Applications of Many Body Dynamics of Solid State Systems to Quantum Metrology and Computation

Abstract

This thesis describes aspects of dynamics of solid state systems which are relevant to quantum metrology and computation. It may be divided into three research directions (parts). For the first part, a new method to enhance precision measurements that makes use of a sensor’s environment to amplify its response to weak external perturbations is described. In this method a “central” spin is used to sense the dynamics of surrounding spins, which are affected by the external perturbations that are being measured. The enhancement in precision is determined by the number of spins that are coupled strongly to the central spin and is resilient to various forms of decoherence. For polarized environments, nearly Heisenberg-limited precision measurements can be achieved. The second part of the thesis focuses on the decoherence of Majorana fermions. Specializing to the experimentally relevant case where each mode interacts with its own bath we present a method to study the effect of external perturbations on these modes. We analyze a generic gapped fermionic environment (bath) interacting via tunneling with individual Majorana modes - components of a qubit. We present examples with both static and dynamic perturbations (noise), and derive a rate of information loss for Majorana memories, that depends on the spectral density of both the noise and the fermionic bath. For the third part of the thesis we discuss vortices in topological superconductors which we model as closed finite systems, each with an odd number of real fermionic modes. We show that even in the presence of many-body interactions, there are always at least two fermionic operators that commute with the Hamiltonian. There is a zero mode corresponding to the total Majorana operator [1] as well as additional linearly independent zero modes, one of which is continuously connected to the Majorana mode in the non-interacting limit. We also show that in the situation where there are two or more well separated vortices their zero modes have non-Abelian Ising statistics under braiding.