arXiv subjects

Michael L. Wall

Publications and source records attributed to Michael L. Wall.

27 records · Page 2Linked to original sources

arXiv2016

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.

cond-mat.quant-gas↗

arXiv2016

Topological phases with long-range interactions

Topological phases of matter are primarily studied in systems with short-range interactions. In nature, however, non-relativistic quantum systems often exhibit long-range interactions. Under what conditions topological phases survive such interactions, and how they are modified when they do, is largely unknown. By studying the symmetry-protected topological phase of an antiferromagnetic spin-1 chain with $1/r^α$ interactions, we show that two very different outcomes are possible, depending on whether or not the interactions are frustrated. While non-frustrated long-range interactions can destroy the topological phase for $α\lesssim3$, the topological phase survives frustrated interactions for all $α>0$. Our conclusions are based on strikingly consistent results from large-scale matrix-product-state simulations and effective-field-theory calculations, and we expect them to hold for more general interacting spin systems. The models we study can be naturally realized in trapped-ion quantum simulators, opening the prospect for experimental investigation of the issues confronted here.

cond-mat.quant-gas↗

arXiv2016

Quantum spin dynamics and entanglement generation with hundreds of trapped ions

Quantum simulation of spin models can provide insight into complex problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. Here we study non-equilibrium, quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of $^9$Be$^+$ ions in a Penning trap. We verify entanglement in the form of spin-squeezed states for up to 219 ions, directly observing 4.0$\pm$0.9 dB of spectroscopic enhancement. We also observe evidence of non-Gaussian, over-squeezed states in the full counting statistics. We find good agreement with ab-initio theory that includes competition between entanglement and decoherence, laying the groundwork for simulations of the transverse-field Ising model with variable-range interactions, for which numerical solutions are, in general, classically intractable.

quant-ph↗

arXiv2015

Ultracold nonreactive molecules in an optical lattice: connecting chemistry to many-body physics

We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter $U$ is replaced by a multi-channel interaction, whose properties we elucidate. The complex, multi-channel collisional physics is unrelated to dipolar interactions, and so occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which consequently measure molecular collision dynamics with a vastly sharper energy resolution than experiments in an ultracold gas.

cond-mat.quant-gas↗

arXiv2015

Synthetic spin-orbit coupling in an optical lattice clock

We propose the use of optical lattice clocks operated with fermionic alkaline-earth-atoms to study spin-orbit coupling (SOC) in interacting many-body systems. The SOC emerges naturally during the clock interrogation when atoms are allowed to tunnel and accumulate a phase set by the ratio of the "magic" lattice wavelength to the clock transition wavelength. We demonstrate how standard protocols such as Rabi and Ramsey spectroscopy, that take advantage of the sub-Hertz resolution of state-of-the-art clock lasers, can perform momentum-resolved band tomography and determine SOC-induced $s$-wave collisions in nuclear spin polarized fermions. By adding a second counter-propagating clock beam a sliding superlattice can be implemented and used for controlled atom transport and as a probe of $p$ and $s$-wave interactions. The proposed spectroscopic probes provide clean and well-resolved signatures at current clock operating temperatures.

cond-mat.quant-gas↗

arXiv2015

Demagnetization dynamics of non-interacting trapped fermions

Motivated by several experimental efforts to understand spin diffusion and transport in ultracold fermionic gases, we study the spin dynamics of initially spin-polarized ensembles of harmonically trapped non-interacting spin-1/2 fermionic atoms, subjected to a magnetic field gradient. We obtain simple analytic expressions for spin observables in the presence of both constant and linear magnetic field gradients, with and without a spin-echo pulse, and at zero and finite temperatures. The analysis shows the relevance of spin-motional coupling in the non-interacting regime where the demagnetization decay rate at short times can be faster than the experimentally measured rates in the strongly interacting regime under similar trapping conditions. Our calculations also show that particle motion limits the ability of a spin-echo pulse to remove the effect of magnetic field inhomogeneity, and that a spin-echo pulse can instead lead to an increased decay of magnetization at times comparable to the trapping period.

cond-mat.quant-gas↗

arXiv2015

Effective many-body parameters for atoms in non-separable Gaussian optical potentials

We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and non-separability. Although these effects are negligible in more conventional optical lattice experiments, they are essential for emerging ultracold atom developments. We focus in particular on two potentials utilized in current ultracold atom experiments: arrays of tightly focused optical tweezers and a one-dimensional optical lattice with transverse Gaussian confinement and highly excited transverse modes. Our main numerical tools are discrete variable representations (DVRs), which combine many favorable features of spectral and grid-based methods, such as the computational advantage of exponential convergence and the convenience of an analytical representation of Hamiltonian matrix elements. Optimizations, such as symmetry adaptations and variational methods built on top of DVR methods, are presented and their convergence properties discussed. We also present a quantitative analysis of the degree of non-separability of eigenstates, borrowing ideas from the theory of matrix product states (MPSs), leading to both conceptual and computational gains. Beyond developing numerical methodologies, we present results for construction of optimally localized Wannier functions and tunneling and interaction matrix elements in optical lattices and tweezers relevant for constructing effective models for many-body physics.

cond-mat.quant-gas↗

arXiv2014

Spin-orbital dynamics in a system of polar molecules

Spin-orbit coupling (SOC) in solids normally originates from the electron motion in the electric field of the crystal. It is key to understanding a variety of spin-transport and topological phenomena, such as Majorana fermions and recently discovered topological insulators. Implementing and controlling spin-orbit coupling is thus highly desirable and could open untapped opportunities for the exploration of unique quantum physics. Here, we show that dipole-dipole interactions can produce an effective SOC in two-dimensional ultracold polar molecule gases. This SOC generates chiral excitations with a non-trivial Berry phase $2π$. These excitations, which we call \emph{chirons}, resemble low-energy quasiparticles in bilayer graphene and emerge regardless of the quantum statistics and for arbitrary ratios of kinetic to interaction energies. Chirons manifest themselves in the dynamics of the spin density profile, spin currents, and spin coherences, even for molecules pinned in a deep optical lattice and should be observable in current experiments.

cond-mat.quant-gas↗

arXiv2010

Finite Temperature Matrix Product State Algorithms and Applications

We review the basic theory of matrix product states (MPS) as a numerical variational ansatz for time evolution, and present two methods to simulate finite temperature systems with MPS: the ancilla method and the minimally entangled typical thermal state method. A sample calculation with the Bose-Hubbard model is provided.

cond-mat.quant-gas↗