# Publications

## Quantum simulators based on the global collective light-matter interaction

Physical Review A American Physical Society (2016)

We show that coupling ultracold atoms in optical lattices to quantized modes of an optical cavity leads to quantum phases of matter, which at the same time posses properties of systems with both short- and long-range interactions. This opens perspectives for novel quantum simulators of finite-range interacting systems, even though the light-induced interaction is global (i.e. infinitely long range). This is achieved by spatial structuring of the global light-matter coupling at a microscopic scale. Such simulators can directly benefit from the collective enhancement of the global light-matter interaction and constitute an alternative to standard approaches using Rydberg atoms or polar molecules. The system in the steady state of light induces effective many-body interactions that change the landscape of the phase diagram of the typical Bose-Hubbard model. Therefore, the system can support non-trivial superfluid states, bosonic dimer, trimers, etc. states and supersolid phases depending on the choice of the wavelength and pattern of the light with respect to the classical optical lattice potential. We find that by carefully choosing the system parameters one can investigate diverse strongly correlated physics with the same setup, i.e., modifying the geometry of light beams. In particular, we present the interplay between the density and bond (or matter-wave coherence) interactions. We show how to tune the effective interaction length in such a hybrid system with both short-range and global interactions.

## Quantum correlations which imply causation.

Scientific reports **5** (2015) 18281-

In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously, motivating us to define a measure of causality that discriminates between spatial and temporal correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements.

## Non-Hermitian Dynamics in the Quantum Zeno Limit

arXiv (2015)

Measurement is one of the most counter-intuitive aspects of quantum physics. Frequent measurements of a quantum system lead to quantum Zeno dynamics where time evolution becomes confined to a subspace defined by the projections. However, weak measurement performed at a finite rate is also capable of locking the system into such a Zeno subspace in an unconventional way: by Raman-like transitions via virtual intermediate states outside this subspace, which are not forbidden. Here, we extend this concept into the realm of non-Hermitian dynamics by showing that the stochastic competition between measurement and a system's own dynamics can be described by a non-Hermitian Hamiltonian. We obtain an analytic solution for ultracold bosons in a lattice and show that a dark state of the tunnelling operator is a steady state in which the observable's fluctuations are zero and tunnelling is suppressed by destructive matter-wave interference. This opens a new venue of investigation beyond the canonical quantum Zeno dynamics and leads to a new paradigm of competition between global measurement backaction and short-range atomic dynamics.

## Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices

arXiv (2015)

We show that global light scattering from ultracold fermions in an optical lattice into a cavity can be used for tailoring local properties of the atomic system. Quantum measurement backaction strongly affects the evolution of the atoms and leads to quantum states with spatial modulations of the density and magnetisation. We propose different detection schemes for realising antiferromagnetic states and density waves. We demonstrate that such long-range correlations are a consequence of the global but spatially structured measurement backaction and cannot be realized with local addressing.

## Incoherent quantum feedback control of collective light scattering by Bose-Einstein condensates

arXiv (2016)

It is well known that in the presence of a ring cavity the light scattering from a uniform atomic ensemble can become unstable resulting in the collective atomic recoil lasing. This is the result of a positive feedback due to the cavity. We propose to add an additional electronic feedback loop based on the photodetection of the scattered light. The advantage is a great flexibility in choosing the feedback algorithm, since manipulations with electric signals are very well developed. In this paper we address the application of such a feedback to atoms in the Bose-Einstein condensed state and explore the quantum noise due to the incoherent feedback action. We show that although the feedback based on the photodetection does not change the local stability of the initial uniform distribution with respect to small disturbances, it reduces the region of attraction of the uniform equilibrium. The feedback-induced nonlinearity enables quantum fluctuations to bring the system out of the stability region and cause an exponential growth even if the uniform state is globally stable without the feedback. Using numerical solution of the feedback master equation we show that there is no feedback-induced noise in the quadratures of the excited atomic and light modes. The feedback loop, however, introduces additional noise into the number of quanta of these modes. Importantly, the feedback opens an opportunity to position the modulated BEC inside a cavity as well as tune the phase of scattered light. This can find applications in precision measurements and quantum simulations.

## Classification of macroscopic quantum effects

OPTICS COMMUNICATIONS **337** (2015) 22-26

## Quantum properties of light scattered from structured many-body phases of ultracold atoms in quantum optical lattices

NEW JOURNAL OF PHYSICS **17** (2015) ARTN 123023

## Multipartite entangled spatial modes of ultracold atoms generated and controlled by quantum measurement.

Physical review letters **114** (2015) 113604-

We show that the effect of measurement backaction results in the generation of multiple many-body spatial modes of ultracold atoms trapped in an optical lattice, when scattered light is detected. The multipartite mode entanglement properties and their nontrivial spatial overlap can be varied by tuning the optical geometry in a single setup. This can be used to engineer quantum states and dynamics of matter fields. We provide examples of multimode generalizations of parametric down-conversion, Dicke, and other states; investigate the entanglement properties of such states; and show how they can be transformed into a class of generalized squeezed states. Furthermore, we propose how these modes can be used to detect and measure entanglement in quantum gases.

## Replicating the benefits of Deutschian closed timelike curves without breaking causality

NPJ QUANTUM INFORMATION **1** (2015) ARTN 15007

## Probing and manipulating fermionic and bosonic quantum gases with quantum light

Atoms **3** (2015) 392-406

© 2015 by the authors. We study the atom-light interaction in the fully quantum regime, with the focus on off-resonant light scattering into a cavity from ultracold atoms trapped in an optical lattice. The detection of photons allows the quantum nondemolition (QND) measurement of quantum correlations of the atomic ensemble, distinguishing between different quantum states. We analyse the entanglement between light and matter and show how it can be exploited for realising multimode macroscopic quantum superpositions, such as Schrödinger cat states, for both bosons and fermions. We provide examples utilising different measurement schemes and study their robustness to decoherence. Finally, we address the regime where the optical lattice potential is a quantum dynamical variable and is modified by the atomic state, leading to novel quantum phases and significantly altering the phase diagram of the atomic system.

## Universal optimal quantum correlator

International Journal of Quantum Information (2015)

© 2015 World Scientific Publishing Company. Recently, a novel operational strategy to access quantum correlation functions of the form Tr[AρB] was provided in [F. Buscemi, M. Dall'Arno, M. Ozawa and V. Vedral, arXiv:1312.4240]. Here we propose a realization scheme, that we call partial expectation values, implementing such strategy in terms of a unitary interaction with an ancillary system followed by the measurement of an observable on the ancilla. Our scheme is universal, being independent of ρ, A, and B, and it is optimal in a statistical sense. Our scheme is suitable for implementation with present quantum optical technology, and provides a new way to test uncertainty relations.

## Majorana transport in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings.

Journal of physics. Condensed matter : an Institute of Physics journal **27** (2015) 225302-

The tunneling experiment is a key technique for detecting Majorana fermion (MF) in solid state systems. We use Keldysh non-equilibrium Green function method to study two-lead tunneling in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings. A zero-bias dc conductance peak appears in our setup which signifies the existence of MF and is in accordance with previous experimental results on InSb nanowire. Interestingly, due to the exotic property of MF, there exists a hole transmission channel which makes the currents asymmetric at the left and right leads. The ac current response mediated by MF is also studied here. To discuss the impacts of Coulomb interaction and disorder on the transport property of Majorana nanowire, we use the renormalization group method to study the phase diagram of the wire. It is found that there is a topological phase transition under the interplay of superconductivity and disorder. We find that the Majorana transport is preserved in the superconducting-dominated topological phase and destroyed in the disorder-dominated non-topological insulator phase.

## Classification of macroscopic quantum effects

Optics Communications **337** (2015) 22-26

© 2014 Elsevier B.V. All rights reserved. We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of systems differ so widely, we use a case by case approach to identifying the different parameters and criteria that capture their behaviour in a quantum mechanical framework. We find it helpful to categorise systems into three broad classes defined by mass, spatio-temporal coherence, and number of particles. The classes are not mutually exclusive and in fact the properties of some systems fit into several classes. We discuss experiments by turn, starting with interference of massive objects like macromolecules and micro-mechanical resonators, followed by self-interference of single particles in complex molecules, before examining the striking advances made with superconducting qubits. Finally, we propose a theoretical basis for quantifying the macroscopic features of a system to lay the ground for a more systematic comparison of the quantum properties in disparate systems.

## Probing matter-field and atom-number correlations in optical lattices by global nondestructive addressing

PHYSICAL REVIEW A **92** (2015) ARTN 013613

## Towards witnessing quantum effects in complex molecules.

Faraday discussions **184** (2015) 183-191

Whether many-body objects like organic molecules can exhibit full quantum behaviour, including entanglement, is an open fundamental question. We present a generic theoretical protocol for entangling two organic molecules, such as dibenzoterrylene in anthracene. The availability of organic dye molecules with two-level energy structures characterised by sharp and intense emission lines are characteristics that position them favourably as candidates for quantum information processing technologies involving single-photons. Quantum entanglement can in principle be generated between several organic molecules by carefully interfering their photoluminescence spectra. Major milestones have been achieved in the last 10 years showcasing entanglement in diverse systems including ions, cold atoms, superconductors, photons, quantum dots and NV-centres in diamond, but not yet in molecules.

## Quantum Optical Lattices for Emergent Many-Body Phases of Ultracold Atoms.

Physical review letters **115** (2015) 243604-

Confining ultracold gases in cavities creates a paradigm of quantum trapping potentials. We show that this allows us to bridge models with global collective and short-range interactions as novel quantum phases possess properties of both. Some phases appear solely due to quantum light-matter correlations. Because of a global, but spatially structured, interaction, the competition between quantum matter and light waves leads to multimode structures even in single-mode cavities, including delocalized dimers of matter-field coherences (bonds), beyond density orders as supersolids and density waves.

## Quantum macroscopicity versus distillation of macroscopic superpositions

PHYSICAL REVIEW A **92** (2015) ARTN 022356

## Generalized Pauli constraints: Hierarchy of pinning and quasipinning-measure

arXiv (2015)

The Pauli exclusion principle (PEP) has a tremendous impact on the properties and the behavior of most fermionic quantum systems. Remarkably, even stronger restrictions on fermionic natural occupation numbers follow from the fermionic exchange statistics. Based on a hierarchy induced by PEP we develop an operationally meaningful measure which allows to quantify the potential physical relevance of those generalized Pauli constraints (GPC) beyond the well-established relevance of PEP. By studying a few fermions in a harmonic trap we explore and confirm for the first time such nontrivial significance of GPC not only for weak couplings but even up to medium interaction strengths.

## A measure of majorization emerging from single-shot statistical mechanics

NEW JOURNAL OF PHYSICS **17** (2015) ARTN 073001

## Quantum optics, molecular spectroscopy and low-temperature spectroscopy: general discussion.

Faraday discussions **184** (2015) 275-303