a Mott insulator phase, tunnel between subsystems establishing quantum correlations between them.

In our experiments, entanglement between subsystems of a quantum many-body system is quantified by entanglement entropy. The entanglement entropy of a subsystem originates from the loss of information contained in its correlations with the remainder of the system, when we trace over the remainder. For entangled subsystems, the measured entropy of either of them exceeds that of the full system - a fact that cannot be explained by classical correlations alone.

We measure second-order Renyi entanglement entropy by preparing two independent and identical copies of a quantum many-body state of four bosons on four lattice sites. The copies are then interfered with each other, and the resulting atom numbers (odd or even) at each site are measured with our high resolution microscope. Analogous to the celebrated Hong-Ou-Mandel interference of two identical single photon states on a beam splitter, two identical many-body bosonic states interfere to produce even number of bosons in the output ports. Thus, the resulting average atom number parity quantifies the purity of the many-body state. This quantum purity is directly related to the second-order Renyi entropy.

These experiments pave the way for investigating quantum many-body physics using entanglement entropy. For large systems, entanglement entropy gives valuable information about the underlying quantum phase of matter, and signals the existence of quantum phase transitions. Entanglement entropy is also a valuable tool to investigate non-equilibrium states of quantum matter.

arXiv:1509.01160 | Nature 528, 77-83 (2015) |

## Strongly Correlated Quantum Walks in Optical Lattices

Science Link | Science Perspective | Arxiv Version |

## "Probing the superfluid to Mott insulator transition at the single atom level" wins the 2011 AAAS Newcomb Cleveland Prize!

Paper | Press release |

## Markus is now a Professor of Physics!

## Orbital Excitation Blockade and Algorithmic Cooling in Quantum Gases

*Nature* DOI: 10.1038/nature10668

Paper | Press release | Nature News and Views | ScienceBlog review |

## Markus wins a MacArthur Fellowship!

MacArthur Foundation Press Release | MacArthur Foundation Profile | Harvard Gazette Article | boston.com Article |

## Quantum simulation of antiferromagnetic spin chains in an optical lattice

*Nature* DOI: 10.1038/nature09994

Paper | Press release | Harvard Gazette Article | Theoretical Proposal | Nature News and Views |

## Probing the superfluid to Mott insulator transition at the single atom level

*Science* DOI: 10.1126/science.1192368

Paper | Press release | Physics Today review | Science perspective | ScienceBlog review |

#### News: Single atom imaging of Mott insulator selected as a top breakthrough of this year by Science

The Quantum Gas Microscope enables high fidelity detection of single atoms in a Hubbard-regime optical lattice, bringing ultracold atom research to a new, microscopic level. We investigate the Bose-Hubbard model using space- and time-resolved characterization of the number statistics across the superfluid - Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition timescales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and open new possibilities for realizing and probing quantum magnetism.