Quantum Simulation of Interacting Spin Models with Trapped Ions

The quantum simulation of complex many body systems holds promise for understanding the origin of emergent properties of strongly correlated systems, such as high-Tc superconductors and spin liquids. Cold atomic systems provide an almost ideal platform for quantum simulation due to their excellent quantum coherence, initialization and readout properties, and their ability to support several forms of interactions. In this thesis, I present experiments on the quantum simulation of long range Ising models in the presence of transverse magnetic fields with a chain of up to sixteen ultracold 171-Yb+ ions trapped in a linear radio frequency Paul trap. Two hyperfine levels in each of the 171-Yb+ ions serve as the spin-1/2 systems. We detect the spin states of the individual ions by observing state-dependent fluorescence with single site resolution, and can directly measure any possible spin correlation function. The spin-spin interactions are engineered by applying dipole forces from precisely tuned lasers whose beatnotes induce stimulated Raman transitions that couple virtually to collective phonon modes of the ion motion. The Ising couplings are controlled, both in sign and strength with respect to the effective transverse field, and adiabatically manipulated to study various aspects of this spin model, such as the emergence of a quantum phase transition in the ground state and spin frustration due to competing antiferromagnetic interactions. Spin frustration often gives rise to a massive degeneracy in the ground state, which can lead to entanglement in the spin system. We detect and characterize this frustration induced entanglement in a system of three spins, demonstrating the first direct experimental connection between frustration and entanglement. With larger numbers of spins we also vary the range of the antiferromagnetic couplings through appropriate laser tunings and observe that longer range interactions reduce the excitation energy and thereby frustrate the ground state order. This system can potentially be scaled up to study a wide range of fully connected spin networks with a few dozens of spins, where the underlying theory becomes intractable on a classical computer

Noise-Induced Subdiffusion in Strongly Localized Quantum Systems

We consider the dynamics of strongly localized systems subject to dephasing noise with arbitrary correlation time. Although noise inevitably induces delocalization, transport in the noise-induced delocalized phase is subdiffusive in a parametrically large intermediate-time window. We argue for this intermediate-time subdiffusive regime both analytically and using numerical simulations on single-particle localized systems. Furthermore, we show that normal diffusion is restored in the long-time limit, through processes analogous to variable-range hopping. Our qualitative conclusions are also valid for interacting systems in the many-body localized phase

Cooperative MAC design for Ad Hoc wireless networks

Cooperative diversity is proposed to combat the detrimental effects of channel fading. In this thesis, we investigate the effectiveness of cooperative diversity in interference limited ad hoc networks. The throughput performance of ad hoc networks that employ cooperative diversity techniques is examined. The negative effects of relay transmission blocking and extra time delay due to using the relay node, on the network throughput are investigated. We show that cooperative diversity based ad hoc networks inherits relay blocking problem which causes net network throughput degradation. To solve the relay blocking problem, we propose a new cooperative medium-access-control (MAC) protocol where each relay is equipped with directive antennas and the transmitter-relay-receiver transmission mode is designed using two frequency channels. Furthermore, we discuss the throughput performance considering single and multiple relay scenarios and analyze the effect of interference on the throughput. Then we investigate the throughput performance of the proposed cooperative MAC protocol in the presence of position estimation errors. In the literature, a perfect position estimation of all nodes is commonly assumed. Here, we focus on the throughput performance of the cooperative network when taking into consideration the effect of directional-of-arrival (DOA) error caused by imperfect global-positioning system (GPS) position estimation. Our results show that using adaptive antennas at the relay becomes advantageous when the DOA error is less than 20 degrees. We noted that increasing the number of antennas (at the relay station) can improve the throughput performance but, on the other hand, the effect of node position error becomes more substantial

Multislip Friction with a Single Ion

A trapped ion transported along a periodic potential is studied as a paradigmatic nanocontact frictional interface. The combination of the periodic corrugation potential and a harmonic trapping potential creates a one-dimensional energy landscape with multiple local minima, corresponding to multistable stick-slip friction. We measure the probabilities of slipping to the various minima for various corrugations and transport velocities. The observed probabilities show that the multislip regime can be reached dynamically at smaller corrugations than would be possible statically, and can be described by an equilibrium Boltzmann model. While a clear microscopic signature of multislip behavior is observed for the ion motion, the frictional force and dissipation are only weakly affected by the transition to multistable potentials.Comment: 8 pages, 7 figure

Single-atom heat machines enabled by energy quantization

Quantization of energy is a quintessential characteristic of quantum systems. Here we analyze its effects on the operation of Otto cycle heat machines and show that energy quantization alone may alter and increase machine performance in terms of output power, efficiency, and even operation mode. Our results demonstrate that quantum thermodynamics enable the realization of classically inconceivable Otto machines, such as those with an incompressible working fluid. We propose to measure these effects experimentally using a laser-cooled trapped ion as a microscopic heat machine

Analysis of Zero Inflated Over dispersed Count Data Regression Models with Missing Values

Discrete data in the form of counts arise in many health science disciplines such as biology and epidemiology. The Poisson distribution is the most commonly used distribution for analysing count data. The Poisson distribution has a property that mean and the variance of the distribution are equal to each other. However, in many count data cases this property of the Poisson distribution does not hold as extra dispersion (variation) is observed in the data, and thus Poisson distribution is not an ideal choice for analysing count data in many applications. The presence of extra dispersion in count data is common in many real life situations. To accommodate this extra dispersion situation in count data a well known model is the negative binomial distribution, which is very convenient and common in practice

Investigations of 2D ion crystals in a hybrid optical cavity trap for quantum information processing

We numerically investigate a hybrid trapping architecture for 2D ion crystals using static electrode voltages and optical cavity fields for in-plane and out-of-plane confinements, respectively. By studying the stability of 2D crystals against 2D-3D structural phase transitions, we identify the necessary trapping parameters for ytterbium ions. Multiple equilibrium configurations for 2D crystals are possible, and we analyze their stability by estimating potential barriers between them. We find that scattering to anti-trapping states limits the trapping lifetime, which is consistent with recent experiments employing other optical trapping architectures. These 2D ion crystals offer an excellent platform for quantum simulation of frustrated spin systems, benefiting from their 2D triangular lattice structure and phonon-mediated spin-spin interactions. Quantum information processing with tens of ions is feasible in this scheme with current technologies.Comment: 10 pages, 7 figures, 1 tabl

Measuring entanglement entropy through the interference of quantum many-body twins

Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in diverse fields ranging from condensed matter to quantum gravity. Despite this generality, measuring entanglement remains challenging. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Leveraging our single-site resolved control of ultra-cold bosonic atoms in optical lattices, we prepare and interfere two identical copies of a many-body state. This enables us to directly measure quantum purity, Renyi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly-correlated many-body systems.Comment: 14 pages, 12 figures (6 in the main text, 6 in supplementary material