Synchronization transition in dipole-coupled two-level systems with positional disorder

We study the decoherence dynamics of dipole-coupled two-level quantum systems in Ramsey-type experiments. We focus on large networks of two-level systems, confined to two spatial dimensions and with positional disorder giving rise to disordered dipolar couplings. This setting is relevant for modeling the decoherence dynamics of the rotational excitations of polar molecules confined to deep optical lattices, where disorder arises from the random filling of lattice sites with occupation probability p. We show that the decoherence dynamics exhibits a phase transition at a critical filling pc≃0.15. For ppc the dipolar interactions dominate the disorder, and the system behaves as a collective spin-ordered phase, representing synchronization of the two-level systems and persistent Ramsey oscillations with divergent T2 for large systems. For a finite number of two-level systems N, the spin-ordered phase at p>pc undergoes a crossover to a collective spin-squeezed state on a time scale τsq∝√N. We develop a self-consistent mean-field theory that is capable of capturing the synchronization transition at pc, and provide an intuitive theoretical picture that describes the phase transition in the long-time dynamics. We also show that the decoherence dynamics appear to be ergodic in the vicinity of pc, the long-time behavior being well described by the predictions of equilibrium thermodynamics. The results are supported by the results of exact diagonalization studies of small systems.We are grateful for helpful discussions with Andreas Nun- nenkamp and Ana Maria Rey, and for financial support from EPSRC Grants No. EP/K030094/1 and No. EP/P009565/1, and the Simons Foundation. Statement of compliance with EPSRC policy framework on research data: All data accompanying this publication are directly available within the publication

Beta event-related desynchronization as an index of individual differences in processing human facial expression: further investigations of autistic traits in typically developing adults

The human mirror neuron system (hMNS) has been associated with various forms of social cognition and affective processing including vicarious experience. It has also been proposed that a faulty hMNS may underlie some of the deficits seen in the autism spectrum disorders (ASDs). In the present study we set out to investigate whether emotional facial expressions could modulate a putative EEG index of hMNS activation (mu suppression) and if so, would this differ according to the individual level of autistic traits [high versus low Autism Spectrum Quotient (AQ) score]. Participants were presented with 3 s films of actors opening and closing their hands (classic hMNS mu-suppression protocol) while simultaneously wearing happy, angry, or neutral expressions. Mu-suppression was measured in the alpha and low beta bands. The low AQ group displayed greater low beta event-related desynchronization (ERD) to both angry and neutral expressions. The high AQ group displayed greater low beta ERD to angry than to happy expressions. There was also significantly more low beta ERD to happy faces for the low than for the high AQ group. In conclusion, an interesting interaction between AQ group and emotional expression revealed that hMNS activation can be modulated by emotional facial expressions and that this is differentiated according to individual differences in the level of autistic traits. The EEG index of hMNS activation (mu suppression) seems to be a sensitive measure of the variability in facial processing in typically developing individuals with high and low self-reported traits of autism

Scattering theory for Floquet-Bloch states

Motivated by recent experimental implementations of artificial gauge fields for gases of cold atoms, we study the scattering properties of particles that are subjected to time-periodic Hamiltonians. Making use of Floquet theory, we focus on translationally invariant situations in which the single-particle dynamics can be described in terms of spatially extended Floquet-Bloch waves. We develop a general formalism for the scattering of these Floquet-Bloch waves. An important role is played by the conservation of Floquet quasi-energy, which is defined only up to the addition of integer multiples of $\hbar\omega$ for a Hamiltonian with period $T=2\pi/\omega$. We discuss the consequences of this for the interpretation of "elastic" and "inelastic" scattering in cases of physical interest. We illustrate our general results with applications to: the scattering of a single particle in a Floquet-Bloch state from a static potential; and, the scattering of two particles in Floquet-Bloch states through their interparticle interaction. We analyse examples of these scattering processes that are closely related to the schemes used to general artifical gauge fields in cold-atom experiments, through optical dressing of internal states, or through time-periodic modulations of tight-binding lattices. We show that the effects of scattering cannot, in general, be understood by an effective time-independent Hamiltonian, even in the limit $\omega \to \infty$ of rapid modulation. We discuss the relative sizes of the elastic scattering (required to stablize many-body phases) and of the inelastic scattering (leading to deleterious heating effects). In particular, we describe how inelastic processes that can cause significant heating in current experimental set-up can be switched off by additional confinement of transverse motion.This work was supported by EPSRC Grant No. EP/K030094/1.This is the accepted manuscript of a paper published in Physical Review A (Bilitewski T, Cooper NR, Physical Review A 2015, 91, 033601, doi:10.1103/PhysRevA.91.033601). The final version is available at http://dx.doi.org/10.1103/PhysRevA.91.03360

Adiabatic control of atomic dressed states for transport and sensing

We describe forms of adiabatic transport that arise for dressed-state atoms in optical lattices. Focussing on the limit of weak tunnel-coupling between nearest-neighbour lattice sites, we explain how adiabatic variation of optical dressing allows control of atomic motion between lattice sites: allowing adiabatic particle transport in a direction that depends on the internal state, and force measurements via spectroscopic preparation and readout. For uniformly filled bands these systems display topologically quantised particle transport.This work was supported by EPSRC Grant EP/K030094/1, by the JILA Visiting Fellows Program, the NSF (PIF-1211914 and PFC-1125844), AFOSR, AFOSR-MURI, NIST and ARO individual investigator awards.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevA.92.02140

Superradiance Induced Particle Flow via Dynamical Gauge Coupling.

We study fermions that are gauge coupled to a cavity mode via Raman-assisted hopping in a one-dimensional lattice. For an infinite lattice, we find a superradiant phase with an infinitesimal pumping threshold which induces a directed particle flow. We explore the fate of this flow in a finite lattice with boundaries, studying the nonequilibrium dynamics including fluctuation effects. The short-time dynamics is dominated by superradiance, while the long-time behavior is governed by cavity fluctuations. We show that the steady state in the finite lattice is not unique and can be understood in terms of coherent bosonic excitations above a Fermi surface in real space.This work was supported by EPSRC Grant No. EP/K030094/1.This is the author accepted manuscript. The final version is available from American Physical Society via https://doi.org/10.1103/PhysRevLett.117.17530

Synthetic dimensions in the strong-coupling limit: Supersolids and pair superfluids

We study the many-body phases of bosonic atoms with $N$ internal states confined to a 1D optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The $N$ internal states of the atoms are coupled via Raman transitions creating the synthetic magnetic field in the space of internal spin states corresponding to recent experimental realisations. We focus on the case of strong \mbox{SU}(N) invariant local density-density interactions in which each site of the 1D lattice is at most singly occupied, and strong Raman coupling, in distinction to previous work which has focused on the weak Raman coupling case. This allows us to keep only a single state per site and derive a low energy effective spin $1/2$ model. The effective model contains first-order nearest neighbour tunnelling terms, and second-order nearest neighbour interactions and correlated next-nearest neighbour tunnelling terms. By adjusting the flux $\phi$ one can tune the relative importance of first-order and second-order terms in the effective Hamiltonian. In particular, first-order terms can be set to zero, realising a novel model with dominant second-order terms. We show that the resulting competition between density-dependent tunnelling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-ranged pair-superfluid correlations. The method can be straightforwardly extended to higher dimensions and lattices of arbitrary geometry including geometrically frustrated lattices where the interplay of frustration, interactions and kinetic terms is expected to lead to even richer physics.Engineering and Physical Sciences Research Council (Grant ID: EP/K030094/1)This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevA.94.02363

Population dynamics in a Floquet realization of the Harper-Hofstadter Hamiltonian

We study the recent Floquet-realisation of the Harper-Hofstadter model in a gas of cold bosonic atoms. We study in detail the scattering processes in this system in the weakly interacting regime due to the interplay of particle interactions and the explicit time dependence of the Floquet states that lead to band transitions and heating. We focus on the experimentally used parameters and explicitly model the transverse confining direction. Based on transition rates computed within the Floquet-Fermi golden rule we obtain band population dynamics which are in agreement with the dynamics observed in experiment. Finally, we discuss whether and how photon-assisted collisions that may be the source heating and band population dynamics might be suppressed in the experimental setup by appropriate design of the transverse confining potential. The suppression of such processes will become increasingly important as the experiments progress into simulating strongly interacting systems in the presence of artificial gauge fields.This work was supported by EPSRC Grant No EP/K030094/1.This is the accepted manuscript. The final version is available at http://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.063611

Fragility of time-reversal symmetry protected topological phases

The second law of thermodynamics points to the existence of an `arrow of time', along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators and the Haldane phase of quantum magnets. Here, we demonstrate that such TRS-protected effects are fundamentally unstable against coupling to an environment. Irrespective of the microscopic symmetries, interactions between a quantum system and its surroundings facilitate processes which would be forbidden by TRS in an isolated system. This leads not only to entanglement entropy production and the emergence of macroscopic irreversibility, but also to the demise of TRS-protected phenomena, including those associated with certain symmetry-protected topological phases. Our results highlight the enigmatic nature of TRS in quantum mechanics, and elucidate potential challenges in utilising topological systems for quantum technologies.Simons Foundatio

Decay rates and energies of free magnons and bound states in dissipative XXZ chains

Chains of coupled two-level atoms behave as 1D quantum spin systems, exhibiting free magnons and magnon bound states. While these excitations are well studied for closed systems, little consideration has been given to how they are altered by the presence of an environment. This will be especially important in systems that exhibit nonlocal dissipation, e.g. systems in which the magnons decay due to optical emission. In this work, we consider free magnon excitations and two-magnon bound states in an XXZ chain with nonlocal dissipation. We prove that whilst the energy of the bound state can lie outside the two-magnon continuum of energies, the decay rate of the bound state has to always lie within the two-magnon continuum of decay rates. We then derive analytically the bound state solutions for a system with nearest-neighbour and next-nearest-neighbour XY interaction and nonlocal dissipation, finding that the inclusion of nonlocal dissipation allows more freedom in engineering the energy and decay rate dispersions for the bound states. Finally, we numerically study a model of an experimental set-up that should allow the realisation of dissipative bound states by using Rydberg-dressed atoms coupled to a photonic crystal waveguide (PCW). We demonstrate that this model can exhibit many key features of our simpler models

Phases of driven two-level systems with nonlocal dissipation

We study an array of two-level systems arranged on a lattice and illuminated by an external plane wave which drives a dipolar transition between the two energy levels. In this set up, the two-level systems are coupled by dipolar interactions and subject to nonlocal dissipation, so behave as an open many-body quantum system. We investigate the long-time dynamics of the system at the mean-field level, and use this to determine a phase diagram as a function of external drive and detuning. We find a multitude of phases including antiferromagnetism, spin density waves, oscillations and phase bistabilities. We investigate these phases in more detail and explain how nonlocal dissipation plays a role in the long-time dynamics. Furthermore, we discuss what features would survive in the full quantum description