Breakdown of local convertibility through Majorana modes in a quantum quench

The local convertibility of quantum states, measured by the R\'enyi entropy, is concerned with whether or not a state can be transformed into another state, using only local operations and classical communications. We found that in the one-dimensional Kitaev chain with quenched chemical potential $\mu$, the convertibility between the state for $\mu$ and that for $\mu+\delta\mu$, depends on the quantum phases of the system ($\delta\mu$ is a perturbation). This is similar to the adiabatic case where the ground state is considered. Specifically, when the quenched system has edge modes and the subsystem size for the partition is much larger than the correlation length of the Majorana fermions which forms the edge modes, the quenched state is locally inconvertible. We give a physical interpretation for the result, based on analyzing the interactions between the two subsystems for various partitions. Our work should help to better understand the many-body phenomena in topological systems and also the entanglement properties in the Majorana fermionic quantum computation.Comment: 8 pages, 5 figures, accepted by Physical Review

Parametric amplification in single-walled carbon nanotube nanoelectromechanical resonators

The low quality factor (Q) of Single-walled carbon nanotube (SWNT) resonators has limited their sensitivity in sensing application. To this end, we employ the technique of parametric amplification by modulating the spring constant of SWNT resonators at twice the resonant frequency, and achieve 10 times Q enhancement. The highest Q obtained at room temperature is around ~700, which is 3-4 times better than previous Q record reported for doubly-clamped SWNT resonators. Furthermore, efficient parametric amplification is found to only occur in the catenary vibration regime. Our results open up the possibility to employ light-weight and high-Q carbon nanotube resonators in single molecule and atomic mass sensing.Comment: 14 pages, 3 figure

Quench Dynamics of Topological Maximally-Entangled States

We investigate the quench dynamics of the one-particle entanglement spectra (OPES) for systems with topologically nontrivial phases. By using dimerized chains as an example, it is demonstrated that the evolution of OPES for the quenched bi-partite systems is governed by an effective Hamiltonian which is characterized by a pseudo spin in a time-dependent pseudo magnetic field $\vec{S}(k,t)$. The existence and evolution of the topological maximally-entangled edge states are determined by the winding number of $\vec{S}(k,t)$ in the $k$-space. In particular, the maximally-entangled edge states survive only if nontrivial Berry phases are induced by the winding of $\vec{S}(k,t)$. In the infinite time limit the equilibrium OPES can be determined by an effective time-independent pseudo magnetic field \vec{S}_{\mb{eff}}(k). Furthermore, when maximally-entangled edge states are unstable, they are destroyed by quasiparticles within a characteristic timescale in proportional to the system size.Comment: 5 pages, 3 figure

Extracting entangled qubits from Majorana fermions in quantum dot chains through the measurement of parity

We propose a scheme for extracting entangled charge qubits from quantum-dot chains that support zero-energy edge modes. The edge mode is composed of Majorana fermions localized at the ends of each chain. The qubit, logically encoded in double quantum dots, can be manipulated through tunneling and pairing interactions between them. The detailed form of the entangled state depends on both the parity measurement (an even or odd number) of the boundary-site electrons in each chain and the teleportation between the chains. The parity measurement is realized through the dispersive coupling of coherent-state microwave photons to the boundary sites, while the teleportation is performed via Bell measurements. Our scheme illustrates \emph{localizable entanglement} in a fermionic system, which serves feasibly as a quantum repeater under realistic experimental conditions, as it allows for finite temperature effect and is robust against disorders, decoherence and quasi-particle poisoning.Comment: Accepted by Scientific Report

Entanglement in composite free-fermion systems

We consider fermionic chains where the two halves are either metals with different bandwidths or a metal and an insulator. Both are coupled together by a special bond. We study the ground-state entanglement entropy between the two pieces, its dependence on the parameters and its asymptotic form. We also discuss the features of the entanglement Hamiltonians in both subsystems and the evolution of the entanglement entropy after joining the two parts of the system.Comment: 20 pages, 13 figures, published version, minor corrections, references adde

Thermalization and Quantum Correlations in Exactly Solvable Models

The generalized Gibbs ensemble introduced for describing few body correlations in exactly solvable systems following a quantum quench is related to the nonergodic way in which operators sample, in the limit of infinite time after the quench, the quantum correlations present in the initial state. The nonergodicity of the correlations is thus shown \emph{analytically} to imply the equivalence with the generalized Gibbs ensemble for quantum Ising and XX spin chains as well as for the Luttinger model the thermodynamic limit, and for a broad class of initial states and correlation functions of both local and nonlocal operators.Comment: 12 pages, 4 figures. Expanded in response to Referee criticis

Carbon Based Nanoelectromechanical Resonators.

Owing to their light mass and high Young’s modulus, carbon nanotubes (CNTs) and graphene are promising candidates for nanoelectromechanical resonators capable of ultrasmall mass and force sensing. Unfortunately, the mass sensitivity of CNT resonators is impeded by the low quality factor (Q) caused by intrinsic losses. Therefore, one should minimize dissipations or seek an external way to enhance Q in order to overcome the fundamental limits. In this thesis, I first carried out a one-step direct transfer technique to fabricate pristine CNT nanoelectronic devices at ambient temperature. This process technique prevents unwanted contaminations, further reducing surface losses. Using this technique, CNT resonators was fabricated and a fully suspended CNT p-n diode with ideality factor equal to 1 was demonstrated as well. Subsequently, the frequency tuning mechanisms of CNT resonators were investigated in order to study their nonlinear dynamics. Downward frequency tuning caused by capacitive spring softening effect was demonstrated for the first time in CNT resonators adopting a dual-gate configuration. Leveraging the ability to modulate the spring constant, parametric amplification was demonstrated for Q enhancement in CNT resonators. Here, the simplest parametric amplification scheme was implemented by modulating the spring constant of CNTs at twice the resonance frequency through electrostatic gating. Consequently, at least 10 times Q enhancement was demonstrated and Q of 700 at room temperature was the highest record to date. Moreover, parametric amplification shows strong dependence on DC gate voltages, which is believed due to the difference of frequency tunability in different vibrational regimes. Graphene takes advantages over CNTs due to the availability of wafer-scale graphene films synthesized by chemical vapor deposition (CVD) method. Thus, I also examined graphene resonators fabricated from CVD graphene films. Ultra-high frequency (UHV) graphene resonators were demonstrated, and the Qs of graphene resonators are around 100. Future directions of graphene resonators include investigating the potential losses, exploring the origin of nonlinear damping, and demonstrating parametric amplification for Q enhancement.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91487/1/chungwu_1.pd