Conference

Critical values of the integrable system correspond to singular spectral curves. In this talk we shall discuss critical points, points in the moduli space where one of the Hamiltonian vector fields vanishes. These involve torsion-free sheaves on the spectral curve instead of line bundles and a lifting to a 3-manifold which fibres over the cotangent bundle. The case of rank 2 will be described in more detail.

Understanding the causal influences that hold among the parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common cause acting on both. Here, we show that it is possible to have a coherent mixture of these two possibilities. We realize such a nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's paradox. (Joint work with Katja Ried and Kevin Resch)

Sets or pairs of incompatible observables, such as momentum and position, play a pivotal role in a wide range of distinctly quantum effects and applications, including quantum cryptography, the Heisenberg Uncertainty Principle, quantum state tomography, and Bell’s inequalities. In particular, in quantum physics, we are prohibited from precisely measuring the values of incompatible observables, a fact that is at the heart of the nature of the quantum state. In this talk, I will explore an assortment of strategies that simple-mindedly attempt to circumvent this prohibition. Motivated by these naïve strategies, we experimentally investigate the use of weak measurement and optimal quantum cloning to perform joint measurements on photons. The direct outcome of these measurements are, depending on the strategy, the wavefunction, the Dirac distribution, and the density matrix of the measured quantum system. Consequently, these naïve strategies provide new ways to characterize quantum systems and to understand the very entities that we are measuring, such as the wavefunction.

Tradeoffs in measurement and information are among the central themes of quantum mechanics. I will try to summarize in this talk a few of our experiments related to modern views of these topics. In particular, I will try to give an example or two of the power of "weak measurements," both for fundamental physics and for possible precision metrology. One example will involve revisiting the question of Heisenberg's famous principle, and an interpretation which is widespread but has now been experimentally shown to be incorrect. Then I will also discuss our recent work on a "quantum data compression" protocol which would allow a small-scale quantum memory to store all the extractable information from a larger ensemble of identically prepared systems. Finally, I will talk about our experiment entangling two optical beams to demonstrate "weak-value amplification," and the ongoing controversy about when if ever this technique could be useful in practice.

One of the most successful theories in physics until now is quantum mechanics. However, the physical origins of its mathematical structure are still under debate, and a "generalized" quantum theory to unify quantum mechanics and gravity is still missing. Recently, in an effort to better understand the mathematical structure of quantum mechanics, theories containing the essence of quantum mechanics, while also having a broader description of physical phenomena, have been proposed. These so-called "post-quantum theories" have only been recently tested at the lab. In this talk, I will present the results of our experimental test using single photons to probe one of these post-quantum theories; namely, hyper-complex quantum theories. Interestingly, in hyper-complex theories simple phases do not necessarily commute. To study this effect, we apply two physically different optical phases, one with a positive and one with a negative refractive index, to single photons inside of a Sagnac interferometer. Through our measurements we are able put bounds on this particular prediction of hyper-complex quantum theories.

The scientific journey from the first hints of quantum behaviour to the Bloch sphere in your textbook was a long and tortuous one. But using some of the technological and conceptual fruits of that journey, we show that an experiment can manifest the Bloch sphere via an analysis that doesn't require any quantum theory at all. Our technique is to fit experimental data to a generalised probabilistic theory, which allows us to infer both the dimension and shape of the state and measurement spaces of the system under study. We test our technique on an experiment measuring a variety of single-photon polarization states. As expected, the reconstructed state space closely resembles the Bloch sphere, and we are able to place small upper bounds on how much the true theory describing our experiment could possibly deviate from quantum mechanics.

I will review recent results from applying the conformal bootstrap to 3D CFTs, including precise determinations of critical exponents and in the 3D Ising and O(N) vector models, new constraints on 3D Gross-Neveu models, and general bounds on correlation function coefficients of currents and stress tensors.

In this talk, we examine the behavior of the retarded Green’s function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the Green’s function is fixed (up to normalization) by symmetry, the generic Lifshitz Green’s function can a priori depend on an arbitrary function Nevertheless, we demonstrate that the imaginary part of the retarded Green’s function (i.e. the spectral function) of scalar operators is exponentially suppressed in a window of frequencies near zero. This behavior is universal in all Lifshitz theories without additional constraining symmetries. On the gravity side, this result is robust against higher derivative corrections, while on the field theory side we present two z>1 examples where the exponential suppression arises from summing the perturbative expansion to infinite order, as a consequence of the energy-momentum conservation.

A hydrodynamic theory of transport in quantum mechanically phase-disordered superconductors is possible when supercurrent relaxation can be treated as a slow process. We obtain general results for the frequency-dependent conductivity of such a regime. With time-reversal invariance, the conductivity is characterized by a Drude-like peak, with width given by the supercurrent relaxation rate. Using the memory matrix formalism, we obtain a formula for this width (and hence also the dc resistivity) when the supercurrent is relaxed by short range Coulomb interactions. This leads to a new -- effective field theoretic and fully quantum -- derivation of a classic result on flux flow resistance. With strong breaking of time-reversal invariance, the optical conductivity exhibits what we call a `hydrodynamic supercyclotron' resonance. We obtain the frequency and decay rate of this resonance for the case of supercurrent relaxation due to an emergent Chern-Simons gauge field. The supercurrent decay rate in this `topologically ordered superfluid vortex liquid' is determined by the conductivities of the normal component of the liquid. Our work gives a controlled framework for low temperature metallic phases arising from phase-disordered superconductivity.