# Research

Over the course of my short research career, I have become particularly interested in several foundational areas in quantum physics. However, I always try to think how, as a theorist, my work will be incorporated with the tools and techniques used by experimentalists—so I try to spend a lot of time modelling and thinking about the data. n any case, these are the three foundational areas I’m most interested in:

**Stochastic Quantum Thermodynamics,**and the study of how quantum trajectories—that is the dynamical behaviour of quantum systems that are continuously monitored—impacts our understanding of thermodynamics. Since the inception of quantum mechanics, the role of measurement has been somewhat problematic since it does not comport with our theory and requires it’s on set of rules. If you include a serious treatment of the measurement process into any thermodynamic analysis, you come across Stochastic Quantum Thermodynamics.was the field that piqued my interest in doing a PhD in quantum physics. Like classical information theory, quantum information theory attempts to understand how we can encode, compress, and transmit information using quantum systems. Moreover, just like classical information theory, there are close and interesting parallels to the study of thermodynamics.**Quantum Information Theory**isn’t just relevant to physics, but it plays a special role in quantum theory. When we make a measurement of a quantum system, we are trying to learn about some underlying parameters. Unlike classical systems the act of measurement also perturbs the very system you are trying to measure! This creates a very unique environment to study parameter inference and the application of Bayesian statistics.**Bayesian inference**

# Select Projects

### First Passage Times for Continuous Quantum Measurement Currents

https://arxiv.org/pdf/2308.07810.pdf

The First Passage Time (FPT) is the time taken for a stochastic process to reach a desired threshold. Over the years it has found wide application in various fields (such as biology, chemistry, and finance) and has recently become a particularly important concept in stochastic thermodynamics, due to its relation to kinetic uncertainty relations (KURs). In this paper we show how can compute the FPT distribution associated with the stochastic measurement current in the case of continuously measured quantum systems. Our approach is based on a charge-resolved master equation, which is related to the Full-Counting statistics of charge detection. In the quantum jump unravelling we show that this takes the form of a coupled system of master equations, while for quantum diffusion it becomes a type of quantum Fokker-Planck equation. In both cases, we show that the FPT can be obtained by introducing absorbing boundary conditions, making their computation extremely efficient—this is actually very similar to the methodology employed in classical physics. The versatility of our framework is demonstrated with two relevant examples. First, we show how our method can be used to study the tightness of recently proposed KURs for quantum jumps. Second, we study the homodyne detection of a single two level atom, and show how our approach can unveil various non-trivial features in the FPT distribution.

### Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics

https://arxiv.org/abs/2303.04270

Continuously measured quantum systems are characterized by an output current (the measurement signal), in the form of a stochastic and correlated time series which conveys crucial information about the underlying quantum system. The many tools used to describe fluctuation in these currents scattered across different communities: quantum opticians often use stochastic master equations, while a prevalent approach in condensed matter physics is provided by full counting statistics. These, however, are simply different sides of the same coin. Our goal in with this tutorial is to provide a unified toolbox for describing current fluctuations. This not only provides novel insights, by bringing together different fields in physics, but also yields various analytical and numerical tools for computing quantities of interest. To illustrate our results with four pedagogical examples that are commonly found in the field, and connect them with topical fields of research, such as waiting-time statistics, quantum metrology, thermodynamic uncertainty relations, quantum point contacts and Maxwell's demons.

**Diverging current fluctuations in critical Kerr resonators**

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.033707

A quintessential quantum optical model is the parametrically pumped Kerr model which describes a driven-dissipative nonlinear cavity, whose nonequilibrium phase diagram features both continuous and discontinuous quantum phase transitions. We consider the consequences of these critical phenomena for the stochastic measurement currents in both direct photodetection (particle counting) and homodyne (phase measurement) detection schemes. However, we find strikingly different current fluctuations for these two detection schemes near the continuous transition, a behavior which is explained by the complementary information revealed by measurements in different bases. To obtain these results, we develop mathematical formulas to efficiently compute the diffusion coefficient—which characterizes the long-time current fluctuations—directly from the quantum master equation, thus connecting the formalisms of full counting statistics and stochastic quantum trajectories.