Simulating generic spin-boson models with matrix product states

The global coupling of few-level quantum systems ("spins") to a discrete set of bosonic modes is a key ingredient for many applications in quantum science, including large-scale entanglement generation, quantum simulation of the dynamics of long-range interacting spin models, and hybrid platforms for force and spin sensing. We present a general numerical framework for treating the out-of-equilibrium dynamics of such models based on matrix product states. Our approach applies for generic spin-boson systems: it treats any spatial and operator dependence of the two-body spin-boson coupling and places no restrictions on relative energy scales. We show that the full counting statistics of collective spin measurements and infidelity of quantum simulation due to spin-boson entanglement, both of which are difficult to obtain by other techniques, are readily calculable in our approach. We benchmark our method using a recently developed exact solution for a particular spin-boson coupling relevant to trapped ion quantum simulators. Finally, we show how decoherence can be incorporated within our framework using the method of quantum trajectories, and study the dynamics of an open-system spin-boson model with spatially non-uniform spin-boson coupling relevant for trapped atomic ion crystals in the presence of molecular ion impurities.Comment: 13 pages+refs. 13 figure

Quasi-molecular bosonic complexes -- a pathway to atomic analog of SQUID with controlled sensitivity

Recent experimental advances in realizing degenerate quantum dipolar gases in optical lattices and the flexibility of experimental setups in attaining various geometries offer the opportunity to explore exotic quantum many-body phases stabilized by anisotropic, long-range dipolar interaction. Moreover, the unprecedented control over the various physical properties of these systems, ranging from the quantum statistics of the particles, to the inter-particle interactions, allow one to engineer novel devices. In this paper, we consider dipolar bosons trapped in a stack of one-dimensional optical lattice layers, previously studied in [1]. Building on our prior results, we provide a description of the quantum phases stabilized in this system which include composite superfluids, solids, and supercounterfluids, most of which are found to be threshold- less with respect to the dipolar interaction strength. We also demonstrate the effect of enhanced sensitivity to rotations of a SQUID-type device made of two composite superfluids trapped in a ring-shaped optical lattice layer with weak links.Comment: Special Issue Articl

Quantum phases of hard-core dipolar bosons in coupled one-dimensional optical lattices

Hard-core dipolar bosons trapped in a parallel stack of N ≥ 2 one-dimensional optical lattices (tubes) can develop several phases made of composites of particles from different tubes: superfluids, supercounterfluids, and insulators as well as mixtures of those. Bosonization analysis shows that these phases are thresholdless with respect to the dipolar interaction, with the key “control knob” being filling factors in each tube, provided the intertube tunneling is suppressed. The effective ab initio quantum Monte Carlo algorithm capturing these phases is introduced and some results are presented.National Science Foundation (U.S.) (Grant CNS-0855217)National Science Foundation (U.S.) (Grant CNS-0958379)National Science Foundation (U.S.) (Grant ACI-1126113

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet

Controllable arrays of ions and ultra-cold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of quantum correlations and coherence are needed, as performing full state tomography does not scale favorably with the number of particles. Here we develop and experimentally demonstrate such a protocol, which uses time reversal of the many-body dynamics to measure out-of-time-order correlation functions (OTOCs) in a long-range Ising spin quantum simulator with more than 100 ions in a Penning trap. By measuring a family of OTOCs as a function of a tunable parameter we obtain fine-grained information about the state of the system encoded in the multiple quantum coherence spectrum, extract the quantum state purity, and demonstrate the buildup of up to 8-body correlations. Future applications of this protocol could enable studies of many-body localization, quantum phase transitions, and tests of the holographic duality between quantum and gravitational systems.Comment: main text: 7 pages, 4 figures; supplement: 9 pages, 4 figure

Engineering spin-spin interactions with optical tweezers in trapped ions

We propose a new method for generating programmable interactions in one- and two-dimensional trapped-ion quantum simulators. Here we consider the use of optical tweezers to engineer the sound-wave spectrum of trapped ion crystals. We show that this approach allows us to tune the interactions and connectivity of the ion qubits beyond the power-law interactions accessible in current setups. We demonstrate the experimental feasibility of our proposal using realistic tweezer settings and experimentally relevant trap parameters to generate the optimal tweezer patterns to create target spin-spin interaction patterns in both one- and two-dimensional crystals. Our approach will advance quantum simulation in trapped-ion platforms as it allows them to realize a broader family of quantum spin Hamiltonians

Few- and many-body physics of dipoles in ion traps and optical lattice simulators

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2014.Cataloged from PDF version of thesis.Includes bibliographical references (pages 219-229).The presence of strong interactions in quantum many-body systems makes the analytical treatment of such systems very difficult. In this thesis we explore two possible proposals for simulating strongly correlated, quantum many-body systems: quantum simulations using trapped-ion quantum computers, and optical lattice simulators. In the first part of the thesis we describe the recent advances in Quantum Information Processing. In particular, we focus on the trapped-ion quantum computer. One of the main experimental roadblocks for this architecture is the "anomalous heating". This refers to the motional heating of the ion after being cooled to its ground state. In this thesis we present the first ab-initio and microscopic model for this noise. This model attributes the noise to fluctuating dipoles formed by adsorbates bound on the trap surface. The second part of the thesis studies three different lattice boson systems. First, we study the Bose-Hubbard model for hard-core bosons, interacting via dipole-dipole interactions. The resulting extended Bose-Hubbard model can be experimentally realized by polar molecules, Rydberg atoms, or magnetic dipoles in optical lattices. We use quantum Monte Carlo simulations, using the two-worm algorithm to study the ground-state phase diagram of dipolar, hard-core bosons, trapped in a bilayer geometry. Each layer is a quasi two-dimensional lattice, the dipole are aligned perpendicular to the layer, and inter-layer hopping is suppressed. We present zero- and finite-temperature results. Next we use a novel multiworm algorithm, along with bosonization, to study the ground-state phase diagram of bosons trapped in a stack of one-dimensional tubes. We study two different inter-particle interactions. First, we consider nearest-neighbor attractive interactions between the layers, and set the intra-layer interactions to zero. Next we study dipolar bosons with their dipole moments aligned perpendicular to the tube axis. Inter-layer tunneling is suppressed in both cases. Finally, we explore the possibility of using few-body phenomena to create exotic quantum many-body systems. We present a novel scheme to realize a tunable, onsite, three-body interaction. We study the resulting extended Bose-Hubbard model with a three-body on-site term using the Gutzwiller mean-field method, as well as quantum Monte Carlo simulations using the Worm algorithm.by Arghavan Safavi-Naini.Ph. D

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The dynamics of quantum information and entanglement is closely linked to the physics of thermalization. A quantum simulator comprised of superconducting qubits has measured the spread of quantum information in a many-body system