Session Q31: Focus Session: Quantum Simulation using AMO Systems

In Situ Observation of Quantum Phase Transition and Quantum Dynamics in Optical Lattices

Ultracold atoms in optical lattices constitute one of the cleanest systems for the realizations of quantum phase transition, a phase transition that occurs even at zero temperature. By tuning the optical lattice depth or the interaction between cold atoms, a weakly-interacting superfluid of atoms can be converted into a strongly correlated Mott insulator. Near the phase boundary, quantum criticality, resembling that of Ising-type magnetic systems in higher dimensions, is expected to emerge with a full universal behavior. Our in situ imaging technique for atoms in 2D optical lattices provides a powerful tool to capture the full quantum state of the many-body system, from the microscopic statistics of site occupancy to the macroscopic thermodynamics. I will describe our efforts to identify the superfluid-Mott insulator phase boundary, to extract thermodynamic evolution time scales, and also future prospects to study quantum criticality based on density profiles of atoms in optical lattices.   

A Universal Cooling Scheme for Quantum Simulations

The relevant energy scales in current Quantum Simulation experiments are so small that one has to reach the temperature and entropy regimes far below those achievable today. Here, we present a general scheme to extract entropy directly out from the region of interest. The later stage of this process is equivalent to a continuous ``evaporation,'' and is able to combat intrinsic heating of the system. In principle, this scheme can reach arbitrarily low temperatures, provided the system is in thermal equilibrium during the process. For illustration, we show how to cool a weak coupling BCS superfluid to $10^{-11}K$ with this simple procedure.   

Probing the Kondo Lattice Model with Alkaline Earth Atoms

It has recently been proposed that alkaline-earth atoms can be used to simulate condensed matter Hamiltonians with both spin and orbital electronic degrees of freedom [1]. For example, it is possible to create two independent optical lattices for trapping the $^1S_0$ and $^3P_0$ clock states, which we then associate with two orbital degrees of freedom [2]. Such a system is particularly well suited to simulation of the Kondo Lattice Model (KLM): by placing one clock state in a deep lattice and the other in a shallow lattice it is possible to mimic the interaction of localized spins with a band of conduction electrons. We suggest simple dynamical probes of the KLM phase diagram that can be implemented with current experimental techniques. In particular, we show how Kondo physics at strong coupling, low density, and in the heavy fermion phase is manifest in the dipole oscillations of the conduction band upon sudden displacement of a parabolic trapping potential. [1] A. V Gorshkov et al. arXiv:0905.2610v2 [cond-mat.quant-gas], Jan 2009. [2] A Daley, M Boyd, J Ye, and P Zoller. Phys. Rev. Lett. 101, 170504 (2008).   

Phonons do not harm some ion-trap quantum simulators

Ion-trap quantum simulators can be used to simulate simple spin Hamiltonians. In this talk, we focus on applying driving laser fields in the transverse direction, detuned from phonon resonances and in the Lamb-Dicke limit. The interaction of the light with the hyperfine states of the ion can cause the system to feel a spin-dependent force, which, in turn, results in an effective spin-spin coupling of the system, one of the simplest spin Hamiltonians to simulate is the transverse field Ising model. For this Hamiltonian, one can show, via an explicit factorization of the evolution operator for the spin and the phonon degrees of freedom, that the phonons completely decouple from the problem and do not affect the time-dependent dynamics of the spins, even if one moves near resonance with a normal mode of the ion chain. This implies that one need not worry about any decoherence effects arising from the phonons, and it implies that the spin Hamiltonian simulation is less susceptible to noise than previously thought. We also discuss how general these results are when one considers other spin Hamiltonians or when one goes beyond the Lamb-Dicke limit.   

Entanglement Entropy and Fluctuations in Bosonic and Spin Systems

Entanglement plays an important role in many-body systems at zero temperature, especially at criticality. In one dimension very general results from conformal theory and exact calculations for certain spin systems have established universal scaling properties of the entanglement entropy between two parts of a system. Despite these profound advances in the theory of entanglement, however, the experimental relevance of entanglement entropy in atomic and condensed matter systems remains unclear, with no obvious means of measuring entanglement entropy. Following recent proposals to measure entanglement entropy through transport measurements in electronic systems, we use a combination of analytical calculation and DMRG to connect certain observables to the entanglement entropy. In particular, observing that in a Bose-Einstein condensate the spatial entanglement is directly related to the number fluctuation, we relate the fluctuations of a conserved quantity (particle number, spin) across two systems coupled by a variable coupling to the entanglement entropy in spin-$1/2$ and Bose-Hubbard chains.   

Controlled Interaction between Ultracold Lithium and Cesium Atoms in Optical Lattices for Quantum Information Processing

We present progress on a quantum information processing experiment using degenerate gases of bosonic $^{133}$Cs and fermionic $^6$Li ,each confined in an independently controlled, overlapping optical lattice. An insulating state of $^6$Li will prepare an initial state with exactly one atom per lattice site. These atoms serve as quantum bits (qubits). $^{133}$Cs atoms are sparsely loaded into a second lattice, and act as messenger bits to carry entanglement between distant qubits. Qubit operations are mediated through magnetic dipole transitions to a $^6$Li-$^{133}$Cs molecular state that is formed only when qubit and messenger are overlapped. The $^{133}$Cs messenger atom can interact with (multiple and distant) $^6$Li qubits through translation of the Cs lattice using an electro-optic modulator array, making this implementation scalable. We present progress on the first spectroscopy experiments of the $^6$Li-$^{133}$Cs molecular states. These findings will guide the best strategies for implementing qubit operations using messenger atoms.   

Searching for Topological Phases in Cold Atom Systems

RVB (Resonating Valence Bond) phases represent a recurring theme in strongly-correlated systems, for example as a mechanism for cuprate pairing and in the search for deconfinement and fractionalization. Although there are few experimental candidates of quantum spin liquid states, engineering a RVB on an optical lattice would be feasible if the underlying Hamiltonian were known. Work by Moessner and Sondhi[1] has shown that a Quantum Dimer model on a triangular model is capable of realizing a short range RVB. In an effort to construct a RVB in a Bose-Hubbard Hamiltonian, we examine a fully frustrated Honeycomb lattice which, in the classical limit, has a duality mapping to the ground state of the classical triangular lattice dimer model. The effect of quantum fluctuations of this ground state is studied by stochastic series expansion quantum Monte Carlo. We have found that the configuration of the frustration give us ground states that can be described as a localized resonating valence bond crystal or a valence bond liquid that freezes into what may be a valence bond glass at low temperatures. [1] R. Moessner and S. L. Sondhi, Phys. Rev. Lett. \textbf{86}, 1881 (2001)   

Decoherence of trapped ion states in passivated aluminum ion traps

Surface electrode ion traps, while promising for large-scale quantum computation, have long been challenged by ion heating rates which increase rapidly as trap length scales are reduced. Existing research shows that ion heating rates are surprisingly sensitive to electrode material and morphology. Here, we report on a new experiment measuring the heating rate out of the motional quantum ground state of a single $Sr^+$ ion in an aluminum ion trap operated at cryogenic temperatures. Aluminium naturally and nearly immediately forms a tough, resistant, surface oxide, alumina, which protects it from further oxidation. Compared to other metal ion traps, aluminum ion traps are more difficult to compensate, and often have short ion lifetimes, perhaps due to this nanometer-thick alumina layer. A series of aluminum traps with different and controlled alumina layer thickness are fabricated and evaluated. We discuss the ion heating rate versus the oxide layer thickness and investigate whether the heating rate is more related to bulk or surface properties.   

Random variable approach to dissipative spin dynamics and Landau-Zener transitions

We present a random variable approach to solve for the dynamics of a dissipative two-state system. Based on an exact functional integral description, our method reformulates the problem as that of non-unitary time evolution of a quantum state vector under a Hamiltonian containing random noise fields. This non-perturbative formalism goes beyond the frequently used Non-Interacting Blip Approximation (NIBA) and is particularly well suited to treat an explicitly time-dependent Hamiltonian. As an example, we consider the renowned Landau-Zener problem in the presence of an Ohmic bath with a large bath cutoff frequency $\omega_c$. We identify an intermediate time regime where the energy separation of the two spin states is much larger than their tunneling coupling $\Delta$, but still smaller than $\omega_c$ such that bath mediated spin transitions still occur. Such a situation can for example be realized with a cold atomic quantum dot setup. We also derive an approximate analytical expression for the decay of the upper spin state population in this regime, which agrees well with our numerical results.   

Novel Ion Trap for Efficient Fluorescence Collection from Trapped Ion Qubits

Efficient ion fluorescence collection is critical for fast reliable qubit state detection and higher photon collection rates from single trapped ions or atoms would lead to more efficient single-photon sources and ion-photon entanglement. By integrating a high N.A. spherical mirror into a linear Paul trap, we recently achieved $10\%$ photon collection efficiency from a single $Ba^+$ qubit. Based on the current successful trap, we designed and built a novel trap in which the reflective optical surface serves as the RF electrode. The new trap geometry is very open and almost 30\% of the photons emitted by the ion will be intercepted. Additionally, the axial symmetry of the trap provides means for self-alignment of the ion trapping position and the optical axis of the spherical mirror. Its smaller size will proportionally reduce the spherical aberration so that we can achieve diffraction-limited ion image, and attempt to couple ion fluorescence into a single mode optical fiber for remote ion entanglement. Compared to refractive optics systems, our solution has the advantage of simplicity, low cost, flexibility and scale-up potential.   

Building Topological Quantum States in Two-Dimensional Optical Lattices

We propose the realization of topological quantum states with cold atoms trapped in an optical lattice with square symmetry. The proposed experimental setup generates a quasi-two-dimensional square superlattice in the presence of a light-induced periodic vector potential and represents the realization with cold atoms of a simple tight-binding model with a complex direction-dependent nearest-neighbor hopping and a real next-nearest-neighbor hopping that takes different values on adjacent plaquettes. We describe the properties of the topological edge states within a multi band tight-binding approximation and discuss possible transitions between topologically distinct states induced by an additional staggered potential or by variations of the parameters characterizing the optical lattice potential and the vector potential. We also discuss the stability of the edge states against finite size effects and their dependence on the confining potential that defines the boundaries of the system.   

Quantum Phase Transitions and Quantum Criticality of Two-Dimensional Ultracold Quantum Gases

Quantum phase transitions in two dimensions (2D) are expected to exhibit universal behavior near the critical point. Intriguing critical phenomena are predicted even at finite temperatures. The availability of 2D quantum gases of ultracold atoms provide appealing opportunities to explore both quantum and classical criticality. Prominent examples include the superfluid (SF) to Mott insulator (MI) transition of ultracold Bose gases in an optical lattice described by the Bose-Hubbard model, and the Berezinsky--Kosterlitz--Thouless transition for 2D Bose gases. We have experimentally realized such a 2D system by loading cesium-133 Bose-Einstein condensates into an optical potential which confines the atoms tightly in one direction, followed by ramping up of a 2D optical lattice to induce the SF-MI transition. We obtain high resolution in-situ images of these samples, revealing density distributions and fluctuations indicative of the local quantum phase and changes in the underlying Hamiltonian. We discuss the extension of these results to the experimental study of critical phenomena in an interacting 2D quantum gas.   

Non-Markovian spontaneous emission and photon localization in a atom-waveguide system

Waveguides can serve as a quantum channel for transporting photon qubits. Here we study the dynamics of a two-level atom in a single-mode waveguide, in particular, the spontaneous emission near the stop-off frequency of the waveguide. We found that even when the atomic transition frequency lies above the stop-off frequency of the waveguide, the emission is not complete due to the formation of a bound polariton state. Rabi oscillation due to splitting between the bound state and a resonance with finite lifetime is observed. This non-Markovian emission near the stop-off frequency reveals the strong coupling between the atom and the continuum. The trapped polariton makes the optical system behave like a cavity without mirror with the density-of-state singularity in a waveguide mimicking a discrete state in a cavity.