A pinboard by
Matthew Rispoli

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.


Realizing and Adiabatically Preparing Bosonic Integer and Fractional Quantum Hall states in Optical Lattices

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

Microscopy of the interacting Harper-Hofstadter model in the two-body limit.

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