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.
Microscopy of the interacting Harper-Hofstadter model in the few-body
The interplay of magnetic fields and interacting particles can lead to
exotic phases of matter exhibiting topological order and high degrees of
spatial entanglement. While these phases were discovered in a solid-state
setting, recent techniques have enabled the realization of gauge fields in
systems of ultracold neutral atoms, offering a new experimental paradigm for
studying these novel states of matter. This complementary platform holds
promise for exploring exotic physics in fractional quantum Hall systems due to
the microscopic manipulation and precision possible in cold atom systems.
However, these experiments thus far have mostly explored the regime of weak
interactions. Here, we show how strong interactions can modify the propagation
of particles in a 2xN, real-space ladder governed by the Harper-Hofstadter
model. We observe inter-particle interactions affect the populating of chiral
bands, giving rise to chiral dynamics whose multi-particle correlations
indicate both bound and free-particle character. The novel form of
interaction-induced chirality observed in these experiments demonstrates the
essential ingredients for future investigations of highly entangled
topological phases of many-body systems.
Experimental realization of a long-range antiferromagnet in the
Hubbard model with ultracold atoms
Many exotic phenomena in strongly correlated electron systems emerge from the
interplay between spin ordering and motional degrees of freedom. For example,
doping an antiferromagnet is expected to give rise to interesting phases
including pseudogap states, stripe-ordering and incommensurate spin order.
Ultracold fermions in optical lattices offer the potential to answer open
questions on the low-temperature regime of the doped Hubbard model, which is
thought to capture essential aspects of the cuprate superconductor phase
diagram but is numerically intractable in that parameter regime.
We have observed antiferromagnetic long-range order in a repulsively
interacting Fermi gas of Li-6 atoms on a 2D square lattice containing about 80
sites. At our lowest temperature of T/t=0.25, the ordered state is directly
detected from a peak in the spin structure factor and a diverging correlation
length of the spin correlation function. When doping away from half-filling
into a numerically intractable regime, we find that long-range order extends
to doping concentrations of about 15%. Our results open the path for a
controlled study of the low-temperature phase diagram of the Hubbard model.
Quantum thermalization through entanglement in an isolated many-body system
Statistical mechanics relies on the maximization of entropy in a system at
thermal equilibrium. However, an isolated quantum many-body system initialized
in a pure state remains pure during Schrödinger evolution, and in this sense
it has static, zero entropy. We experimentally studied the emergence of
statistical mechanics in a quantum state and observed the fundamental role of
quantum entanglement in facilitating this emergence. Microscopy of an evolving
quantum system indicates that the full quantum state remains pure, whereas
thermalization occurs on a local scale. We directly measured entanglement
entropy, which assumes the role of the thermal entropy in thermalization. The
entanglement creates local entropy that validates the use of statistical
physics for local observables. Our measurements are consistent with the
eigenstate thermalization hypothesis.
Site-resolved observations of antiferromagnetic correlations in the Hubbard model
Quantum many-body systems exhibiting magnetic correlations underlie a
wide variety of phenomena. High-temperature superconductivity, for example,
can arise from the correlated motion of holes on an antiferromagnetic Mott
insulator. Strongly correlated many-body systems can be realized using
ultracold fermionic atoms in optical lattices with a tunability that is
unparalleled in conventional solid-state systems.
Using our Fermi Gas Microscope with Li-6 atoms, we have observed
antiferromagnetic correlations in a Hubbard-regime optical lattice with
single-site resolution. Our detection technique relies on a selective
spin-removal technique and subsequent site-resolved imaging. This allows
measuring the spin correlation function, which is found to decay
exponentially. The extraordinary detection capabilities of the microscope also
allow us to study lattice loading dynamics affect and make comparisons to
theory at an unprecedented level of detail. Our temperatures are the lowest
reported in a Hubbard model system with cold atoms and approach the limits of
available numerical techniques. Our results demonstrate that quantum gas
microscopy is a powerful tool for studying fermionic quantum magnetism.
Greiner Lab members take home multiple awards at the 2016 ICAP Poster Session!
Anton and Matthew win awards for their posters on Probing
Antiferromagnetic Ordering and Dynamics with the Fermi Gas Microscope and
Quantum Thermalization in an isolated many-body system, respectively.
Site-resolved imaging of a fermionic Mott insulator
Conventional band theory predicts an insulating behavior of a solid if
the freely moving electrons occupy every possible quantum state in the
highest energy band, whereas the state is conducing otherwise. This
simple picture of band insulating and conducting metallic states is
altered in the presence of strong interactions, which can lead to an
insulating behavior even in the presence of a half-filled energy band.
These Mott insulators, named after the British physicist Sir Nevill F.
Mott, are one of the conceptually simplest examples of many-body
systems, where strong correlations lead to surprising phenomena.
We have observed fermionic Mott insulators, metals and band insulators
with single-site resolution by trapping a repulsively interacting,
two-component mixture of Li-6 atoms in a square optical lattice. We
observe large, defect-free 2D Mott insulators containing more than 400
atoms with an average entropy per particle of 1.0kB.
The images above show single-shot picture of the atomic distribution for
varying interactions U/t, along with the deconvolved images in the
bottom row. The metallic state (left picture) is characterized by a
large occupation variance, the band insulating region appears as a core
of empty sites (middle picture) and the Mott insulator is signaled by an
extended region of constant occupation with one particle per site and
strongly reduced occupation variance (right picture and ring in middle
Measuring entanglement entropy in a quantum many-body system
Entanglement in the ground state of the Bose–Hubbard model. We study the transition from Mott insulator to superfluid with four atoms on four lattice sites in the ground state of the Bose–Hubbard model.
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.
Using a novel single-site addressing scheme, we study the quantum walks of individual and interacting bosonic atoms in an optical lattice. Top: An individual particle, initially localized to one lattice site, performs a free quantum walk and delocalizes over 20 lattice sites (left). An applied gradient reveals the excellent coherence of this motion, forcing the particle to undergo Bloch oscillations in position space (right).
Bottom: We deterministically add more particles to the system, and observe their dynamics with single-particle resolution. We directly detect bosonic bunching in a Hanbury Brown-Twiss experiment of two bosons, and observe the emergence of fermion-type correlations when the repulsive interactions become strong. Our work opens the door to the study of condensed matter problems using quantum walks of interacting particles.
"Probing the superfluid to Mott insulator transition at the single atom level" wins the 2011 AAAS Newcomb Cleveland Prize!
Quantum Magnetism in an Optical lattice. (a) Two spin chains, one
paramagnetically ordered (back), and one antiferromagnetically ordered
(front). The background is a single-shot image from the quantum gas
microscope, demonstrating the scalability of this approach. (b)
Strong magnetic interactions and fast dynamics are realized by mapping
the position degree of freedom of each atom onto the state of a single
spin 1/2 particle. By adiabatically tuning the tilt (E/U) of the
lattice, we drive a phase transition from a paramagnetically ordered
(Mott) state, to an antiferromagnetically ordered state with
density-wave (DW) ordering. Because the DW ordered state is contains
sites with occupations of only n=2,0, it appears dark (podd~0), while
the Mott state appears bright (podd~1). This first demonstration of
quantum magnetism in a lattice should open new perspectives for
studies of criticality, and high temperature superconductivity, with
cold atoms. The work uses a theoretical proposal by Prof. Subir Sachdev
and collaborators, PRB 66, 075128 (2002).
News: Single atom imaging of Mott insulator selected as a top breakthrough of this year by Science
Mott insulator (MI) in a Quantum Gas Microscope. (a) Sketch of Quantum Gas Microscope, enabling high fidelity single lattice site imaging. (b) Mott insulator shell structure with n=1 MI (bright ring), surrounding a n=2 MI core (dark). (c) near perfect n=1 Mott insulator.
Experimentally observed Mott shells (averaged) for increasing atom number.
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.