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Abstract: Luttinger liquid model plays very special role in condensed matter physics because it provides rear opportunity to treat critical behaviour emerging due to interaction. Disorder in these strongly correlated one-dimensional systems leads to quantum phase transitions described by a set of critical exponents. The topology of the phase diagram can be universal and may be predicted by studying critical exponent associated with these phase transitions. There are relations between different exponents (dualities) that impose the phase diagram structure. I will discuss the origin of these dualities in multi-channel Luttinger liquids and show how they can be used to predict universal structure of phase diagrams.
Abstract: In specially engineered light-matter systems photons can be made to interact strongly, which leads to a wide range of collective behaviours from order-disorder phase transitions and superfluidity to topological phases. However, their intrinsically dissipative nature results in highly non-equilibrium conditions leading to new phenomena which only start being explored. I will discuss a few examples of non-equilibrium collective effects in such systems.
In particular, the Berezinskii-Kosterlitz-Thouless mechanism, in which a phase transition is mediated by the proliferation of topological defects, governs the critical behaviour of a wide range of equilibrium two-dimensional systems with a continuous symmetry, ranging from spin systems to superconducting thin films and two-dimensional Bose fluids, such as liquid helium and ultracold atoms. We show that this phenomenon is not restricted to thermal equilibrium, rather it survives more generally in a dissipative highly non-equilibrium system driven into a steady-state. Yet, the exponent of the power-law decay of the first order correlation function in the (algebraically) ordered phase can exceed the equilibrium upper limit: this shows that the ordered phase of driven-dissipative systems can sustain a higher level of collective excitations before the order is destroyed by topological defects. Despite these differences, the universal dynamics following an infinitely fast quench across the transition reveals the same critical exponent as one expected for the equilibrium BKT transition, and the Kibble-Zurek mechanism seem to hold. Finally, despite the fact that the excitations spectra do not satisfy the Landau criterion, the dissipative-driven quantum fluid of light does exhibit some superfluid properties.
One-dimensional boson flow between weakly couple reservoirs - by Professor Igor Lerner, University of Birmingham
Abstract: We study a flow of ultracold bosonic atoms through a one-dimensional channel that connects two macroscopic three-dimensional reservoirs of Bose-condensed atoms via weak links implemented as potential barriers between each of the reservoirs and the channel. We consider reservoirs at equal chemical potentials so that a superflow of the quasicondensate through the channel is driven purely by a phase difference 2Φ imprinted between the reservoirs. We find that the superflow never has the standard Josephson form ∼ sin 2Φ. Instead, the superflow discontinuously flips direction at 2Φ =2π and has metastable branches. We show that these features are robust and not smeared by fluctuations or phase slips. We describe a possible experimental setup for observing these phenomena.
A wave-guided Sagnac Interferometer for Bose-Einstein Condensates - by Dr Patrick Navez, University of Crete and CCQNC (Crete Centre for Quantum Complexity and Nanotechnology)
Abstract: Guided matter wave interferometry offers the possibility to largely increase the duration of the individual measurement event, thus promising a large increase in sensitivity albeit at the cost of reduced precision. In this talk we present a novel matter wave Sagnac interferometer based on state-dependent manipulation of atoms.
Waveguides based on time-averaged adiabatic potentials (TAAP) are generalized to the case of elliptic radio-frequency field. Taking advantage of the change in sign in the Zeeman energy, we derive distinct potentials for even and odd hyperfine components.
We analyze two following configurations, one where the two components are confined in two `buckets' and carried separately in the opposite direction through the ring, and one where these spin components are accelerated and decelerated within a wave guide.
Corrections to the ideal Sagnac phase are also investigated by extending the area theorem beyond a purely adiabatic movement of the atoms.
The interplay between ultracold atoms, semiconductor surfaces and quantum electronic systems - by Professor Mark Fromhold, Department of Physics and Astronomy, University of Nottingham
This talk will consider the mutual interaction between ultracold atom clouds and nearby quantum electronic structures. In particular it will consider the potential advantages of using quantum electronic components to trap, manipulate, and electrically image ultracold atoms. Conversely, it will also consider how the cold atom clouds can be used to provide functional imaging of the electronic systems.
Prof Fromhold will present calculations which predict that current through quantum electronic components fabricated within two-dimensional electron gases can trap ultracold atoms ~200 nm away, with orders of magnitude less spatial and temporal noise than for metal trapping wires. This noise reduction, combined with low Casimir-Polder attraction, may enable the creation of hybrid atom chip structures, which exploit small changes in the conductance of quantum electronic devices to control the trapped atoms. For example, activating a single quantized conductance channel in a quantum point contact can split a Bose-Einstein Condensate (BEC) for atom interferometry. In turn, the response of the BEC to the opening and closure of conduction channels offers a route to functional imaging of quantum devices and transport.
Demystifying the holographic mystique - by Professor Dmitri Khveshchenko, Department of Physics and Astronomy, University of North Carolina - Chapel Hill
Despite great efforts, the progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather slow. It's been argued, however, that the recent proliferation of the ideas of holographic correspondence originating from string theory may offer a possible way out of the stalemate. This discussion aims at establishing the true (as opposed to the desired) status of the applications of holography to condensed matter systems and elucidating the conditions under which it might indeed work.
Weak measurements and quantum optical lattices for ultracold gases of bosons and fermions - by Dr Igor Mekhov, Department of Physics, University of Oxford
We show that the quantum backaction of weak global measurement constitutes a novel source of competitions in many-body systems (in additions to standard short-range tunnelling and interactions in lattices). This leads to novel dynamical effects: multimode oscillations of macroscopic superposition states, nonlocal non-Hermitian Zeno dynamics, long-range correlated pair tunnelling, protection and break-up of fermion pairs, as well as generation of antiferromagnetic states. Quantization of optical lattice potentials enables quantum simulations of various long-range interacting systems unobtainable using classical optical lattices. It leads to new quantum phases (dimers, trimers, etc. of matter waves) beyond density orders (e.g. supersolids) utilizing collective light-matter interaction.
 T. Elliott, W. Kozlowski, S. Caballero-Benitez, and I. B. Mekhov, Phys. Rev. Lett. 114, 113604 (2015).
 S. Caballero-Benitez and I. B. Mekhov, arXiv:1504.06581, tbp in Phys. Rev. Lett. (2015).
Constructing a long-wavelength radiation trapped-ion quantum computer - by Professor Winfried K. Hensinger, Department of Physics & Astronomy, University of Sussex
Computers built with quantum technology (a quantum computer) may fundamentally change what a computer may be able to accomplish. Many problems are so complicated that even the fastest supercomputer would currently take millions of years to provide an answer. Optimising financial transactions, machine learning, chemical reactions, understanding protein folding and breaking codes are just some of the problems where the existence of a quantum computer could change everything.
Trapped ions constitute one of the most successful physical implementations to build such a device. To this point, entanglement operations on ion quantum bits (qubits) have predominantly been performed using lasers. When scaling to larger qubit numbers this will become more challenging due to the required engineering that might be required in order to engineer hundred-thousands of laser beams needed to operate millions of qubits that would be needed for a practical quantum computer. Using long-wavelength radiation along with static magnetic field gradients provides a powerful method capable of significantly simplifying the construction of a large scale quantum computer. Instead of aligning numerous pairs of Raman laser beams into designated entanglement zones, the use of a single microwave horn outside the vacuum system is sufficient. Such gate operations are vulnerable to decoherence due to fluctuating magnetic fields, however the use of microwave-dressed states protects against this source of noise; with radio-frequency fields being used for qubit manipulation.
I will give an introduction to quantum information processing with trapped ions and I will present an industrial blue-print to build a large scale quantum computer. I will report the experimental demonstration of important tools towards this end such as the realisation of spin-motion entanglement, a new method to efficiently prepare dressed state qubits and qutrits, the demonstration of ground state cooling using long wavelength radiation and the demonstration a high-fidelity long-wavelength two-ion quantum gate using dressed states. Finally, I will present results concerning the development of ion microchips that can be used as an architecture for such a quantum computer.
Emergent topological properties in an interacting one-dimensional system - by Dr Sam Carr, School of Physical Sciences, University of Kent
We will review the basics of one-dimensional quantum wires, and specialise to systems with a spin gap and with unbroken time reversal symmetry, often known as a Luther-Emery liquid. We show that there are two possible states of the system satisfying such properties; thermodynamically equivalent, however with rather different correlations. One of these states, with algebraically decaying spin density wave correlations, turns out to have non-trivial topological properties. Firstly — there are fractionalised spin edge modes; and secondly, the system is robust against non-magnetic disorder — leading to perfect conduction at zero temperature. If there is time, we will also demonstrate a specific realistic microscopic model with spin-orbit interaction in which such a state may be realised.
Theory of fermion parity measurement and control in Majorana circuit quantum electrodynamics - by Dr Eran Ginossar, University of Surrey
Combining superconducting qubits with mesoscopic devices that carry topological states of matter may lead to compact and improved qubit devices with properties useful for fault-tolerant quantum computation. We introduce a charge qubit device based on a topological superconductor circuit and show that signatures of Majorana fermions could be detected. This device stores quantum information in coherent superpositions of fermion parity states originating from the Majorana fermions, generating a highly isolated qubit whose coherence time could be greatly enhanced. We study the effect of the Majorana fermions on the quantum electrodynamics of the device embedded within an optical cavity and develop protocols to initialise, control and measure the parity states. We show that, remarkably, the parity eigenvalue is revealed via dispersive shifts of the optical cavity in the strong coupling regime and its state can be coherently manipulated via a second order sideband transition.
Two-dimensional (2D) superconducting interfaces constitute a central venue for realizing topological states of matter. The reason is that the broken inversion symmetry along with the atomic spin-orbit coupling naturally lead to singly degenerate Fermi surfaces with nontrivial spin-textures. In this talk, we will first discuss the general concept of symmetry breaking in superconducting systems. By combining symmetry and energetic arguments, a “design principle”  for having a 2D superconducting instability that spontaneously breaks time-reversal symmetry is deduced. The behavior of the condensate under the reflection of the time-direction is a pivotal property as it determines the topological classification. However, the value of the associated topological indices is in general not fully fixed by symmetries alone, but requires knowledge about microscopic details. As an example of great current interest, we will then focus on a specific physical system, the LaAlO3/SrTiO3 interface electron liquid. Since the microscopic origin of the observed superconductivity is still under debate, both conventional and unconventional pairing scenarios are discussed. It is found  that unconventional pairing, that is superconductivity based on the exchange of particle-hole excitations, leads to a topological phase with Majorana bound states and related non-trivial topological aspects. In contrast, conventional electron-phonon coupling in the same system yields a topologically trivial state. Consequently, topological signatures, in particular Majorana edge states, can be used to detect the microscopic origin of superconductivity. Finally, also the impact of impurity scattering  on the different superconducting states will be analyzed.
 Scheurer and Schmalian, arXiv:1503.03646.
 Scheurer and Schmalian, Nat. Commun. 6, 6005 (2015).
 Scheurer, Hoyer, and Schmalian, arXiv:1505.04919.
Quantum non-linear dynamics of photons and Cooper-pairs in a superconducting circuit - by Andrew Armour, University of Nottingham
Embedding a voltage-biased Josephson junction within a high-Q superconducting microwave cavity provides a way of exploring strongly non-linear quantum dynamics. The cavity is pumped to a far from equilibrium state at resonances where the energy given to a tunnelling Cooper pair by the voltage bias is equal to a multiple of the cavity photon frequency. Intriguingly, the pumping produced by the flow of Cooper pairs can produce non-classical states in the cavity. In this talk I will describe a simple theoretical model for this type of system and outline how the coupled dynamics of the cavity photons and Cooper-pairs can be uncovered using a combination of analytical approximations and numerical methods.