Quantum fluctuations in condensed matter systems: Squeezed states in phonons and Josephson junctions.

Abstract

Quantum fluctuations are an important feature of isolated systems at low temperatures. This quantum noise is unavoidable due to Heisenberg's uncertainty principle. However, squeezed states can lower the quantum noise in one of a pair of variables at the expense of increasing it in the other variable. This ability to reduce quantum fluctuations makes squeezed states very promising in high-precision measurements. This thesis studies the quantum fluctuation properties of two condensed matter systems: phonons and Josephson junctions. In particular, we theoretically investigate several approaches for the generation and detection of squeezed states in these systems. We study for the first time coherent and squeezed quantum states of phonons, in analogy to the coherent and squeezed states of photons. We introduce and study a lattice amplitude operator, which is the phonon analog of the electric field. Our work provides a clear link between quantum mechanical phonon coherent states and the experimentally observed coherent phonons--typically described in classical terms. We then study phonon squeezed states, which can modulate the quantum fluctuations of atomic displacements below the zero-point quantum noise level. We explore the possibility of generating squeezed phonon states with a variety of different approaches, such as a phonon parametric down-conversion process and a polariton-based mechanism. Furthermore, we propose a possible detection scheme based on reflectivity measurements. We also study quantum fluctuation properties of superconducting Josephson junctions, which have the nonlinear interactions necessary for modulating quantum noise. We obtain approximate ground and excited states, and calculate the variances of the charge and phase in various circuit configurations. This thesis provides a first systematic study of quantum noise and its suppression in condensed matter systems. It also proposes different directions for future studies in the control of quantum noise in solids.