# The Quantum Gas Microscope

## New possibilities for quantum simulations of condensed matter models

Ultracold atomic systems can be used as quantum simulators to study a range of phenomena in strongly-correlated materials ranging from high-Tc superconductors to quantum magnets. The micron-scale spacing of atoms in these systems provides an opportunity to optically image fluctuations and correlations in strongly correlated systems in a way not possible in condensed matter. Our quantum gas microscopy (QGM) allows, for the first time, for optical imaging and manipulation of strongly-interacting quantum gases containing thousands of atoms at the single atom level. The ideas introduced in QGM are quite general and can be applied to a range of other systems including fermionic (See our Fermi Gas Microscope experiment) and dipolar gases (See our planned Erbium QGM). In addition, it provides a path to quantum computation in a system with a scalable architecture.

## Recent Experiments

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

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.

### 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.

### 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.

### Direct observation of strongly correlated quantum walks

We study two-particle quantum walk with strong interactions for ultracold bosonic atoms in an optical lattice. We directly measure the spatial correlations arising due to quantum statistics and interactions in multi-particle quantum walks and detect the “fermionization” of strongly repulsive bosons in one dimension. In the presence of a lattice tilt, we observe high-fidelity Bloch oscillations in position space and coherent dynamics of individual repulsively bound pairs. Our techniques, including the deterministic preparation offew-body states and the atom-resolved measurements of correlations, demonstrate quantum walks of ultracold atoms as a tool for the study of correlated many-body dynamics and potentially for quantum information processing.

### Preparing and Imaging Bilayer Quantum Gases

Here we create a toolbox for site-resolved detection and control of atoms in bilayer degenerate quantum gases. Using a collisional blockade, we engineer occupation-dependent inter-plane transport, enabling us to avoid parity projection during imaging and count n = 0 to n = 3 atoms per site. We obtain the first number- and site-resolved images of the Mott insulator “wedding cake” structure. Alternatively, we use the bilayer system for spin-resolved readout of a mixture of two hyperfine states. Potential applications include direct detection of entanglement and Kosterlitz-Thouless-type phase dynamics, as well as studies of coupled planar quantum systems.

### Orbital Excitation Blockade and Algorithmic Cooling in Quantum Gases

We report a new blockade effect that uses the orbital dependence of the interaction between bosons in optical lattices to manipulate the onsite occupation in a strongly interacting quantum gas. We induce coherent orbital excitations by lattice amplitude modulation and observe interaction-induced shifts in the modulation resonances. By sweeping the modulation frequency across several resonances we can deterministically remove atoms on individual sites based upon initial occupation. Using this number filtering approach, we have demonstrated algorithmic entropy removal from a high-temperature gas to the point that it Bose-condenses.

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

Here we present the first realization of quantum magnetism within an optical lattice. We study an Ising spin chain in both transverse and longitudinal fields. By mapping the spin degree of freedom onto dipolar excitations of a Mott Insulator in a tilted optical lattice, we achieve strong spin-spin interactions, and fast dynamics. By sweeping the lattice tilt, we demonstrate a phase-transition from a paramagnetic phase to an anti-ferromagnetic phase. We observe anti-ferromagnetic ordering both *in situ*, taking advantage of the single-site resolution of our quantum gas microscope, and via a 1D quantum noise correlation measurement.

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

Our quantum gas microscope enables high fidelity detection of single atom in optical lattices. 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, and enables us to measure local quantum dynamics and quantum correlations. We achieve low entropy Mott domains with >99% fidelity (corresponding to entropy per particle of order 0.05 kB, which serve as an ideal starting point for quantum simulation experiments.

# Publications:

Quantum thermalization through entanglement in an isolated many-body system

Science Vol. 353, Issue 6301, pp. 794-800 (2016)Ultra-precise holographic beam shaping for microscopic quantum control

Optics Express Vol. 24, Issue 13, pp. 13881-13893 (2016)Measuring entanglement entropy in a quantum many-body system

Nature 528, 77-83 (2015) (News & Views)Quantum gas microscopy with spin, atom-number, and multilayer readout

Phys. Rev. A. 91, 041602 (2015)Strongly correlated quantum walks in optical lattices

Science 347, 1229-1233 (2015)Orbital Excitation Blockade and Algorithmic Cooling in Quantum Gases

Nature 480, 500-503 (2011) (Press release)Photon-Assisted Tunneling in a Biased Strongly Correlated Bose Gas

Phys. Rev. Lett. 107, 095301 (2011)Quantum simulation of antiferromagnetic spin chains in an optical lattice

Nature 472, 307 (2011) (Press release)Probing the Superfluid-to-Mott Insulator Transition at the Single-Atom Level

Science 329, 547 (2010) (Press release)
Quantum Gas Microscope detecting single atoms in a Hubbard regime optical lattice

Nature 462 74-77 (2009).

Two dimensional quantum gas in a hybrid surface trap

Physical Review A 80 021602(R) 2009

The Quantum Gas Microscope

PhD. Thesis of Jonathon Gillen