Talks

Black holes are like bells; once perturbed they will relax through the emission of characteristic waves. The frequency spectrum of these waves is independent of the initial perturbation and, hence, can be thought of as a `fingerprint' of the black hole. Since the 1970s scientists have considered the possibility of using these characteristic modes of oscillation to identify astrophysical black holes. With the recent detection of gravitational waves, this idea has started to turn into reality.
Inspired by the black hole-fluid analogy, we demonstrate the universality of the black-hole relaxation process through the observation of characteristic modes emitted by a hydrodynamical vortex flow. The characteristic frequency spectrum is measured and agrees with theoretical predictions obtained using techniques developed for astrophysical black holes. Our findings allow for the first identification of a hydrodynamical vortex flow through its characteristic waves.
The flow velocities inferred from the observed spectrum agree with a direct flow measurement. Our approach establishes a non-invasive method, applicable to vortex flows in fluids and superfluids alike, to identify the wave-current interactions and hence the effective field theories describing such systems.

The detection of gravitational waves from mergers of compact binaries in the first two runs of the Advanced LIGO-Virgo have brought in valuable insights into fundamental physics and astrophysics. The coalescence process sweeping the components through a range of frequencies at highly relativistic velocities, have enabled some of the first tests of general relativity in its highly dynamical and extremely strong field regime. The recent detection of the binary neutron star merger has shed first light on the elusive neutron star equation of state. Furthermore, with its coincident electromagnetic counterpart, a first "standard-siren" measurement of the Hubble parameter has been made independent of a cosmic distance ladder. Subsequent detections are expected to give us a more direct understanding of the nature of the black holes and the composition of neutron stars, as well as bring in a plethora of results in astrophysics and possibly new insights into cosmology. I will go over some of these exciting new results and talk about future prospects of fundamental physics and cosmology from gravitational-wave observations.

How does classical chaos affect the generation of quantum entanglement? What signatures of chaos exist at the quantum level and how can they be quantified? These questions have puzzled physicists for a couple of decades now. We answer these questions in spin systems by analytically establishing a connection between entanglement generation and a measure of delocalization of a quantum state in such systems. While delocalization is a generic feature of quantum chaotic systems, it is more nuanced in regular systems. We explore when the quantum dynamics mimics a localized classical trajectory, and find criteria to quantify Bohr's correspondence principle in periodically driven spin systems. These criteria are typically violated in a deep quantum regime due to delocalized evolution. Using our criteria, we establish that entanglement is a signature of chaos only in a semiclassical regime. Our work provides a new approach to analyzing quantum chaos and designing systems that can efficiently generate entanglement. This work has been done in collaboration with Prof. Shohini Ghose.

References: arXiv:1806.10545 (2018) and PRE 97, 052209 (2018).

While it’s undeniably sexy to work with infinite-dimensional categories “model-independently,” we contend there is a categorical imperative to familiarize oneself with at least one concrete model in order to check that proposed model-independent constructions interpret correctly. With this aim in mind, we recount the n-complicial sets model of (∞,n)-categories for 0 ≤ n ≤ ∞, the combinatorics of which are quite similar to its low-dimensional special cases: quasi-categories (n=1) and Kan complexes (n=0). We conclude by reporting on an encounter with 2-complicial sets in the wild, where a suitably-defined fibration of 2-complicial sets enables the comprehension construction introduced in joint work with Verity. Special cases of the comprehension construction can be used to “straighten” a co/cartesian fibration of (∞,1)-categories into a homotopy coherent functor, exhibit a quasi-categorical version of the “unstraightening” construction, and define an internal model of the Yoneda embedding for (∞,1)-categories.

Recent advances in scaling photonics for universal quantum computation spotlight the need for a thorough understanding of practicalities such as distinguishability in multimode quantum interference.  Rather than the usual second quantized approach, we can bring quantum information concepts to bear in first quantization.  Distinguishability can then be modelled as entanglement between photonic degrees of freedom, where loss of interference is caused by decoherence due to correlations with an environment carried by the particles themselves.  This shows that multiparticle, multimode Fock states can have natural Schmidt decompositions, corresponding to what has been called unitary-unitary duality in the representation theory of many-body physics.  
We present results along two lines: 
(i) Generalised Hong-Ou-Mandel interference as unambiguous state discrimination (arXiv:1806.01236, with S. Stanisic); we find optimised interferometers that discriminate between indistinguishable and interesting distinguishable states by projecting onto non-symmetric irreps of the unitary group of interferometers.  We give analytic and numerical results for up to nine photons in nine modes.
(ii) Quantum simulation of noisy boson sampling (arXiv:1803.03657, with A. Moylett); we provide quantum circuits that simulate bosonic sampling with arbitrarily distinguishable particles, based on the quantum Schur-Weyl transform.  This makes clear how particle distinguishabililty leads to decoherence in the standard quantum circuit model.  We show how ideal samples can be postselected, how photon loss can also be modelled, and how standard results in the classical simulation of noisy quantum computations fail to apply to the boson sampling case.