Ruichao Ma

Quantum simulation of antiferromagnetic spin chains in an optical lattice

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications for systems ranging from high-temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers, owing to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we use a degenerate Bose gas of rubidium atoms confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary a magnetic field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase, the interaction between the spins is overwhelmed by the applied field, which aligns the spins. In the antiferromagnetic phase, the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, thereby improving our understanding of real magnetic materials.

Probing the Superfluid–to–Mott Insulator Transition at the Single-Atom Level

From Superfluid to Mott Insulator One of the most attractive characteristics of cold atomic gases in optical lattices is their ability to simulate condensed-matter systems. The results of these quantum simulations are usually averaged over the atomic ensemble, or course-grained over several lattice sites. Now, Bakr et al. (p. 547, published online 17 June; see the Perspective by DeMarco) provide a single lattice site view onto the transition of a Bose gas of Rb-87 from the superfluid to the Mott-insulating state. Characteristic concentric shells of uniform number density were observed deep in the Mott insulator regime, and probing the local quantum dynamics revealed unexpectedly short time scales. The low-defect Mott structures identified may provide a starting point for quantum magnetism experiments. Imaging of atoms that were optically trapped in lattice sites reveals local dynamics of a quantum phase transition. Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We used single atom–single lattice site imaging to investigate the Bose-Hubbard model on a microscopic level. Our technique enables 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 time scales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low-entropy phases in a lattice.

Measuring entanglement entropy in a quantum many-body system.

Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.

Orbital excitation blockade and algorithmic cooling in quantum gases

Interaction blockade occurs when strong interactions in a confined, few-body system prevent a particle from occupying an otherwise accessible quantum state. Blockade phenomena reveal the underlying granular nature of quantum systems and allow for the detection and manipulation of the constituent particles, be they electrons, spins, atoms or photons. Applications include single-electron transistors based on electronic Coulomb blockade and quantum logic gates in Rydberg atoms. Here we report a form of interaction blockade that occurs when transferring ultracold atoms between orbitals in an optical lattice. We call this orbital excitation blockade (OEB). In this system, atoms at the same lattice site undergo coherent collisions described by a contact interaction whose strength depends strongly on the orbital wavefunctions of the atoms. We induce coherent orbital excitations by modulating the lattice depth, and observe staircase-like excitation behaviour as we cross the interaction-split resonances by tuning the modulation frequency. As an application of OEB, we demonstrate algorithmic cooling of quantum gases: a sequence of reversible OEB-based quantum operations isolates the entropy in one part of the system and then an irreversible step removes the entropy from the gas. This technique may make it possible to cool quantum gases to have the ultralow entropies required for quantum simulation of strongly correlated electron systems. In addition, the close analogy between OEB and dipole blockade in Rydberg atoms provides a plan for the implementation of two-quantum-bit gates in a quantum computing architecture with natural scalability.

Photon-Assisted Tunneling in a Biased Strongly Correlated Bose Gas

We study the impact of coherently generated lattice photons on an atomic Mott insulator subjected to a uniform force. Analogous to an array of tunnel-coupled and biased quantum dots, we observe sharp, interaction-shifted photon-assisted tunneling resonances corresponding to tunneling one and two lattice sites either with or against the force and resolve multiorbital shifts of these resonances. By driving a Landau-Zener sweep across such a resonance, we realize a quantum phase transition between a paramagnet and an antiferromagnet and observe quench dynamics when the system is tuned to the critical point. Direct extensions will produce gauge fields and site-resolved spin flips, for topological physics and quantum computing.

Ultra-precise holographic beam shaping for microscopic quantum control

High-resolution addressing of individual ultracold atoms, trapped ions or solid state emitters allows for exquisite control in quantum optics experiments. This becomes possible through large aperture magnifying optics that project microscopic light patterns with diffraction limited performance. We use programmable amplitude holograms generated on a digital micromirror device to create arbitrary microscopic beam shapes with full phase and amplitude control. The system self-corrects for aberrations of up to several λ and reduces them to λ/50, leading to light patterns with a precision on the 10-4 level. We demonstrate aberration-compensated beam shaping in an optical lattice experiment and perform single-site addressing in a quantum gas microscope for 87Rb.

Engineering Topological Many-Body Materials in Microwave Cavity Arrays

We present a scalable architecture for the exploration of interacting topological phases of photons in arrays of microwave cavities, using established techniques from cavity and circuit quantum electrodynamics. A time-reversal symmetry breaking (non-reciprocal) flux is induced by coupling the microwave cavities to ferrites, allowing for the production of a variety of topological band structures including the

Autonomous stabilizer for incompressible photon fluids and solids

\alpha=1/4

Quarter-flux Hofstadter lattice in a qubit-compatible microwave cavity array

Hofstadter model. Effective photon-photon interactions are included by coupling the cavities to superconducting qubits, and are sufficient to produce a

Hamiltonian tomography of photonic lattices

\nu=1/2