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bstract: Nonlinear optics (NLO) plays a key role in creating quantum states of light used in the field of light-based quantum information. A well-known example is the process of spontaneous parametric down-conversion (SPDC), which is routinely used to produce entangled photon pairs. In SPDC, an intense laser beam excites a second-order, that is, a c(2), NLO crystal. Some fraction of the photons in the incident beam split into two photons of lower energy. These daughter photons constitute an entangled photon pair; the properties of one photon are inherently linked to the properties of the other photon. This entangled state is an example of a quantum state of light, that is, a state that cannot be described using classical physics

The relationship between NLO and the creation of quantum states of light exists at a very fundamental level. Most common light sources, such as sunlight, lasers, discharge lamps, and LED light bulbs, produce classical light. (A useful definition of classical light is that the Wigner distribution of its phase quadratures is necessarily non-negative.) Classical light cannot be transformed into quantum light by means of a linear transformation. Only a nonlinear transformation can turn classical light into quantum light. There has been considerable recent interest in other situations involving quantum light and NLO. For example, the process of high-order harmonic generation (HHG) is modified when excited by quantum light [1,2].

Materials with superior nonlinear optical properties are expected to play a key role in the development of future photonic devices and protocols for applications including quantum technologies, machine learning, and image acquisition and processing. Recent research approaches on means to achieve these enhanced optical properties include the following: Optical materials display greatly enhanced nonlinear optical response at wavelengths for which the real part of the permittivity vanishes (this is the so-called epsilon-near-zero, or ENZ condition). Recent work stresses the development of both homogeneous ENZ materials and of metamaterials designed to display ENZ behavior at desired wavelengths. One example of this latter approach is the use of metal-dielectric multilayer stacks, with the optical materials and layer thicknesses selected to produce ENZ behavior at any wavelength in the visible range REF. Still another approach entails the fabrications of nanoscale optical cavities comprised of one linear end mirror and one nonlinear end mirror. These cavities display highly nonlinear and complex dynamic behavior because of the interplay between cavity resonances and the resonance behavior of the nonlinear cavity end mirror. The usefulness of these novel materials will be illustrated by examples of their use in several current applications.

One crucial application is the creation of quantum states of light. Quantum states of light lend themselves to applications not possible with classical light. The field of quantum sensing is concerned with developing means to perform measurements more precisely through use of quantum light. A specific sort of quantum sensing is quantum imaging, a research area that seeks to produce “better” images using quantum methods. Quantum imaging is a research area that seeks to produce “better” images using quantum methods [3]. The image can be better in one of several different ways. It might possess better spatial resolution, it might display better signal-to-noise ratio, or it might be able to be formed using a very small number of photons. From an operational standpoint, we can consider quantum imaging to be an imaging modality that seeks to exploit the quantum properties of the transverse structure of light fields. In this presentation, we describe several different recent examples of advances in the field of quantum imaging.

Other examples of quantum imaging methods will be described in this talk. Quantum imaging has been shown to be a versatile method for enhancing the performance of optical imaging systems. One can expect additional improvements in imaging performance to be developed in the coming years.

Abstract: Quantum interference is one of the most intriguing phenomena in quantum physics at the very heart of the development of quantum technology in the current quantum industry era. It underpins fundamental tests of the quantum mechanical nature of our universe as well as applications in quantum computing, quantum sensing and quantum communication.

I will give an overview of multiphoton sensing techniques enabling the ultimate quantum sensitivity, given by the quantum Cramér-Rao bound, by employing sampling measurements which resolve the inner degrees of freedom, such as time, frequency, position, and polarization, of single photons interfering at a beam splitter. This includes: quantum-enhanced estimation of phonic emission times [1,2], positions [3-5], momenta [6] and displacements [7] for applications in synchronization and time transfer in optical network, localization microscopy and imaging of nanostructures, by circumventing the requirements of high-precision detection time resolution in standard direct time measurements and of imaging at the diffraction limit and of highly magnifying objectives in direct spatial detection; multi-parameter estimation of the polarization state of two interfering photonic qubits for applications in quantum information networks [8]; ultimate quantum sensitivity in single-photon spectroscopy without the need of high-precision single-photon spectrometers [9]; superresolution imaging beyond the Rayleigh limit of incoherent sources [10], time-resolution at the quantum limit [11], and quantum-limited sub-Rayleigh identification.

This research opens a new paradigm based on the interface between the physics of quantum interference and quantum sensing with experimentally feasible “real world” photonic sources.

Abstract: in the process of spontaneous parametric down conversion, a pump photon spontaneously splits inside a quadratic nonlinear crystal to signal and idler photons. By either structuring the nonlinear coefficient or by shaping the pump beam, it is possible to control the correlations of the down-converted signal and idler photons in different degrees of freedom [1]. Here I will focus on generating spatially encoded entangled photons. Specifically, using structured nonlinear crystals we directly generated spatially entangled signal-idler pairs, including a bi-photon Bell state in the Hermite-Gauss basis, as well as a state with three dominant pairs of coincidences [2]. Alternatively, by shaping the pump beam, we generated bi-photon qubits and qutrits in the Laguerre-Gauss basis. The bi photon qutrit enabled us to realize three-dimensional entanglement-based quantum key distribution.

Shaped pump beams were also used for generating high brightness N00N states, which were then used for super-resolved quantum rotation sensing [3]. This sensor enabled to measure the rotational Doppler shift of slowly rotating objects, at rates that are comparable to the Earth's spin. Moreover, by measuring the coincidence between 4 photons, together with high dimensional structured light, we observed 512-fold enhancement in rotation resolution.

Abstract: Classically, the Hammersley-Clifford Theorem characterizes the probability distributions that are Markov for an undirected graph as the Gibbs states of Hamiltonians that are local on the cliques of the graph. This shows that physical structure (locality of a Hamiltonian) is equivalent to correlational structure (conditional independence conditions) and explains why Gibbs states are widely applicable outside of physics, e.g. in machine learning. In quantum theory, Markovianity implies Gibbs local, but the converse is not true. A partial converse is known for graphs without triangles, in which Markovianity is shown to be equivalent to locally commuting Hamiltonians. In this talk, I report progress towards characterizing the set of graphs on which Markov is equivalent to locally commuting, by exploiting an equivalence between Markovianity and causal structure of a Hamiltonian. Using this, we have been able to extend the result to some graphs with triangles, but the full extent of the result is unknown.

This is joint work with Sayani Ghosh, Nick Ormrod and Tein van der Lugt

AbstracT : THE quantum bouncer problem concerns the quantum dynamics of a particle in a uniform field, confined to moving along the half-line. One example would be the reflection of a free-falling neutron from an absolutely reflective surface. The object of our study is the evolution of the very narrow wave packet whose accurate representation requires a large number of energy eigenstates. It was shown that the shape of the quantum probability density reflects the shape of the classical caustic pattern generated by the family of classical trajectories associated with the wave packet. Specificity of this system is the appearance of caustic lines, carrying a significant amount of the quantum probability density extending high into the classically forbidden region above the reflective plane. The extent of the quantum caustics was related to the wave packet's position uncertainty and the maximum exited energy state. The distribution of the wave packet’s phase singularities, occurring at wave nodes, was investigated, and it was found to be organized around caustics. We have identified many pairs of singularities where the real part of the energy weak value assumes large positive and negative values, with magnitudes exceeding the energy of the maximal excited state.

Besides superbehavior driven by dynamics, we have also investigated the possibility of engineering an initial state that acquires a specified value of super energy in the desired region of space and time. It was shown that the described optimization problem always has a solution, even for a moderate number of energy eigenstates. By manipulating the integral representation of energy eigenfunctions, we have constructed new superbehaving wave functions, unique to the quantum bouncer, that exist in the whole accessible region for a finite time. In the end, we have investigated patterns generated by the evolution of the finite approximation of the superbehaving wavefunction. It has been shown that superbehaving parts are now organized into stripes whose area increases with the number of allowed eigenstates