california institute of technology phd thesis

Minnich Group

California institute of technology.

Welcome to the Minnich Group

Our group focuses on the growth and processing of thin-film electronic and quantum materials. We work at the intersection of materials science, engineering, and physics.  We are part of a vibrant quantum science and engineering environment at Caltech.

Our group is committed to promoting diversity, equity, and inclusion in our division , at Caltech, and in the research community.

Latest publications

Hirsh Kamakari posts his paper on scalable cross-entropy benchmarking to detect measurement-induced phase transitions on a superconducting quantum processor

Mar 1, 2024

David Catherall publishes his paper on ho t-hole transport and noise phenomena in silicon at cryogenic temperatures from first principles

Dec 19, 2023

Hirsh successfully defends his thesis. Congratulations Dr. Kamakari!

March 13, 2024

Shi-Ning successfully defends his thesis. Congratulations Dr. Sun!

March 6, 2024

Congrats to Hirsh on his  paper  posted to arxiv!

March 5, 2024

Welcome our new graduate students Yifei Yan, Mariya Talib Ezzy, and Gabriela M. Corea Moran

February 16, 2024

Click  here  for more publications.

Click  here  for more news.

Future transformative solid-state technology exploiting quantum effects such as entanglement will require new methods to grow and process highly delicate quantum materials into functioning devices. Our group’s present research focuses on inventing these methods and applying them to the fabrication of novel solid-state quantum technologies.

Low noise transistor microwave amplifiers

We are developing transistor microwave amplifiers with ultra low-noise performance into the millimeter-wave spectrum.

Atomic layer etching

We are developing atomic layer etching processes which will enable subtractive manufacturing of electronic and quantum devices with atomic precision for the first time.

Thermal laser epitaxy

We are developing a new method for the epitaxial growth of thin-film quantum materials by laser-based evaporation of refractory elements.

Principal Investigator

Austin J. Minnich

Professor of Mechanical Engineering and Applied Physics

Professional Preparation

BS University of California Berkeley, 2006

MS Massachusetts Institute of Technology, 2008

PhD Massachusetts Institute of Technology, 2011 

Appointments

Professor, California Institute of Technology, 2017-Present

Assistant Professor, California Institute of Technology, 2011-2017

Click here for a copy of Austin's CV

Deputy Chair, Division of E&AS, 2022 - Present

Current group members

Research scientist

Graduate student

Research scientist. PhD, Caltech Research interests: precision measurement, low-noise amplifiers, nanofabrication Joined group: 2021

BTech, Indian Institute of Technology, Delhi Research interests: Atomic layer etching Joined group: 2024

BS, University of Science and Technology of China Research interests: Atomic layer etching and Thermal laser epitaxy Joined group: 2024

BS, Massachusetts Institute of Technology Research interests: nanofabrication, low noise amplifiers Joined group: 2024

BS, University of Texas at Austin Research interests: Atomic layer etching Joined group: 2024

BS, University of Minnesota Research Interests: transport and noise in semiconductors Joined group: 2022

BS, Harvey Mudd College Research interests: Atomic layer etching Joined group: 2022

BS, University of Science and Technology of China Research interests: Transport and fluctuations in semiconductors Joined group: 2022

BS, University of Rochester Research interests: Low noise amplifiers, noise in semiconductors Joined group: 2022

BS, UCLA Research interests: Atomic layer processing Joined group: 2021

HBS, Oregon State University Research interests: Low-noise amplifiers, atomic layer etching Joined group: 2021

BS, Georgia Tech Research interests: First-principles hot electron noise in semiconductors. Joined group: 2019

Click here  to see our group alumni.

Spring 2024

APh 138b: Quantum Hardware and Techniques

This class covers multiple quantum technology platforms and related theoretical techniques, and will provide students with broad knowledge in quantum science and engineering. It will be split into three-week modules covering: applications of near-term quantum computers, superconducting qubits, trapped atoms and ions, topological quantum matter, solid state quantum bits, tensorproduct states.

P: (626)-395-3385

F: (626)-583-4963

Minnich Lab

1200 E. California Blvd, M.C. 104-44

Pasadena, CA 91125

Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization

Pablo a. parrilo, phd dissertation, california institute of technology, may 2000.

In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI) whose optimal solution can be characterized exactly. This family corresponds to the case where the associated linear operator maps the cone of positive semidefinite matrices onto itself. In this case, the optimal value equals the spectral radius of the operator. It is shown that some rank minimization problems, as well as generalizations of the structured singular value ($\mu$) LMIs, have exactly this property.

In the same spirit of exploiting structure to achieve computational efficiency, an algorithm for the numerical solution of a special class of frequency-dependent LMIs is presented. These optimization problems arise from robustness analysis questions, via the Kalman-Yakubovich-Popov lemma. The procedure is an outer approximation method based on the algorithms used in the computation of \hinf\ norms for linear, time invariant systems. The result is especially useful for systems with large state dimension.

The other main contribution in this thesis is the formulation of a convex optimization framework for semialgebraic problems, i.e., those that can be expressed by polynomial equalities and inequalities. The key element is the interaction of concepts in real algebraic geometry (Positivstellensatz) and semidefinite programming.

To this end, an LMI formulation for the sums of squares decomposition for multivariable polynomials is presented. Based on this, it is shown how to construct sufficient Positivstellensatz-based convex tests to prove that certain sets are empty. Among other applications, this leads to a nonlinear extension of many LMI based results in uncertain linear system analysis.

Within the same framework, we develop stronger criteria for matrix copositivity, and generalizations of the well-known standard semidefinite relaxations for quadratic programming.

Some applications to new and previously studied problems are presented. A few examples are Lyapunov function computation, robust bifurcation analysis, structured singular values, etc. It is shown that the proposed methods allow for improved solutions for very diverse questions in continuous and combinatorial optimization.

Fluid Dynamics with Incompressible Schrödinger Flow

This thesis introduces a new way of looking at incompressible fluid dynamics. Specifically, we formulate and simulate classical fluids using a \({\Bbb C}^2\)-valued Schrödinger equation subject to an incompressibility constraint. We call such a fluid flow an incompressible Schrödinger flow (ISF). The approach is motivated by Madelung's hydrodynamical form of quantum mechanics, and we show that it can simulate classical fluids with particular advantage in its simplicity and its ability of capturing thin vortex dynamics. The effective dynamics under an ISF is shown to be an Euler equation modified with a Landau-Lifshitz term. We show that the modifying term not only enhances the dynamics of vortex filaments, but also regularizes the potentially singular behavior of incompressible flows. Another contribution of this thesis is the elucidation of a general, geometric notion of Clebsch variables. A geometric Clebsch variable is useful for analyzing the dynamics of ISF, as well as representing vortical structures in a general flow field. We also develop an algorithm of approximating a ``spherical'' Clebsch map for an arbitrarily given flow field, which leads to a new tool for visualizing, analyzing, and processing the vortex structure in a fluid data.

• W. P. Carey & Co. Prize for outstanding doctoral dissertations in applied mathematics, 2017
• Full text [pdf; 90 MB]
• Full text (reduced size) [pdf; 7.6 MB]
• Caltech Thesis

@phdthesis{chern:2017:ISF, title={Fluid Dynamics with Incompressible Schr{\"o}dinger Flow}, author={Chern, Albert}, year={2017}, school={California Institute of Technology} }

The Schrödinger equation