Forcing Mutual Coherence in Diode Laser Stacks

This paper will discuss both theoretical and experimental attempts to improve the spatial beam quality of diode laser stacks using an external optical system. An overview and derivation of the mathematics of both the optical system and diode lasers will be discussed. The experimental setup will be presented, as well as the fundamental theoretical and experimental results that suggest the external optical system used for this thesis fails to improve the beam quality of a diode laser stack

The Quest for High Power Lasers: Forcing Mutual Coherence in Broad Area Diode Lasers

This poster explains efforts to improve spatial beam quality of diode array stacks using an external optical feedback system to force coherence of individual diodes

Childhood as a Philosophical Means to a Political End: Liberalism, Stability, and the Deficiency Model of Childhood

Childhood as a Philosophical Means to a Political End: Liberalism, Stability, and the Deficiency Model of Childhoo

Variational Schrieffer-Wolff transformations for quantum many-body dynamics

Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a unitary rotation, which leads to effective dynamics in a computationally tractable reduced Hilbert space. The generators of these rotations are computed variationally and thus go beyond standard perturbative methods, with error controlled by the locality of the variational ansatz. The method is demonstrated on two models. First, in the attractive Fermi-Hubbard model with onsite disorder, we find indications of a lack of observable many-body localization in the thermodynamic limit due to the inevitable mixture of different spinon sectors. Second, in the low-energy sector of the XY spin model with a broken U(1) symmetry, we analyze ground-state response functions by combining the variational Schrieffer-Wolf transformation with the truncated spectrum approach.Published versio

Cluster Truncated Wigner Approximation in Strongly Interacting Systems

We present a general method by which linear quantum Hamiltonian dynamics with exponentially many degrees of freedom is replaced by approximate classical nonlinear dynamics with the number of degrees of freedom (phase space dimensionality) scaling polynomially in the system size. This method is based on generalization of the truncated Wigner approximation (TWA) to a higher dimensional phase space, where phase space variables are associated with a complete set of quantum operators spanning finite size clusters. The method becomes asymptotically exact with the increasing cluster size. The crucial feature of TWA is fluctuating initial conditions, which we approximate by a Gaussian distribution. We show that such fluctuations dramatically increase accuracy of TWA over traditional cluster mean field approximations. In this way we can treat on equal footing quantum and thermal fluctuations as well as compute entanglement and various equal and non-equal time correlation functions. The main limitation of the method is exponential scaling of the phase space dimensionality with the cluster size, which can be significantly reduced by using the language of Schwinger bosons and can likely be further reduced by truncating the local Hilbert space variables. We demonstrate the power of this method analyzing dynamics in various spin chains with and without disorder and show that we can capture such phenomena as long time hydrodynamic relaxation, many-body localization and the ballistic spread of entanglement.Comment: 17 pages, 9 figure

Cluster phase space and variational subspace approaches to the quantum many-body problem

Simulating the nonequilibrium behavior of interacting quantum systems is an important way to understand results of experimental quantum simulators, motivate new materials, and refine new quantum algorithms. However, this is a challenging task due to the exponential difficulty of such systems, which motivates dimensional reduction methods, such as semiclassical limits. This work extends semiclassical phase space methods to spin systems with no clear classical limit with the cluster truncated Wigner approximation (cTWA), and improves on Schrieffer-Wolff low energy effective dynamics with variational adiabatic generators. The cTWA was used to compute nonequilibrium dynamics in spin chains, finding behavior such as signatures of many body localization; rapid thermalization and preservation of fluctuations; effective thermodynamic classical behaviors; and signatures of quantum chaos and butterfly velocities, in 1d spin 1/2 chains. Variational Schrieffer-Wolff methods were used to find efficient non-perturbative dressings for the Hubbard model and find effective quasiparticle dynamics and nonthermal states in quantum chaotic spin chains. These methods are potentially effective tools to separate essential quantum behavior from classical behavior, and can be used to diagnose quantum thermalization behavior in interacting quantum systems