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Entangled Photon Interferometry: Development of Photonic Systems Towards Quantum Spectroscopy
Get PDFEntangled photon spectroscopy is an emergent field offering the potential to perform nonlinear and non-classical measurements at low photon fluxes. The entangled photon pairs which are generated using a continuous-wave laser pumped spontaneous parametric downconversion (SPDC) process simultaneously display strong correlations in time and anti-correlations in frequency space. Measuring changes in these correlations provides classical and non-classical information about the underlying dynamics and fluctuations of the sample-system. Further, because these two variables are not Fourier conjugates, entangled photon spectroscopy makes it possible to exploit the spectral resolution of continuous-wave lasers, while leveraging the temporal relationship of the near-simultaneously generated photon pairs which effectively mimics an ultrafast pulsed laser experiment. Nonlinear and ultrafast measurements can therefore be performed with low-power sources while also achieving superior signal-to-noise ratios due to the underlying quantum statistics. As photons in a pair can be separately manipulated, spectroscopic setups using these quantum states of light have marked benefits in contrast to measurements performed using traditional single photon states.
Here, we describe our efforts towards implementing quantum interferometers to test the abilities of entangled photon pairs in nonlinear spectroscopic studies. Specifically, we present work on the development of free-space, fiber-optic, and nanophotonic systems that leverage nonlinear materials to generate narrow to broadband entangled photon pairs via SPDC. The numerical methods used for designing and tailoring these entangled photon sources are outlined together with associated experimental limitations. The spectral-temporal correlations of the two-photon states are characterized using fourth-order interferometry, demonstrating Hong-Ou-Mandel interference with picoseconds to femtoseconds coherence times, and wavelengths ranging from the IR to the UV. A monolithic nanophotonics architecture is proposed for completely on-chip, entangled, ultrafast, and nonlinear spectroscopy.</p
New Examples and Monotonicity Formula for Mean Curvature Flow
Get PDFThe first main result of this thesis is the proof of the superconvexity of the heat kernel on hyperbolic space. We prove a conjecture of Bernstein that the heat kernel on hyperbolic space of any dimension is supercovex in a suitable coordinate and, hence, there is an analog of Huisken’s monotonicity formula for mean curvature flow in hyperbolic space of all dimensions.
In the second part of the thesis, we construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For t ≪ 0 it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle α(t) = -t, and closed off by a small copy of the Grim Reaper translating soliton.</p
Two-Dimensional Transition Metal Dichalcogenides for Ultrathin Solar Cells
Get PDFUltrathin solar cells, with absorber layers less than one micron thick, have the potential to use orders of magnitude less high-quality semiconducting material than current silicon solar cells. This could be advantageous in applications that require high power output per unit weight, such as vehicle-integrated photovoltaics, or where reducing the capital cost of solar cell manufacturing is important. Transition metal dichalcogenides are a promising candidate for the semiconducting absorber layer of ultrathin solar cells due to their intrinsically passivated surfaces and their high absorption per unit thickness.
This thesis explores two-dimensional transition metal dichalcogenides for ultrathin photovoltaics. We start with the simplest type of solar cell, which collects carriers via a Schottky junction formed by sandwiching the absorber layer between two metal contacts with different work functions. To enable this geometry and avoid Fermi-level pinning, we develop a new process for gently transferring van der Waals metal contacts onto transition metal dichalcogenides. We measure an open-circuit voltage of 250 mV and a power conversion efficiency of 0.5% in Schottky-junction solar cells. To improve upon this efficiency, we next make carrier-selective contact solar cells, which employ wide bandgap semiconductors to selectively collect electrons on one side and holes on the other side of the absorber layer. We measure an open-circuit voltage of 520 mV and a power conversion efficiency greater than 2% in devices based on perovskite solar cell geometries, with PTAA and C60 as selective contact layers. We demonstrate that short carrier lifetimes limit the voltage in these solar cells to 750 mV, well below the detailed balance voltage limit. This motivates a more thorough understanding of the carrier dynamics at play, and we use a new pump-probe optical microscopy technique, stroboSCAT, to spatiotemporally track heat and carrier evolution in transition metal dichalcogenides. When paired with a kinetic model, we show that this technique can be used to measure lifetimes and other important material parameters even in materials with low radiative efficiencies.
We conclude by outlining future research directions towards achieving power conversion efficiencies greater than 10% in transition metal dichalcogenide solar cells.</p
Combinatorics and Stochasticity for Chemical Reaction Networks
Get PDFStochastic chemical reaction networks (SCRNs) are a mathematical model which serves as a first approximation to ensembles of interacting molecules. SCRNs approximate such mixtures as always being well-mixed and consisting of a finite number of molecules, and describe their probabilistic evolution according to the law of mass-action. In this thesis, we attempt to develop a mathematical formalism based on formal power series for defining and analyzing SCRNs that was inspired by two different questions. The first question relates to the equilibrium states of systems of polymerization. Formal power series methods in this case allow us to tame the combinatorial complexity of polymer configurations as well as the infinite state space of possible mixture states. Chapter 1 presents an application of these methods to a model of polymerizing scaffolds. The second question relates to the expressive power of SCRNs as generators of stochasticity. In Chapter 2, we show that SCRNs are universal approximators of discrete distributions, even when only allowing for systems with detailed-balance. We further show that SCRNs can exactly simulate Boltzmann machines. In Chapter 3, we develop a formalism for defining the semantics of SCRNs in terms of formal power series which grew as a result of work included in the previous chapters. We use that formulation to derive expressions for the dynamics and stationary states of SCRNs. Finally, we focus on systems that satisfy complex balance and conservation of mass and derive a general expressions for their factorial moments using generating function methods
Monsoonal Precipitation in a Model Hierarchy: Impact of Continental Geometry and Global Warming
Get PDFMonsoon systems around the world vary in their onset timing and precipitation spatial extent, suggesting that continental geometry could play an important role in differentiating between different monsoons systems. Since over half the world's population is dependent on monsoonal precipitation, it is of crucial importance to understand what controls the strength, seasonal evolution, and spatial extent of the tropical circulation and its associated precipitation and how they will evolve in a warmer climate. Recent studies suggest that individual monsoon regions will respond differently to climate change, highlighting the potential influence continental geometry may have on the current and future monsoon. In this thesis, we study the response of monsoonal precipitation, in its precipitation intensity, pattern, and onset timing, to idealized continent and climate change using a model hierarchy. By progressively building up complexity, we can gain insight from the idealized cases to determine responsible mechanisms in the responses to warming found in individual monsoon regions within the full general circulation models (GCMs).
First, we study the influence of continental geometry on the timing and spatial distribution of monsoonal precipitation under our current climate using an idealized aquaplanet model run with different zonally symmetric configurations of Northern Hemispheric land. We show that having continent extending to the tropical latitudes is necessary to generate monsoons that feature a rapid migration of the convergence zone over the continent, similar to observed monsoons. Without these regions, the tropical circulation is not able to rapidly transition into an angular momentum conserving monsoon regime. Next, we focus only on the effect of climate warming on the monsoon by using a set of idealized aquaplanet simulations with uniform mixed-layer depth, run with different atmospheric longwave optical depths to simulate a large range of both colder and warmer climates than the current climate. We show that as the climate warms, during the spring the atmospheric energy storage increases, which compensates the thermal forcing and allows for the tropical circulation transitions to be delayed, resulting in a delay in monsoon onset. Furthermore, we find that in extremely warm climates, the compensating effect of the energy storage is limited due to complex changes in the surface temperature seasonality. As a result, eventually the monsoon onset delay with warming saturates. These results highlight the important role the surface, both in its physical conditions and energy balance, has on setting the monsoon.</p
A Journey with Dust: from Protoplanetary Disks to Planetary Atmospheres and Outflows
Get PDFDust in astronomy is often perceived as a hindrance to true characterization of celestial bodies. However, it is the humble dust particles that often run the show in planet formation and evolution. In this thesis, I present four different observationally inspired problems, which span a vast chronological range from core formation to atmospheric escape, and show how dust holds sway over them. In Chapter 2, I demonstrate that protoplanetary disks that are capable of forming giant planets are also capable of hosting close-in super-Earths within the giant planet’s orbit, in line with the observed correlation between the occurrence rates of these two sub-populations. In Chapter 3, I show how dust dynamics and differences in grain properties across the water ice line create a region at intermediate distances where gas accretion is rapid. This might explain the preponderance of giant planets at such distances from their host stars, independently or complementarily to prevalent ideas on where massive cores form. Subsequently, since our understanding of the simultaneous accretion of dust and gas during planet formation remains poor, I argue in Chapter 4 that atmospheric characterization of Neptune-class planets is valuable for advances in this area. In particular, I discuss my efforts to characterize one such planet (HAT-P-11b) that, as a low metallicity Neptune, serves as an instructive challenge for formation models. Finally, in Chapter 5, I substantiate the idea that dust in the form of photochemical hazes must be present in outflowing atmospheres of super-puffs (i.e. planets with super-Earth-like masses but giant planet-like radii) by using the transmission spectrum and bulk properties of the canonical super-puff Kepler-79d.</p
Accurate and Transferable Molecular-Orbital-Based Machine Learning for Molecular Modeling
Get PDFQuantum simulation is a powerful tool for chemists to understand the chemical processes and discover their nature accurately by expensive wavefunction theory or approximately by cheap density function theory (DFT)\nomenclature{DFT}{Density Functional Theory}. However, the cost-accuracy trade-offs in electronic structure methods limit the application of quantum simulation to large chemical and biological systems. In this thesis, an accurate, transferable, and physical-driven molecular modelling framework, i.e., molecular-orbital-based machine learning (MOB-ML), is introduced to provide accurate wavefunction-quality molecular descriptions with at most mean-field level computational cost. Instead of directly predicting the total molecular energies, MOB-ML describes the post-Hartree-Fock correlation energy from molecular orbital information at the cost of Hartree-Fock computations.
Preserving all the physical constraints, molecular orbital based (MOB) features represent the chemical space faithfully in both supervised clustering and unsupervised learning for chemical space explorations. The development of local regressions with scalable exact Gaussian processes within clusters further allows MOB-ML to provide the most accurate approach in both low and big data regimes. As exciting and general new tool to tackle various problems in chemistry, MOB-ML offers great accuracies of predicting total energies and serves as a universal density functional for organic molecules and non-covalent interactions in various chemical systems. With the availability of analytical nuclear gradients, MOB-ML is also capable of generating accurate PESs with few reference high-level electronic structure computations in the diffusion Monte Carlo accurately and efficiently for computational spectroscopy.</p
A Spectroscopic Study of Electronic Correlations in Twisted Bilayer Graphene by Scanning Tunneling Microscopy
Get PDFTwisted bilayer graphene around the magic angle has shown variety of correlated phases such as superconductivity, correlated insulators, and magnetism due to its flat band structure. The unconventional nature of the superconductivity and its pos- sible relation to high temperature superconductors have sparked a lot of theoretical and experimental efforts to understand the properties of the magic angle twisted bilayer graphene. While electrical transport measurements revealed the interesting phases, spectroscopic understanding is strongly needed to connect the phases with theoretical calculations. We present the spectroscopic studies of gate-tunable magic angle twisted bilayer graphene using scanning tunneling microscopy. We report that the band structure is significantly modified even at charge neutrality due to exchange interaction. We apply a perpendicular magnetic field and develop a novel method that enables scanning tunneling microscopy to reveal Landau fan diagrams. We discover topologically non-trivial states appearing at finite magnetic field, and from spectroscopy we are able to identify the mechanism. Finally, we verify inter- action driven band flattening experimentally in twisted bilayer graphene, which is responsible for creating strong correlations.</p
Prototype Interferometry in the Era of Gravitational Wave Astronomy
Get PDFSince the first direct detection of gravitational wave signals from the coalescence of a pair of stella-mass black holes on 14 September 2015, a global network of terrestrial interferometric detectors, with kilometer-scale arms, have opened a new window through which the astrophysical universe can be probed. This success was the result of decades of exploratory work done on smaller-scale prototype interferometers. Even though the detection of astrophysical gravitational wave signals has become almost a routine event, prototype interferometers remain an essential tool in developing technologies for future generations of kilometer-scale detectors. They are unique in that they are large enough to probe physics that cannot be easily investigated on the table-top, but have no obligation to function as an observatory, and so can be readily modified for a wide variety of experiments. This thesis focuses on one direction in which prototype interferometry can be taken, serving as a testbed for testing the laws of quantum mechanics at the macroscopic scale. While this is in itself an interesting experimental program, it can make a direct contribution to the field of gravitational wave astronomy since future generations of terrestrial detectors are expected to be limited in their sensitivity due to measurement limits set by the Heisenberg uncertainty principle. Techniques to evade these limits can be demonstrated on a prototype interferometer, before embarking on an expensive program to implement them at the scale necessary for kilometer-scale observatories.</p
Three Essays in Applied Economics
Get PDFThis thesis consists of three papers, two studying the effectiveness of policy interventions curbing the opioid crisis, and one studying the value of network ties in the Chinese bureaucracy. The two chapters on the opioid crisis are coauthored with Daniel Guth, a fellow Caltech graduate student.
The first chapter studies the effectiveness of the OxyContin reformulation in reducing opioid misuse and overdose. Purdue Pharma reformulated OxyContin in 2010 to make it more difficult to abuse. Previous research argued that OxyContin misuse fell dramatically and OxyContin users switched directly to heroin. Using a novel and fine-grained source of all oxycodone sales from 2006-2014, we show that the reformulation led users to substitute from OxyContin to generic oxycodone and the reformulation had no overall impact on opioid or heroin mortality. In addition, the chapter finds that generic oxycodone, instead of OxyContin, was the driving factor in the transition to heroin in recent years. These findings highlight the important role generic oxycodone played in the opioid epidemic and the limited effectiveness of a partial supply-side intervention.
The second chapter studies the spatial spillover effect of Prescription Drug Monitoring Programs (PDMPs). PDMPs seek to potentially reduce opioid misuse by restricting the sale of opioids in a state. This chapter examines discontinuities along state borders, where one side may have a PDMP and the other side may not. We find that electronic PDMP implementation, whereby doctors and pharmacists can observe a patient's opioid purchase history, reduces a state's opioid sales but increases opioid sales in neighboring counties on the other side of the state border. We also find systematic differences in opioid sales and mortality between border counties and interior counties. These differences decrease when neighboring states both have PDMPs, which is consistent with the hypothesis that the differences were caused by cross-border opioid shopping. Our work highlights the importance of understanding the opioid market as connected across counties or states, as we show that states are affected by the opioid policies of their neighbors.
The third chapter examines the value of patronage ties at lower levels of Chinese bureaucracy. A growing literature shows that connection with the right higher-level politicians is beneficial for advancements in the Communist Party of China. In this chapter, I use a self-collected data set to examine the value of patronage ties in the city committees, a previously overlooked but important level of the Chinese government. I present empirical evidence that the party secretaries are involved in the appointment of committee members. But upon departure, the party secretaries' career success does not improve the committee members' future promotion likelihood. This work highlights that the value of interpersonal connection in China is highly dependent on which level of the government is under inspection.</p