Condensed Matter Theory Seminar - Herbstsemester 2009

The ability to store information is of fundamental importance to any computer, be it classical or quantum. Identifying systems for quantum memories which rely, analogously to classical memories, on passive error protection ('self-correction') is of greatest interest in quantum information science. While systems with topological ground states have been considered to be promising candidates, a large class of them was recently proven unstable against thermal fluctuations. Here, we propose new two-dimensional (2D) spin models unaffected by this result. Specifically, we introduce repulsive long-range interactions in the toric code and establish a memory lifetime polynomially increasing with the system size. This remarkable stability is shown to originate directly from the repulsive long-range nature of the interactions. We study the time dynamics of the quantum memory in terms of diffusing anyons and support our analytical results with extensive numerical simulations.

We apply quantum control techniques to control a large spin chain by only acting on two qubits at one of its ends, thereby implementing universal quantum computation by a combination of quantum gates on the latter and swap operations across the chain. It is shown that the control sequences can be computed and implemented efficiently. We discuss the application of these ideas to physical systems such as superconducting qubits in which full control of long chains is challenging.

We discuss two cases of metal-insulator transition in 1D wire caused by the spin-orbit coupling. First we study the ground-state properties of electrons confined to a quantum wire and subject to a smoothly modulated Rashba spin-orbit coupling. We show, that when the period of the modulation becomes commensurate with the band filling, the Rashba coupling drives a quantum phase transition to a nonmagnetic insulating state. Using bosonization and a perturbative renormalization group approach, we find that this state is robust against electron-electron interactions. The gaps to charge- and spin excitations scale with the amplitude of the Rashba modulation with a common interaction-dependent exponent. As a second example we study the current-voltage characteristic of a one-dimensional band insulator with magnetic field and Rashba spin-orbit coupling which is connected to nonmagnetic leads. Without spin-orbit coupling we find a complete spin-filtering effect, meaning that the electric transport occurs in one spin channel only. In addition, for a large magnetic field which closes the band gap, we show that spin-orbit coupling leads to a transition from metallic to insulating behavior.

The aim of this talk is to present how one can, through the algebraic Bethe ansatz, use integrability in order to study the quantum quench dynamics of the Richardson Hamiltonian, a discrete version of the celebrated Bardeen-Cooper-Schrieffer Hamiltonian . Although the interaction quench (instantaneous change of the interaction between Cooper pairs) in this system has been studied before using a mean-field approach, it is only exact in the thermodynamic limit. Using the numerical techniques described here allows one to study, in a nearly exact manner, finite size systems in which quantum fluctuations can play an essential role.

Not only does integrability give access to the exact eigenstates and eigenenergies of the system, in this problem it also naturally provides an efficient way to truncate the effective Hilbert space. This drastic truncation grants access to system sizes which would be untreatable with matrix diagonalization while keeping the numerical error under perfect control.

In the closely related Central spin model describing a single electronic spin coupled via hyperfine interactions to a mesoscopic ensemble of nuclear spins, the inclusion of quantum fluctuations is of the utmost importance. Indeed, in the physical scenario of a qubit realized by an electron spin in a quantum dot, a finite number of background nuclear spins interacts with the electronic spin. Moreover, the most relevant regime is that of weak external magnetic field. These facts make quantum fluctuations a potentially dominant feature. The parallels between both models will therefore be discussed in order to show how similar techniques could be applied to study the relaxation and decoherence of such a qubit.

We propose and analyze a scheme where laser excited Rydberg atoms in large spacing lattices provide an efficient implementation of a universal quantum simulator for spin models. This includes the simulation of Hamiltonian dynamics of spin models involving n-particle interaction terms such as in Kitaev's toric code, color code, and lattice gauge theories. In addition, it provides the ingredients for dissipative preparation of entangled states based on engineering n-particle reservoir couplings. The key building blocks of our architecture are efficient and high-fidelity n-qubit entangling Rydberg gates, which combine electromagnetically induced transparency with strong and long-range Rydberg-Rydberg interactions. Including a possible dissipative time step via optical pumping, this allows to mimic both the coherent and dissipative time evolution of the spin system by a sequence of fast, parallel and high-fidelity n-particle gates.

Nanoelectromechanical systems (NEMS) have been proposed as ultra-sensitive detectors. Experiments over the past years have shown that it is possible to bring mesoscopic mechanical resonators close to the quantum regime and to measure their displacement with an accuracy close to the Heisenberg uncertainty limit. The ultimate detection of a quantum state, however, remains an open challenge. One of the hallmarks of quantum mechanics is the existence of entangled states. We propose a system, which is within reach of current experiments, and which would make it possible to detect entanglement of a mechanical resonator and a qubit in a NEMS setup.

Numerical simulation of strongly-driven electron dynamics in nanostructures and other confined environments remains a challenging problem. Many systems of interest are too large to be treated by accurate wave-function or many-body approaches, while mean-field methods are often inadequate due to strong correlations. Density functional theory is a widely used alternative because it strikes a balance between accuracy and the ability to treat large systems. We explore a related approach in which an electron system is described through its one-body reduced density matrix (one-matrix). The equation of motion of the one-matrix is "closed" by introducing an adiabatic functional approximation for the two-body terms. To evaluate the performance of this approach, we have carried out simulations on a simple Hubbard model. Remarkably, the adiabatic functional approximation is able to capture quite well Landau-Zener transitions and Stueckelberg oscillations, which are canonical nonadiabatic effects. Correlation is found to have a significant effect on the dynamics. Varying the interaction strength U over a range of values does not lead to regular, monotonic variations in nonadiabatic observables but rather reveals a striking resonance behavior.