Quantum Simulation with Low-Dimensional Ultracold Atomic Gases

When a gas of atoms is cooled to extremely low temperatures, below one microkelvin, quantum effects emerge and its behaviour changes dramatically. A gas of identical bosons (particles with integer spin) undergoes Bose-Einstein condensation, a phase transition to a new state of matter which was predicted in 1925 but experimentally observed only in 1995. The difference between this fully coherent matter-wave, described by a single macroscopic quantum mechanical wave function, and a classical gas (such as air) is analogous to the difference between the light from a laser and that from a light bulb. Bose-Einstein condensate (BEC) also exhibits superfluidity, the ability to flow without any friction. In contrast, identical fermions (particles with half-integer spin) have to occupy different quantum mechanical states, but can also pair up into composite bosons and undergo a more complicated form of condensation. Such pairing and condensation are at the heart of the phenomenon of superconductivity. Thanks to the relative ease with which we can manipulate them, ultra-cold atomic gases have become extremely useful for studies of these and many other fundamental collective quantum phenomena. For example, precise tools of atomic physics allow us to tune the strength of the interactions between the atoms, and to trap them in artificial crystals of different geometries, which are formed by interfering laser beams. We can thus quantum simulate complex many-body Hamiltonians with more flexibility than is available in conventional condensed matter systems. This idea of quantum simulation was first put forward by Feynman, who pointed out that a behaviour of a complex quantum system can be efficiently simulated only by another quantum system, rather than for example using a classical computer. Ultimately we hope that these made to measure quantum systems will allow us to answer many open questions in condensed matter physics, a prominent example being the unsolved puzzle of high-temperature superconductivity (HTSC). This would also allow for a more systematic design of novel materials for practical applications. In this work we will experimentally address several important outstanding questions related to designing and probing of increasingly more intricate Bose and Fermi many-body systems. We will concentrate on low-dimensional gases, which are fascinating because of the increased importance of quantum and thermal fluctuation in reduced dimensionality. Layered two-dimensional systems which we will study are also particularly interesting because of their structural similarity to HTSC materials. We will also work on the development of interferometric methods which allow direct access to the phase of the many-body wave function, thus offering a powerful probe of the complex correlations among the particles. Finally, we will explore new ways to introduce long-range interactions in atomic gases, an essential missing ingredient for a complete analogy between atomic systems and the electron gases which interact via the long-range Coulomb potential, and investigate the out-of equilibrium many-body physics in systems with rapidly changing Hamiltonians. Going beyond the topics of many-body condensed matter physics and possible applications to material science, we will also explore the possibility to use low-dimensional atomic gases for quantum simulation of outstanding problems in other fields, ranging from statistical to high energy physics. This would establish ultra-cold gases as truly general quantum simulators, in the sense envisioned by Feynman. Our work on dynamically changing Hamiltonians may also be relevant for new approaches to quantum computation. This work will be carried out in the Quantum Gases & Collective Phenomena subgroup within the Atomic, Mesoscopic and Optical Physics (AMOP) group in the University of Cambridge Department Of Physics.