James Q. Quach

Reconfigurable quantum metamaterials

By coupling controllable quantum systems into larger structures we introduce the concept of a quantum metamaterial. Conventional meta-materials represent one of the most important frontiers in optical design, with applications in diverse fields ranging from medicine to aerospace. Up until now however, metamaterials have themselves been classical structures and interact only with the classical properties of light. Here we describe a class of dynamic metamaterials, based on the quantum properties of coupled atom-cavity arrays, which are intrinsically lossless, reconfigurable, and operate fundamentally at the quantum level. We show how this new class of metamaterial could be used to create a reconfigurable quantum superlens possessing a negative index gradient for single photon imaging. With the inherent features of quantum superposition and entanglement of metamaterial properties, this new class of dynamic quantum metamaterial, opens a new vista for quantum science and technology.

Domain structures in quantum graphity

Quantum graphity offers the intriguing notion that space emerges in the low-energy states of the spatial degrees of freedom of a dynamical lattice. Here we investigate metastable domain structures which are likely to exist in the low-energy phase of lattice evolution. Through an annealing process we explore the formation of metastable defects at domain boundaries and the effects of domain structures on the propagation of bosons. We show that these structures should have observable background-independent consequences including scattering, double imaging, and gravitational lensing-like effects.

Which-way double-slit experiments and Born-rule violation

In which-way double-slit experiments with perfect detectors, it is assumed that having a second detector at the slits is redundant, as it will not change the interference pattern. We however show that if higher-order or non-classical paths are accounted for, the presence of the second detector will have an effect on the interference pattern. Accounting for these non-classical paths also means that the Sorkin parameter in triple-slit experiments is only an approximate measure of Born rule violation. Using the difference between single and double which-way detectors, we give an alternative parameter which is an exact measure of Born rule violation.

Foldy-Wouthuysen transformation of the generalized Dirac Hamiltonian in a gravitational-wave background

Goncalves et al. derived a non-relativistic limit of the generalised Dirac Hamiltonian in the presence of a gravitational wave, using the exact Foldy-Wouthuysen transformation. This gave rise to the intriguing notion that spin-precession may occur even in the absence of a magnetic field. We argue that this effect is not physical as it is the result of a gauge-variant term that was an artefact of a flawed application of the exact Foldy-Wouthuysen transformation. In this paper we derive the correct non-relativistic limit of the generalised Dirac Hamiltonian in the presence of a gravitational wave, using both the exact and standard Foldy-Wouthuysen transformation. We show that both transformations consistently produce a Hamiltonian where all terms are gauge-invariant. Unfortunately however, we also show that this means the novel spin-precession effect does not exist.

Disorder-correlation-frequency-controlled diffusion in the Jaynes-Cummings–Hubbard model

We investigate time-dependent stochastic disorder in the one-dimensional Jaynes-Cummings-Hubbard model and show that it gives rise to diffusive behaviour. We find that disorder correlation frequency is effective in controlling the level of diffusivity. In the defectless system the mean squared displacement (MSD), which is a measure of the diffusivity, increases with increasing disorder frequency. Contrastingly, when static defects are present the MSD increases with disorder frequency only at lower frequencies; at higher frequencies, increasing disorder frequency actually reduces the MSD.