Available Research Projects 2012

Schrodinger’s cat and multiparticle entanglement (Margaret Reid)

Understanding the transition from microscopic to macroscopic quantum mechanics remains an important challenge in modern physics. Key issues are whether mesoscopic superpositions can be realized, and, if so, how to resolve the Schrodinger cat paradox. The aim of this theoretical project is how to generate Schrodinger cat superpositions using Bose Einstein condensates or optomechanical devices, to enable tests of macroscopic quantum mechanics for massive systems. The mesoscopic superposition needs to be characterized, in terms of genuine multiparticle entanglement, violation of Leggett-Garg inequalities, and the potential to test Diosi-Penrose theories.

Tests of macroscopic local realism and Furry’s hypothesis (Margaret Reid)

The Einstein Podolsky Rosen (EPR) paradox showed the fundamental incompatibility of the completeness of quantum mechanics with local realism. Failure of local realism may thought of as a “spooky action at a distance”. Though work by Bell later challenged the validity of local realism, this was at a microscopic level only. Local realism is thought to be the basis for theories describing macroscopic systems. Furry proposed as a possible resolution to the EPR paradox that there are inherent in nature mechanisms that mean entanglement decays with distance. The aim of this theoretical project is to quantify Einstein, Podolsky Rosen’s “action at a distance”, so that one can develop tests of mesoscopic and macroscopic, as opposed to microscopic, local realism. Hence, while Furry’s hypothesis appears wrong for microscopic systems, it can be tested at a more macroscopic level.

Few-body physics and virial expansions (Xia-Ji Liu)

Few-body systems have become increasingly crucial to the physics of strongly correlated ultracold atomic gases. Because of large interaction parameters, conventional perturbation theory approaches such as mean-field theory, simply break down. A small ensemble of a few fermions and/or bosons, which is either exactly solvable or numerically tractable, is more amenable to non-perturbative quantal calculations. The few-body solutions can be efficiently used for investigating high- temperature properties of strongly correlated quantum gases, through the well-documented virial expansion method.

This project will investigate few-body exact solutions and high-temperature properties of ultracold atomic gases with s-wave and p-wave interactions.

Low dimensional physics of multi-species Fermi gases (Xia-Ji Liu)

Recently, ultracold low-dimensional atomic gases have attracted a great deal of interest as they show unique quantum signatures not encountered in 3D. For example, a 1D gas of bosonic atoms with strongly repulsive interactions acquires fermionic properties. A 1D gas of fermionic atoms may exhibit exotic inhomogeneous superfluidity and cluster pairing. In two dimensions, the Berezinskii-Kosterlitz-Thouless phase transition differs completely from the usual finite temperature phase transitions. Experimentally, ultracold low-dimensional atomic systems are conveniently accessible on introducing tight confinement via optical lattices that remove one or two spatial degrees of freedom.

This project will investigate exotic inhomogeneous superfluidity and Berezinskii-Kosterlitz- Thouless transition in multi-species atomic Fermi gases.

Entanglement, correlations and coherent manipulations of ultracold Fermi gases (Hui Hu)

Spin-orbit (SO) coupling leads to many fundamental phenomena in a wide range of quantum systems from nuclear physics, condensed matter physics to atomic physics. For instance, in electronic condensed matter systems spin-orbit coupling can form quantum spin Hall states or topological insulators, which have potential applications in future quantum devices. Recently, SO coupling has been induced in ultracold spinor Bose gases of 87Rb atoms by the so-called synthetic non-Abelian gauge fields. Combined with unprecedented controllability of interactions and geometry in ultracold atoms, this manipulation of SO coupling opens an entirely new paradigm for studying strong correlations of quantum many-body systems under non-Abelian gauge fields.

This project will investigate exotic state of matter in spin-orbit coupled atomic Fermi gases, such as topological superfluids and Majorana fermions, as a platform for topological quantum computation. Particular interest will be given to characterize topological quantum phase transition.

Quantitative strong-coupling theory of ultracold Fermi gases (Hui Hu)

The theory of strongly interacting fermions is of great interest. Interacting fermions are involved in some of the most important unanswered questions in condensed matter physics, nuclear physics, astrophysics, and cosmology. Though weakly interacting fermions are well understood, new approaches are required to treat strong interactions. In these cases, one encounters a “strongly correlated” picture which occurs in many fundamental systems ranging from strongly interacting electrons to quarks.

This project will investigate different many-body approaches and look for a quantitative strongly- coupling theory of ultracold Fermi gas.

Quantum Brownian motion and interferometry in a BEC (Peter Drummond)

Ultra-cold atoms are the coldest environment known, with achievable temperatures below 10-9 Kelvin. It is fascinating to ask what happens when a mesoscopic particle or nano-mechanical oscillator is immersed in a BEC or quantum Fermi gas, with the potential of achieving record low temperatures for macroscopic objects. Research into quantum Brownian motion in a BEC environment will be carried out using stochastic methods with non-local and non-Markoffian correlations. Quantum Brownian motion theory for either impurity atoms or nano-oscillators coupled to a BEC, will be compared to other cooling techniques like radiative cooling.

Quantum phase space dynamics for multi-mode fermion systems (Peter Drummond)

The focus in this phase-space research will be the use of Gaussian basis-sets, combined with variational error reductions and the use of symmetry projections to improve sampling error. Co-operation with other groups using our methods - like the computational physics groups at Tokyo University - will be encouraged, in order to disseminate these ideas, and get useful feedback about technical improvements. The main goal is to be able to model the quantum dynamical collision of two ultra-cold, strongly interacting Fermi gases, as studied experimentally in the SUT Fermi labs.

High spin topological phases in BEC (Peter Drummond)

The physics of an ultra-cold high-spin liquids and lattices will be investigated using both mean-field and Monte-Carlo methods. Here the question of interest is the physics of an optically trapped ultra-cold Bose or Fermi gas in the case of a large intrinsic nuclear angular momentum. This is distinct from the usual spin liquid of condensed matter physics, which applies to a spin-half system. With high-spin atomic BEC or Fermi gas systems, the quantum ground state is currently unknown, and will have relevance to issues such as mesoscopic entanglement and causality in multipartite systems.

Genetic correlations in RNA virus evolution (Peter Drummond)

In evolution, one must calculate the probability of any number of individuals having any genotype. Statistical fluctuations can be treated using a master equation or Markov chain approach, but only at the expense of introducing an astronomically large set of possible state descriptions. To overcome this, direct Markov chain simulation methods will be used, with modifications to improve efficiency and allow large genetic spaces to be explored. Theoretical developments in this field will introduce the idea of genetic correlations calculated using stochastic phase methods. The immediate focus of the project will be on the stochastic properties of the combined effects of genetic drift and spatial diffusion, and their effects on virus-immune system interactions and viral ecosystem dynamics, with mathematical biologists at Auckland University.