# Available Research Projects 2014

Thesis topics are divided up into main research categories below. Within each category there are suggested PhD thesis research programs.

For shorter Honours and M.Sc. programs, please contact the supervisors listed below in your area of interest.

Please note that PhD scholarships are available for both international and domestic students. International prospective PhD students can also find detailed application instructions.

**The next scholarship deadline is October 28**, but late applications may be considered for outstanding candidates. You will need to choose a topic and discuss this with the associated supervisor before applying.

Topics that we offer fall into the following categories:

## Ultracold Fermi Gases

## 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. |

## Entanglement and Nonlocality in Quantum Mechanics

Research into these foundations of quantum theory has a wide importance both in fundamental science and also in quantum information. Quantum optics and atom-optics are uniquely placed to investigate these issues.

## 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. |

## Quantum Simulations

## (1) Early universe simulations:A common feature in theories of the early universe is the use of relativistic scalar quantum fields. Quantum fluctuations of these fields are thought responsible for large-scale structures in the universe. Therefore, it would be extremely useful to have an engineered laboratory model of this type of interacting field. This would enable comparisons of experiment both with analytic theories, and more precise quantum simulations. This can be achieve in ultra cold physics. Consider two coupled Bose gas components, which are either different nuclear spin degrees of freedom in a dipole trap, or else two spatially separated Bose gases in either one or two dimensional traps. Expanding about the potential minimum, gives the Sine-Gordon Lagrangian. On treating this as a quantum field, one has a relativistic field equation, in which the speed of light is replaced by the phonon velocity. Hence, the relative phase of two non-relativistic Bose fields - which can be created in a laboratory experiment - is able to emulate an interacting relativistic scalar field in the early universe. The Sine-Gordon Lagrangian is similar to that for the axion field. This is proposed to explain dark matter, which is the largest part of mass distributions in the universe. In this project, the original BEC fields will be treated, including dissipation and a study of the initial state temperature effects for comparison to experiment. Secondly, the relativistic field will be simulated, in order to determine how well the reduction to a single phase variable is able to replicate the full dynamics. The problem treated will be non-equilibrium evolution from a metastable potential maximum to the ground state, creating new particles and excitations. A variety of simulations are possible - in 1, 2 or 3 dimensions - to examine formation of topological structures in different dimensions, which have cosmological implications. The main purpose of the simulation will be to investigate the feasibility of potential experiments given available atomic species, the extent to which the Sine-Gordon model can be replicated with this method, and the potential applicability to analyzing cosmological data. Experiments using flat dipolar traps to test these predictions are potentially feasible at Cambridge. The project will also investigate non-equilibrium initial conditions, and the possibility of observing thermalization rates and the approach to thermal equilibrium in low dimensions.
## (2) Quantum enhanced BEC interferometry and atom lasersThis project will be to carry out quantum dynamical modeling of BEC interferometry atom lasers and thermalization. Sensitivity in BEC interferometry can be improved by increasing the signal (more atoms) or by reducing the quantum noise using correlations. Current measurements at SUT with composite pulse splitting of relatively large BECs with 40000 atoms are now approaching the atom shot noise level. The project will proceed in the following stages: (a) First the existing experimental configuration will be analyzed to determine the cause of current decoherence. In particular, finite temperature initial conditions will be treated, rather than coherent state initial conditions as in previous modeling. This will use a truncated Wigner code, together with Bogoliubov initial conditions. Computational work will be carried out using a Python interface to a graphical processor unit (GPU). (b) Next, the project will explore the use of correlated (entangled) beams in two ports of an interferometer to beat the SQL at much larger atom numbers than in previous experiments, to benefit from both types of improvement. (c) The simulation code will be extended to treat polaritonic BEC interferometry and coherence properties, for comparison with experiments underway at The Australian National University. (d) Variational enhancements to the truncated Wigner techniques for full first-principles dynamic simulations will be investigated. (e) Just as a laser has coherence limits, applications like atom interferometry raise the issue of the coherence limits of a BEC. This leads to an important question, which is the fundamental limit to quantum fluctuations in a trapped BEC caused by the non-equilibrium nature or the state preparation. Using a variationally enhanced quantum simulation, quantum evaporative cooling will be investigated with more realistic parameters than previously treated in quantum cooling calculations. (f) The fundamental issue of quantum transport in a BEC is a non-equilibrium problem which is just starting to be investigated in pioneering experiments at Cambridge. A particularly important problem is the question of motion of an impurity in a BEC. This process will be simulated directly using the quantum simulator code developed for two-component Bose gases. The objective will be to understand the ‘dressing’ process by which an impurity develops a new effective mass through its interactions.
## (3) Correlations of strongly interacting Fermi systemsOne of the most striking recent developments in ultra-cold atomic physics has been the rapid growth of interest in atomic fermions - atoms with half-integer spin. The two-dimensional Fermi gas (2DFG) is a perfect experimental model, with no lattice or disorder, unless these are deliberately engineered into the system in a controllable way. The Fermi-Hubbard model extends this to include a lattice, and is a popular model for describing a class of atypical superconductors, including high Tc cuprate superconductors, and more recently the iron pnictide and organic superconductors. This is one of the simplest models of strongly correlated fermions, and is accessible using ultra cold atoms. However, this model has no known solutions, and is difficult to treat using computational Monte-Carlo techniques due to the Fermi sign problem. In this project, symmetry projections will be applied to investigate novel ground states and quantum phase-transitions of the Fermi-Hubbard model and the 2DFG over a much wider range of conditions than previously. The best two-dimensional (2D) computational study to date was carried out in Tokyo, using the fermionic phase-space technique. However, the Tokyo study did not treat the full range of parameter values, nor the anisotropic three-dimensional case, which is relevant to a real superconductor. This work at Tokyo has shown that symmetry projection is a powerful tool for increasing the accuracy of the Gaussian phase-space representation originally developed in Australia. The project will proceed in three stages: (a) The Imada (Tokyo) algorithm will be recoded for GPU processors for greatly improved speed. This will allow a survey of ground-state correlations over a range of filling factors and dimensionless coupling constants. The algorithm will be recast as a finite temperature simulation code using variational optimization of sampling error. Finally, the effects of anisotropic coupling of several layers in three dimensions will be investigated in order to understanding issues relevant to high Tc superconductors, in particular the question of long-range order, with comparisons to earlier SUT measurements of the Tan contact. (b) The 2dFG limit will be investigated by taking a low filling-factor limit of the Fermi-Hubbard code. In recent work from SUT, a controllable virial expansion was used to obtain the effects of correlations at relatively high temperatures, based on exact two and three body quantum few-body solutions. This means that the results of the 2DFG simulations can be tested by comparison with high-temperature virial expansions developed earlier, and with SUT experiments. (c) Strongly interacting two-dimensional Fermi gas quantum simulations will be carried out to understand the unitary limit of Fermi gases. The focus will be on calculating spin-spin correlation functions. There are numerous possibilities of expanding these studies to include the effects of different types of dispersion (e.g., spin-orbit coupling and topological insulators), interactions (e.g., dipole coupling), and disorder. (e) These results will be extended to higher spin fermionic cases.
## (4) Quantum dynamics of spins and Schrodinger catsThe main goal of this part of the project will be to use variational methods to extend earlier successful demonstrations of phase-space sampling of ion-trap qubit states to full dynamical simulations that can be compared to experiments underway at NIST and Innsbruck. There are several different positive quasi-probability distributions in quantum mechanics. These exist for every quantum state. They have statistical moments which correspond exactly to correlations of the type commonly observed in Bell violations, an important signature of mesoscopic superpositions. The advantage of probabilistic sampling in quantum simulations is that the exponential dependence of memory size on the number of qubits is removed. In probabilistic simulations, the required computational memory scales linearly, not exponentially, with the number of qubits. This eliminates the problem of exponential scaling in memory size found in direct calculations. Ion traps are devices that use electrostatic interactions with charged ions to suspend them in free space at low temperatures. This allows excellent control on the interactions of nuclear spins. Highly entangled and correlated quantum states can be generated, and individual spins measured via laser interactions. An N-ion quantum Hamiltonian is known to generate Schrodinger cat states in simple cases, but no general solution to time-evolution is available. An important issue is the typical random time-dependence of the magnetic field, which causes super-decoherence due to magnetic field noise. While there is strong evidence for the formation of mesoscopic superpositions, the inhomogeneity, exponential complexity and time-dependence of the system - especially for larger numbers of spins - make it essential to develop better theoretical techniques. Once these methods are developed for two-level qubits, they will be extended to treat lattices of high-spin interacting atoms, with potential for comparisons to recent 1D Ytterbium experiments in Florence.
## (5) Non-equilibrium physics and X-ray laser coherenceThe objective of these simulations will be to understand coherence properties of high harmonic generation (HHG) having wavelengths down to X-ray levels. The project will integrate a quantum simulator of the electron response with a quantum simulator of the the corresponding electromagnetic field. This will allow a better understanding of quantum noise effects, which are the ultimate limit to coherence properties and bandwidth. Just as an ordinary laser is limited by quantum spontaneous emission, an X-ray HHG laser is limited by quantum wave-packet spreading. The underlying Lagrangian used will be the standard minimal coupling Lagrangian, appropriate to treating highly excited electrons, with the Nobel gas atoms treated as static effective potentials. The resulting quantum theory will be modeled using a truncated Wigner representation, valid for large photon numbers and high electronic quantum numbers. The initial focus of this work will be to understand the observed Rydberg resonances and wave-packet tunneling effects in multiple-pulse excitation of Nobel gas atoms and diatomic molecules. The quantum interference between electron paths and potential quantum effects in the generated X-ray field are of central interest. Since the SUT X-ray laser laboratories have a program to investigate these effects, these first-stage predictions can be compared to experiment. This theory has substantial differences and improvements compared to earlier theoretical approaches following that of Lewenstein, which typically use a semi-classical and dipole approximation, with the electron motion treated using the Schrodinger equation. The approach to be used here will be more efficient at treating large electron excursions, and will have greater accuracy in handling interactions with radiation. As a second stage, this code will be integrated with a traveling-wave radiation-field Maxwell equation solver. This will allow, for the first time, the inclusion of quantum noise.
## (6) Quantum limited optomechanics and circuit QEDThe goal of this project will be to develop quantum simulation tools for optomechanics and circuit QED experiments. These experiments have now reached the mechanical ground state of a macroscopic object. The first target problem will be treat the quantum correlations of a system of coupled optomechanical oscillators using full quantum simulations in the positive-P representation. The main purpose of the work will be to determine if it is possible to create genuine entanglement and steering between the coupled oscillators. Initial simulations will proceed using stochastic methods to calculate the correlations. Both nonlinear dynamics and quantum correlated input beams will be investigated. These are dynamical simulations, and will also involve cooperation with experimentalists at the Albert Einstein Institute (Hannover) to investigate the applicability of these techniques to gravity wave detectors. In addition to this, investigations of artificial atom simulations will be carried out for superconducting waveguide systems. These calculations are relevant to the circuit QED experiments in Nori’s group at Tokyo, as well as experiments at University of Queensland, NIST and elsewhere. This work will proceed in parallel with fundamental quantum entanglement and EPR signature investigations in the SUT Quantum Foundations project. |