Signatures of Superradiance as a Witness to Multipartite Entanglement.

Generation and detection of entanglement is at the forefront of most quantum information technologies. There is a plethora of techniques that reveal entanglement on the basis of only partial information about the underlying quantum state, including entanglement witnesses. Superradiance refers to the phenomenon of highly synchronized photon emission from an ensemble of quantum emitters that is caused by correlations among the individual particles and has been connected by Dicke himself to the presence of multipartite entangled states.

Observation of two-dimensional Anderson localisation of ultracold atoms.

Anderson localisation -the inhibition of wave propagation in disordered media- is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased.

Variety, the spice of life and essential for robustness in excitation energy transfer in light-harvesting complexes.

For over a decade there has been some significant excitement and speculation that quantum effects may be important in the excitation energy transport process in the light harvesting complexes of certain bacteria and algae, in particular via the Fenna-Matthews-Olsen (FMO) complex. Whilst the excitement may have waned somewhat with the realisation that the observed long-lived oscillations in two-dimensional electronic spectra of FMO are probably due to vibronic coherences, it remains a question whether these coherences may play any important role. We review our recent work showing how important the site-to-site variation in coupling between chloroplasts in FMO and their protein scaffold environment is for energy transport in FMO and investigate the role of vibronic modes in this transport.

Environment mediated multipartite and multidimensional entanglement.

Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir.

A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.

Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms.

Rotons in interacting ultracold bose gases.

In three dimensions, noninteracting bosons undergo Bose-Einstein condensation at a critical temperature, T(c), which is slightly shifted by ΔT(c), if the particles interact. We calculate the excitation spectrum of interacting Bose systems, (4)He and (87)Rb, and show that a roton minimum emerges in the spectrum above a threshold value of the gas parameter. We provide a general theoretical argument for why the roton minimum and the maximal upward critical temperature shift are related.

Quantum mechanical potentials related to the prime numbers and Riemann zeros.

Prime numbers are the building blocks of our arithmetic; however, their distribution still poses fundamental questions. Riemann showed that the distribution of primes could be given explicitly if one knew the distribution of the nontrivial zeros of the Riemann zeta(s) function. According to the Hilbert-Pólya conjecture, there exists a Hermitian operator of which the eigenvalues coincide with the real parts of the nontrivial zeros of zeta(s) .

Riemann zeros, prime numbers, and fractal potentials.

Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one dimension.