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Title:  Quantum simulation in strongly correlated optical lattices 
Author(s):  Mckay, David 
Director of Research:  DeMarco, Brian L.; Thywissen, Joseph H. 
Doctoral Committee Chair(s):  Kwiat, Paul G. 
Doctoral Committee Member(s):  DeMarco, Brian L.; Thywissen, Joseph H.; Ceperley, David M.; Selvin, Paul R. 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Ultracold atoms
Quantum simulation Optical Lattice Hubbard model BoseHubbard FermiHubbard Rubidium87 (87Rb) Potassium40 (40K) SpinDependent Lattice Toolkit BoseEinstein condensate Superfluid MottInsulator Lattice Atomic Physics Laser cooling 
Abstract:  An outstanding problem in physics is how to understand strongly interacting quantum manybody systems such as the quarkgluon plasma, neutron stars, superfluid 4He, and the hightemperature superconducting cuprates. The physics approach to this problem is to reduce these complex systems to minimal models that are believed to retain relevant phenomenology. For example, the Hubbard model — the focus of this thesis — describes quantum particles tunneling between sites of a lattice with onsite interactions. The Hubbard model is conjectured to describe the lowenergy charge and spin properties of hightemperature superconducting cuprates. Thus far, there are no analytic solutions to the Hubbard model, and numerical calculations are difficult and even impossible in some regimes (e.g., the FermiHubbard model away from halffilling). Therefore, whether the Hubbard model is a minimal model for the cuprates remains unresolved. In the face of these difficulties, a new approach has emerged — quantum simulation. The premise of quantum simulation is to perform experiments on a quantum system that is welldescribed by the model we are trying to study, has tunable parameters, and is easily probed. Ultracold atoms trapped in optical lattices are an ideal candidate for quantum simulation of the Hubbard models. This thesis describes work on two such systems: a 87Rb (boson) optical lattice experiment in the group of Brian DeMarco at the University of Illinois to simulate BoseHubbard physics, and a 40K (fermion) optical lattice experiment in the group of Joseph Thywissen at the University of Toronto to simulate FermiHubbard physics. My work on the 87Rb apparatus focuses on three main topics: simulating the BoseHubbard (BH) model out of equilibrium, developing thermometry probes, and developing impurity probes using a 3D spindependent lattice. Theoretical techniques (e.g., QMC) are adept at describing the equilibrium properties of the BH model, but the dynamics are unknown — simulation is able to bridge this gap. We perform two experiments to simulate the BH model out of equilibrium. In the first experiment, published in Ref. [1], we measure the decay rate of the centerofmass velocity for a BoseEinstein condensate trapped in a cubic lattice. We explore this dissipation for different BoseHubbard parameters (corresponding to different lattice depths) and temperatures. We observe a decay rate that asymptotes to a finite value at zero temperature, which we interpret as evidence of intrinsic decay due to quantum tunneling of phase slips. The decay rate exponentially increases with temperature, which is consistent with a crossover from quantum tunneling to thermal activation. While phase slips are a wellknown dissipation mechanism in superconductors, numerous effects prevent unambiguous detection of quantum phase slips. Therefore, our measurement is among the strongest evidence for quantum tunneling of phase slips. In a second experiment, published in Ref. [2] with theory collaborators at Cornell University, we investigate condensate fraction evolution during fast (i.e., millisecond) ramps of the lattice potential depth. These ramps simulate the BH model with timedependent parameters. We determine that interactions lead to significant condensate fraction redistribution during these ramps, in agreement with meanfield calculations. This result clarifies adiabatic timescales for the lattice gas and strongly constrains bandmapping as an equilibrium probe. Another part of this thesis work involves developing thermometry techniques for the lattice gas. These techniques are important because the ability to measure temperature is required for quantum simulation and to evaluate inlattice cooling schemes. In work published in Ref. [3], we explore measuring temperature by directly fitting the quasimomentum distribution of a thermal lattice gas. We attempt to obtain quasimomentum distributions by bandmapping, a process in which the lattice depth is reduced slowly compared to the bandgap but fast with respect to all other timescales. We find that these temperature measurements fail when the thermal energy is comparable to the bandwidth of the lattice. This failure results from two main causes. First, the quasimomentum distribution is an insensitive probe at high temperatures because the band is occupied (i.e., additional thermal energy cannot be accommodated in the kinetic energy degrees of freedom). Second, the bandmapping process does not produce accurate quasimomentum distributions because of smoothing at the Brillouin zone edge. We determine that measuring temperature using the insitu width overcomes these issues. The insitu width does not asymptote to a finite value as temperature increases, and the insitu width can be measured directly without using a mapping procedure. In a second experiment, we investigate using condensate fraction (obtained from the timeofflight momentum distribution) as an indirect means to measure temperature in the superfluid regime of the BH model. Since no standard fitting procedure exists for the lattice timeofflight distributions, we define and test a procedure as part of this work. We measure condensate fraction for a range of lattice depths varying from deep in the superfluid regime to lattice depths proximate to the Mottinsulator transition. We also vary the entropy per particle, which is measured in the harmonic trap before adiabatically loading into the lattice. As expected, the condensate fraction increases as entropy decreases, and the condensate fraction decreases at high lattice depths (due to quantum depletion). We compare our experimental results to condensate fraction predicted by the noninteracting, HartreeFockBogoliubovPopov, and sitedecoupledmeanfield theories. Theory and experiment disagree, which motivates several future extensions to this work, including calculating condensate fraction (and testing our fit procedure) using quantum Monte Carlo numerics, and experimentally and theoretically investigating the dynamics of the lattice load process (for the finitetemperature strongly correlated regime). Finally, we develop impurity probes for the BoseHubbard model by employing a spindependent lattice. A primary accomplishment of this thesis work was to develop the first 3D spindependent lattice in the strongly correlated regime (published in Ref. [4]). The spindependent lattice depth is proportional to gFmF, enabling the creation of mixtures of atoms trapped in the lattice (nonzero mF) cotrapped with atoms that do not experience the lattice (mF = 0). We use the nonlattice atoms as an impurity probe. We investigate using the impurity to probe the lattice temperature, and we determine that thermalization between the impurity and lattice gas is suppressed for larger lattice depths. Using a comparison to a Fermi’s golden rule calculation of the collisional energy exchange rate, we determine that this effect is consistent with suppression of energyexchanging collisions by a mismatch between the impurity and lattice gas dispersion. While this result invalidates the concept of an impurity thermometer, it paves the way for a unique cooling scheme that relies on interspecies thermal isolation. We also explore impurity transport through the lattice gas. In other preliminary measurements, we also identify the decay rate of the centerofmass motion as a prospective impurity probe. A separate aspect of this thesis work is the design and construction of a new 40K apparatus for singlesite imaging of atoms to simulate the 2D FermiHubbard model. The main component of this apparatus is high resolution fluorescence imaging on the 4S5P transition of K at 404.5nm. Fluorescence imaging using this transition has two advantages over imaging on the standard D2 transition at 767nm: a smaller wavelength and therefore higher resolution, and a lower Doppler temperature limit which enables longer imaging times. To validate this approach, we demonstrate the first 40K magnetooptical trap (MOT) using the 404.5nm transition. 
Issue Date:  20130203 
URI:  http://hdl.handle.net/2142/42387 
Rights Information:  Copyright 2012 David McKay 
Date Available in IDEALS:  20130203 
Date Deposited:  201212 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois