Talks

 I will present a modification of the Sachdev-Ye-Kitaev model which demonstrates ergodicity breaking phenomenon, while retaining its' solvable structure (which is one of the signatures of the model). I will present results from various probes that detect the ergodicity breaking, and demonstrate a roadmap that will lead to a solution.

Quantum trajectory theory, also known as quantum state filtering, enables us to estimate the state of a quantum system conditioned on the measurement we perform. In cases where we measure the fluorescence from a driven two-level atom with an inefficient photo detector, the conditioned state of the atom is generally not pure, except immediately after a photon detection since then we know that the atom is in the ground state. For the detection schemes such as homodyne measurement the state is never pure since it gives rise to quantum state diffusion and not quantum state jumps. In these scenarios questions can be asked as: 
Given that I did use a photo detector and did see a particular time sequence of detections, how would the atom have behaved if instead I had chosen to measure the fluorescence using a homodyne detection scheme?
These questions are called counterfactual questions. Counterfactuality has played significant roles and has a long history in philosophy of trying to make sense of such questions. There are various approaches in how to evaluate such counterfactual questions. One such influential and attractive approach is that of David Lewis where he has a generalized analysis for counterfactuals. 

Analysis 2. A counterfactual " If it were that A, then it would be that C" is (non-vacuously) true if and only if some (accessible) world where both A and C are true is more similar to our actual world, overall, than is any world where A is true, but C is false. 

To evaluate our atom counterfactual problem we use his approach under the two main considerations:

1) To avoid any big, widespread, diverse violations of law. 

The antecedent of our counterfactual ( the thing that we propose to change) is our choice of measurement and that is within the laws of Quantum theory. 

2) Maximize the spatiotemporal region throughout which perfect match of particular fact prevails. 

Thus, in evaluating the counterfactual problem, any information not collected by the primary detector can be modeled as photon absorptions and should be held fixed, under the above consideration. 

Denoting these other 'clicks' , described by some list of times M, and using the actual observed record of photon-counts denoted by the list of times, N, we can calculate a conditional probability of M given N. Following this we evaluate a second conditional probability with which we are most likely to observe a homodyne record over time ,Y , if we were ( counterfactually) making a homodyne measurement given M ( since M remains fixed). Conditioning the actual state (the state conditioned on all the measurements in the counterfactual case) of the atom on these probabilities and performing an ensemble average over all possible M and Y would give us the best ( relative to trace-mean-square-deviation cost function) estimate of the counterfactual state which answers the question. 

Achieving high-fidelity and fast quantum state manipulation under realistic dissipation conditions remains a pivotal challenge in quantum computing and quantum information processing. Real-world quantum systems face dual sources of dissipation: environmental noise and drive-induced effects, which are often overlooked in existing control protocols. These limitations hinder the practical implementation of high-speed, accurate quantum operations.

In this work, we propose a method for designing pulse profiles that drive a quantum system from an initial state to a target state with both high fidelity and minimal time. Leveraging the GRAPE algorithm, our approach explicitly accounts for both environmental and drive-induced dissipation, ensuring robust performance across diverse quantum platforms.

Our findings highlight two critical insights: (1) the existence of an optimal evolution time that maximizes fidelity and (2) the counterintuitive enhancement of fidelity at lower drive strengths. These results pave the way for robust quantum control in open systems, addressing key obstacles to scaling quantum technologies. By improving the efficiency and accuracy of quantum operations, our method contributes to the realization of practical quantum computers and advanced quantum sensing technologies, even in the presence of realistic dissipation.

I plan to review several ways of testing if the gravitational field has quantum aspects in the low energy regime.  I explain why the hybrid (half quantum/half classical) models are inadequate and how they could be ruled out. Furthermore, I maintain that there is no prima facie reason to expect problems when quantizing gravity in the linear regime; I summarise the main perceived difficulties only to dismiss them as irrelevant. Going beyond the linear regime is challenging in the lab, and one might have to look towards astrophysics and cosmology of the early universe instead.  Finally, many interesting features of quantum field theory could be explored in the low-energy regime that may not necessarily be specific to gravity.

Rydberg atoms are giant atoms with the outer electron in a highly excited state with large values of the principal quantum number n. Rydberg atoms are highly sensitive to external fields, imparting these atoms extraordinary characteristics for Quantum sensing of electromagnetic fields.

In this talk, I will describe our recent results on Doppler-enhanced Quantum magnetometry with Rydberg atoms. We demonstrate in this work that one can harness Doppler shifts in an unconventional configuration of laser beams for Rydberg excitation to produce an order-of-magnitude enhanced response to a magnetic field as compared to the commonly used conventional configuration. We explain and generalize our findings with theoretical modelling and simulations based on a Lindblad master equation.
I will also discuss our recent observations on the effect of interatomic interaction in Autler-Townes splitting in ultra-cold Rydberg atoms. Our measurements on highly excited Rydberg atoms are directed towards Quantum sensing, Quantum computing and Quantum simulation of many-body physics with individual Rydberg atoms in an array of optical tweezers.

After motivating the need for a study of Open Quantum Systems, I introduce, briefly, some recent developments in the efforts to understand non-Markovian phenomenon.
The discussion about non-Markovian behaviour is made in the backdrop of the Garraway model. This is followed by an introduction to notions such as ergotropy, entropy production, power, in the context of quantum thermodynamics.
Two types of Quantum Thermodynamic devices: Quantum Battery and Quantum Heat Engine are discussed.
These are then illustrated on open system models; (a). the Garraway type, (b). central spin model, (c). Quantum Brownian Motion, (d). two-qubit decoherence.

In this lecture, we provide an introduction to quantum trajectory theory. We present various mathematical problems that arise within this context. In particular, we introduce approaches for analyzing the asymptotic behavior, convergence speed, and stabilization of quantum trajectories toward different states or subspaces through feedback control strategies. Our study includes both quantum non-demolition (QND) measurements and generic (non-QND) measurements in discrete-time and continuous-time settings.

We introduce and study bipartite quantum states that are invariant under the local action of the cyclic sign group. Due to symmetry, these states are sparse and can be parameterized by a triple of vectors. Their important semi-definite properties, such as positivity and positivity under partial transpose (PPT), can be simply characterized in terms of these vectors and their discrete Fourier transforms. We study in detail the entanglement properties of this family of symmetric states, showing in particular that it contains PPT entangled states. For states that are diagonal in the Dicke basis, deciding separability is equivalent to a circulant version of the complete positivity problem. We provide some geometric results for the PPT cone, showing in particular that it is polyhedral. In local dimension less than 5, we completely characterize these sets and construct entanglement witnesses; some partial results are also obtained for d = 6, 7. Finally, we present some novel graph-theoretic techniques to detect entanglement in quantum states with symmetry, and construction of various families of PPT entangled states in all dimensions. 

Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing an exchange of finite quanta with the environment. In this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles classified as engine-like, cooling-like, or idle. We analyze the statistics of individual cycle types and their durations, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of a given type. Central to our analysis is the notion of intermittency, which captures the operational consistency of the machine by assessing the frequency and distribution of idle cycles. Our framework offers a novel approach to characterizing thermal machines, with significant relevance to experiments involving mesoscopic transport through quantum dots.