Graduate Student, Harvard University
Ultra cold atomic quantum gases used to study exotic condensed matter phenomena
My research applies the refined tools of studying atomic systems to the complicated unsolved models developed in condensed matter systems. These tools give a precise way to probe how the sometimes rather simple models can give rise to exotic phenomena such as superconductivity. The process of using well understood quantum system to solve a more complicated one was championed by Richard Feynman as a method to solve problems too difficult too calculate. He coined the name "quantum simulation" for this method. A simple analogy to this method is exemplified by how analog simulations are sometimes used to calculate the answer for a desired problem. A simple example would be how a simple system, such as a rubber band stretched around two points on a surface, will naturally contract to the shortest distance between the two points. While this simple example can be solved by some geometry for flat surfaces, it becomes a bit more complicated for a curved surface such as a globe. The rubber bands simple system properties, that are well understood, enable someone to solve more complicated problems that may not be as readily solvable. This is conceptually the same as what we do with ultra cold atoms in condensed matter models. Many condensed matter models are used to describe how electrons behave in semiconductor materials by hopping from ion to ion in the semiconductor crystal structure. We simulate this in our system by projecting an optical lattice, or crystal of laser light, that acts as our semiconductor crystal. Our ultra cold atoms hop from site-to-site in this optical lattice simulating the electron movement in the crystal. We additionally have the ability to prepare specific initializations of these experiment and then actually image optically where the atoms are in the lattice. This would be akin to measuring which atom an electron had hopped to, which is simply not possible in the real material systems and therefore make it difficult to probe what exactly in the model contribute to celebrated, nobel prize winning physical phenomena such as super conductivity or the fractional quantum Hall effect. Our most recent work has combined the necessary ingredients for simulating these exotic phases of matter from the ground up. By adding these ingredients one at a time we study how the model leads to the phenomena and then read out the system with a high resolution imaging system. The control of our system affords us the ability to uniquely study such phenomena.
Abstract: We study the ground states of 2D lattice bosons in an artificial gauge field. Using state of the art DMRG simulations we obtain the zero temperature phase diagram for hardcore bosons at densities $n_b$ with flux $n_\phi$ per unit cell, which determines a filling $\nu=n_b/n_\phi$. We find several robust quantum Hall phases, including (i) a bosonic integer quantum Hall phase (BIQH) at $\nu=2$, that realizes an interacting symmetry protected topological phase in 2D (ii) bosonic fractional quantum Hall phases including robust states at $\nu=2/3$ and a Laughlin state at $\nu=1/2$. The observed states correspond to the bosonic Jain sequence ($\nu=p/(p+1)$) pointing towards an underlying composite fermion picture. In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation beginning in the independent chain limit of 1D Luttinger liquids, and ramping up interchain couplings. Using time dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. We utilize a simple physical signature of these phases, the non-monotonic behavior of a two-point correlation, a direct consequence of edge states in a finite system, to numerically assess the effectiveness of the preparation scheme. Our proposal only utilizes existing experimental capabilities.
Pub.: 01 Mar '17, Pinned: 29 Jun '17
Abstract: Exotic phenomena in systems with strongly correlated electrons emerge from the interplay between spin and motional degrees of freedom. For example, doping an antiferromagnet is expected to give rise to pseudogap states and high-temperature superconductors. Quantum simulation using ultracold fermions in optical lattices could help to answer open questions about the doped Hubbard Hamiltonian, and has recently been advanced by quantum gas microscopy. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a two-dimensional square lattice of about 80 sites at a temperature of 0.25 times the tunnelling energy. The antiferromagnetic long-range order manifests through the divergence of the correlation length, which reaches the size of the system, the development of a peak in the spin structure factor and a staggered magnetization that is close to the ground-state value. We hole-dope the system away from half-filling, towards a regime in which complex many-body states are expected, and find that strong magnetic correlations persist at the antiferromagnetic ordering vector up to dopings of about 15 per cent. In this regime, numerical simulations are challenging and so experiments provide a valuable benchmark. Our results demonstrate that microscopy of cold atoms in optical lattices can help us to understand the low-temperature Fermi-Hubbard model.
Pub.: 26 May '17, Pinned: 29 Jun '17
Abstract: 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.
Pub.: 20 Aug '16, Pinned: 29 Jun '17
Abstract: Full control over the dynamics of interacting, indistinguishable quantum particles is an important prerequisite for the experimental study of strongly correlated quantum matter and the implementation of high-fidelity quantum information processing. We demonstrate such control over the quantum walk-the quantum mechanical analog of the classical random walk-in the regime where dynamics are dominated by interparticle interactions. Using interacting bosonic atoms in an optical lattice, we directly observed fundamental effects such as the emergence of correlations in two-particle quantum walks, as well as strongly correlated Bloch oscillations in tilted optical lattices. Our approach can be scaled to larger systems, greatly extending the class of problems accessible via quantum walks.
Pub.: 15 Mar '15, Pinned: 28 Jun '17
Abstract: 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.
Pub.: 02 Dec '15, Pinned: 28 Jun '17
Abstract: Philip Zupancic, Philipp M. Preiss, Ruichao Ma, Alexander Lukin, M. Eric Tai, Matthew Rispoli, Rajibul Islam, Markus GreinerHigh-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 ... [Opt. Express 24, 13881-13893 (2016)]
Pub.: 27 Jun '16, Pinned: 28 Jun '17
Abstract: The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement. Although these phases were discovered in a solid-state setting, recent innovations in systems of ultracold neutral atoms-uncharged atoms that do not naturally experience a Lorentz force-allow the synthesis of artificial magnetic, or gauge, fields. This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in cold-atom systems. However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated many-body states. Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a two-body system with a chiral band structure. We observe and explain the way in which interparticle interactions induce chirality in the propagation dynamics of particles in a ladder-like, real-space lattice governed by the interacting Harper-Hofstadter model, which describes lattice-confined, coherently mobile particles in the presence of a magnetic field. We use a bottom-up strategy to prepare interacting chiral quantum states, thus circumventing the challenges of a top-down approach that begins with a many-body system, the size of which can hinder the preparation of controlled states. Our experimental platform combines all of the necessary components for investigating highly entangled topological states, and our observations provide a benchmark for future experiments in the fractional quantum Hall regime.
Pub.: 24 Jun '17, Pinned: 28 Jun '17
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