As a member of the LIGO Scientific Collaboration (LSC) I contribute to fundamental research and development of their mirror coatings. Ground based gravitational wave detectors (GWDs) consists of a Fabry-Perot interferometer with mirrors at the end of 4km long arms. Laser light is bounced off the seismically isolated mirrors through a vacuum tube hundreds of times to achieve an effective length of hundreds of kilometers.

The first detection of a black hole merger in 2015 by GWDs has ushered in a new age in astronomy [1]. If the target 3G (redshift Z=3) precision can be reached, the detectors will be able to observe further back into the history of the universe to the formation of the first astronomical objects. Brownian motion of atoms in the mirror coatings of the GWD cause thermal noise and is a major limiting factor to the precision of the detectors [2]. Reducing thermal noise requires low mechanical loss materials; however, there is no known solution given current technology and significant advancements are required to reach the target sensitivity. Amorphous solids are leading candidates for new mirror coatings due to their low mechanical loss, optical properties, and ability to be produced at scale [2]. 

Reducing thermal noise requires low mechanical loss materials; however, there is no known solution given current technology and significant advancements are required to reach the target sensitivity. Amorphous solids are leading candidates for new mirror coatings due to their low mechanical loss, optical properties, and ability to be produced at scale.

Typically, mechanical loss is estimated based on the two-level system (TLS) model. A TLS comprises two energy minima separated by an energy barrier (Fig. 1 inset). The two minima correspond to inherent structures of the system (minimal energy atomic configurations), and the barrier to the peak in energy along the transition path between the inherent structures. Mechanical loss is the result of acoustic vibrations altering the asymmetry between the minima, resulting in energy dissipation with independent contributions from each TLS. Through atomistic modelling, I have shown that the energy landscape does not form independent pairs of TLS but instead forms a scale-free network of inherent structures with topologically unique architecture that cannot be reduced to the TLS model (Fig. 1).

I have developed an analytic stochastic thermodynamic model for the mechanical loss of the full network of inherent structures (Fig. 1), which shows significant qualitative differences from the conventional TLS model [3]. The key outcome of this framework is the identification of new descriptors for guiding the design of low-loss materials, including energy landscape connectivity and the statistical distribution of energy minima. Having developed this model and the computational framework surrounding it, now is an opportune time to rapidly evaluate the performance of candidate materials and sample preparation procedures to correlate key materials, dopants, and annealing protocols with reduced mechanical loss. I will test the effects of simulated annealing on amorphous silicon and titanium dioxide. I will then test leading candidates for GWD coatings, such as germanium oxide and doped titanium oxides, to correlate mechanical loss and energy landscape connectivity and distribution. Working closely with the material synthesis laboratory of Prof. Zou and the characterization laboratory of Prof. Young in the QMI we will synthesize and test these candidate materials and processing procedures for GWD mirror coatings.

Achieving long lifetimes and coherence is a primary objective and persistent challenge in the construction of near-term quantum computers, with superconducting qubits based on amorphous alumina Josephson junctions (JJ) at the forefront of many research efforts. A major limiting factor in the performance of such qubits is decoherence from dielectric loss, which is ascribed to interactions with TLSs in the disordered amorphous alumina [5-7]. Like mechanical loss, these TLSs are described by stable minima of the underlying energy landscape; however, at the low operating temperatures of the device, transitions occur via quantum tunneling rather than thermal excitation. Measurements of dielectric loss observe telegraphic switching and diffusive drift in the frequency spectrum which cannot be explained by the TLS model without ad-hoc thermal transitions and interactions [6]. 

The failing of the TLS model hints at interesting underlying physics. Telegraphic and diffusive dielectric loss may arise naturally by accounting for the connectivity of the energy landscape. I will extend my molecular simulations to include amorphous aluminum oxide and adapt my network model to account for tunneling transitions in both a semi-classical rate equation and a full open quantum system Lindblad approach [5,7]. If the network connectivity does not significantly impact these systems at low temperature, I will study the impact of nonequilibrium driving, using the same theoretical and computational techniques. This project synergizes exceptionally well with the mechanical loss of amorphous materials: both projects employ the same molecular dynamics simulation pipeline, both concern the fundamental nature of the energy landscape of amorphous solids and observing similar materials at both high and low temperatures may yield unique and unexpected insights into their nature. The ultimate goal of this project is to provide a unifying framework for mechanical and dielectric loss that spans high to low temperature regimes.

Quantum dots (QDs) are nano-scale quantum circuits with confined electronic regions that are tunnel-coupled to metallic leads. By precisely controlling the voltage in the leads, electrons can be added to the confined region one at a time. This allows for the precise measurements of thermodynamic quantities such as heat, work, and entropy at the single-electron scale. Entropy measurements in driven QDs are a key tool for understanding of exotic many-body states of quantum matter. Improvements in QD entropy measurements could result in measurements of Kondo effects, the fractional entropy of Majorana zero modes, and topological entanglement entropy [11-15]. 

In collaboration with the laboratory of Prof. Folk in the QMI, I am studying the theory of entropy measurements in driven quantum dots. I use stochastic and quantum thermodynamics to clarify the connections between the Maxwell relations used to measure entropy in QDs and nonequilibrium measures of free energy, and develop theory that supports the experimental implementation. The theoretical and numerical methods are master equation and Lindblad dynamics and provide deeper insight into the quantum thermodynamics of driven systems, complementing the study of dielectric loss. These theoretical advances could considerably simplify and improve entropy measurements in driven QDs, potentially resulting in new quantum materials.

Historically, thermodynamics has always focused on the design of efficient engines, starting with Carnot’s in 1824. While macroscopic systems are well described by equilibrium quasistatic and adiabatic processes, these assumptions no longer hold for stochastic and quantum devices. When a stochastic fluctuating system is driven out of equilibrium by some time-dependent control, thermodynamic quantities like work, heat, and entropy become strongly path and history dependent. This makes the design of optimally efficient nanoscopic devices difficult if not impossible to treat analytically or exactly in all but the simplest situations. However, approximation methods and numerical tools can guide our understanding of the design principles underlying efficient nanoscopic devices and demonstrate many surprising and counterintuitive results.

To measure the entropy of the quantum dot-device described in the previous section, the energy difference between the dot and the reservoir must be driven from low to high energy to push the electron from the reservoir into the dot. In controlling the device, there is a freedom in the choice of time dependent control protocol. We can speed up and slow down the driving while keeping the total duration fixed and the entropy measurement remains valid. A linear (constant speed) protocol is often chosen for simplicity; however, this will not in general be optimal. One natural metric for determining the optimality of a protocol is by its energetic cost quantified by the work done on the system. Using a short-time approximation, I have shown that to minimize the energetic cost for any Markovian stochastic system, the protocol generically has jumps at the beginning and end [29,30]. Having filled out the limits of fast, slow, weak, and strong control (Fig. 4), we have a firm grasp on optimal control for minimizing energy cost in Markovian and overdamped systems [29]. However, comparatively little is known about optimal control of non-Markovian and underdamped systems which include coherent quantum devices. 

First, I will apply current optimal control theory to improve entropy measurements in quantum dot devices and design optimal annealing protocols for simulated and real amorphous solids used in gravitational wave detectors and superconducting qubits. Driven quantum dot devices are firmly in the slow limit of optimal control, and the methods of thermodynamic geometry can be used to determine the protocol that minimizes energy cost. Results will be compared to direct numerical optimization of the precision using standard machine-learning algorithms. By using optimal control strategies, we will improve measurements at no extra cost. In amorphous solids one of the strongest impacts on mechanical and dielectric loss is in the quality of annealing [6]. Well relaxed systems generically have lower mechanical and dielectric loss. It is known that energy minimizing protocols maintain the system close to equilibrium and therefore would result in better annealed samples. By applying optimal control theory, I will design annealing protocols with nonlinear time dependent temperature variations with the goal of improving the degree of annealing and reducing mechanical and dielectric loss. These will be applied to computer simulated systems, compared to direct numerical optimization, and tested by experimental colleagues in the LIGO-Virgo-KAGRA collaboration.

Second, I will study optimal control of non-Markovian and underdamped systems. To measure the entropy of more complex systems (Kondo, Majorana zero modes, and topological entanglement entropy) with a quantum dot device it will be necessary to account for quantum coherences which breaks the Markovianity of the system. This will have a non-trivial effect on the optimal control theory as it breaks one of the fundamental assumptions. Applying approximation methods similar to those used for Markov systems, I will understand the underlying design principles and how they change based on quantum coherences.