arXiv subjects

Stephen R. Clark

Publications and source records attributed to Stephen R. Clark.

35 records · Page 2Linked to original sources

arXiv2018

Heat current rectification and mobility edges

We investigate how the presence of a single-particle mobility edge in a system can generate strong heat current rectification. Specifically, we study a quadratic bosonic chain subject to a quasi-periodic potential and coupled at its boundaries to spin baths of differing temperature. We find that rectification increases by orders of magnitude depending on the spatial position in the chain of localized eigenstates above the mobility edge. The largest enhancements occur when the coupling of one bath to the system is dominated by a localized eigenstate, while the other bath couples to numerous delocalized eigenstates. By tuning the parameters of the quasi-periodic potential it is thus possible to vary the amplitude, and even invert the direction, of the rectification.

cond-mat.stat-mech↗

arXiv2018

Hidden Order in Quantum Many-body Dynamics of Driven-Dissipative Nonlinear Photonic Lattices

We study the dynamics of nonlinear photonic lattices driven by two-photon parametric processes. By means of matrix-product-state based calculations, we show that a quantum many-body state with long-range hidden order can be generated from the vacuum. This order resembles that characterizing the Haldane insulator. A possible explanation highlighting the role of the symmetry of the drive, and the effect of photon loss are discussed. An implementation based in superconducting circuits is proposed and analyzed

quant-ph↗

arXiv2018

Efficient characterisation of large deviations using population dynamics

We consider population dynamics as implemented by the cloning algorithm for analysis of large deviations of time-averaged quantities. Using the simple symmetric exclusion process as a prototypical example, we investigate the convergence of the results with respect to the algorithmic parameters, focussing on the dynamical phase transition between homogeneous and inhomogeneous states, where convergence is relatively difficult to achieve. We discuss how the performance of the algorithm can be optimised, and how it can be efficiently exploited on parallel computing platforms.

cond-mat.stat-mech↗

arXiv2018

Asymmetry in energy versus spin transport in certain interacting, disordered systems

We study energy transport in XXZ spin chains driven to nonequilibrium configurations by thermal reservoirs of different temperatures at the boundaries. We discuss the transition between diffusive and subdiffusive transport regimes in sectors of zero and finite magnetization at high temperature. At large anisotropies we find that diffusive energy transport prevails over a large range of disorder strengths, which is in contrast to spin transport that is subdiffusive in the same regime for weak disorder strengths. However, when finite magnetization is induced, both energy and spin currents decay as a function of system size with the same exponent. Based on this, we conclude that diffusion of energy is much more pervasive than that of magnetization in these disordered spin-1/2 systems, and occurs across a significant range of the interaction-disorder parameter phase-space; we suggest this is due to conservation laws present in the clean XXZ limit.

cond-mat.dis-nn↗

arXiv2017

Ultra-fast control of magnetic relaxation in a periodically driven Hubbard model

Motivated by cold atom and ultra-fast pump-probe experiments we study the melting of long-range antiferromagnetic order of a perfect Néel state in a periodically driven repulsive Hubbard model. The dynamics is calculated for a Bethe lattice in infinite dimensions with non-equilibrium dynamical mean-field theory. In the absence of driving melting proceeds differently depending on the quench of the interactions to hopping ratio $U/J_0$ from the atomic limit. For $U \gg J_0$ decay occurs due to mobile charge-excitations transferring energy to the spin sector, while for $J_0 \gtrsim U$ it is governed by the dynamics of residual quasi-particles. Here we explore the rich effects strong periodic driving has on this relaxation process spanning three frequency $ω$ regimes: (i) high-frequency $ω\gg U,J_0$, (ii) resonant $lω= U > J_0$ with integer $l$, and (iii) in-gap $U > ω> J_0$ away from resonance. In case (i) we can quickly switch the decay from quasi-particle to charge-excitation mechanism through the suppression of $J_0$. For (ii) the interaction can be engineered, even allowing an effective $U=0$ regime to be reached, giving the reverse switch from a charge-excitation to quasi-particle decay mechanism. For (iii) the exchange interaction can be controlled with little effect on the decay. By combining these regimes we show how periodic driving could be a potential pathway for controlling magnetism in antiferromagnetic materials. Finally, our numerical results demonstrate the accuracy and applicability of matrix product state techniques to the Hamiltonian DMFT impurity problem subjected to strong periodic driving.

cond-mat.str-el↗

arXiv2017

Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks

Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose amplitudes can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the lattice, called correlators. Recently Carleo and Troyer Science 355, 602 (2017) introduced a new type sampleable ansatz called neural-network quantum states (NQS) that are inspired by the restricted Boltzmann model used in machine learning. By employing the formalism of tensor networks we show that NQS are a special form of CPS with novel properties. Diagramatically a number of simple observations become transparent. Namely, that NQS are CPS built from extensively sized GHZ-form correlators, which are related to a canonical polyadic decomposition of a tensor, making them uniquely unbiased geometrically. Another immediate implication of the equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superposition of weighed-graph states, the Laughlin state, toric code states, and the resonating valence bond state. These examples reveal the potential of using higher dimensional hidden units and a second hidden layer in NQS. The major outlook of this study is the elevation of NQS to correlator operators allowing them to enhance conventional well-established variational Monte Carlo approaches for strongly correlated fermions.

quant-ph↗

arXiv2017

The Tensor Network Theory Library

In this technical paper we introduce the Tensor Network Theory (TNT) library -- an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice systems. We also discuss different options for gaining access to the software available at http://www.tensornetworktheory.org.

quant-ph↗

arXiv2017

Dephasing enhanced spin transport in the ergodic phase of a many-body localizable system

We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime when bulk dephasing is present. We find that while dephasing always renders the transport diffusive, there is nonetheless a remnant of the diffusive to sub-diffusive transition found in a system without dephasing manifested in the behaviour of the diffusion constant with the dephasing strength. By studying finite-size effects we show numerically and theoretically that this feature is caused by the competition between large crossover length scales associated to disorder and dephasing that control the dynamics observed in the thermodynamic limit. We demonstrate that this competition may lead to a dephasing enhanced transport in this model.

cond-mat.dis-nn↗

arXiv2017

Out-of-equilibrium physics in driven dissipative coupled resonator arrays

Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, opening the road for exploration of many body regimes beyond the reach of other approaches. In this chapter, we review some of the physics arising in driven dissipative coupled resonator arrays including photon fermionisa- tion, crystallisation, as well as photonic quantum Hall physics out of equilibrium. We start by briefly describing possible experimental candidates to realise coupled resonator arrays along with the two theoretical models that capture their physics, the Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the analytical and sophisticated numerical methods required to tackle these systems is included.

quant-ph↗

arXiv2015

Parametric Amplification of a Terahertz Quantum Plasma Wave

Many applications in photonics require all-optical manipulation of plasma waves, which can concentrate electromagnetic energy on sub-wavelength length scales. This is difficult in metallic plasmas because of their small optical nonlinearities. Some layered superconductors support weakly damped plasma waves, involving oscillatory tunneling of the superfluid between capacitively coupled planes. Such Josephson plasma waves (JPWs) are also highly nonlinear, and exhibit striking phenomena like cooperative emission of coherent terahertz radiation, superconductor-metal oscillations and soliton formation. We show here that terahertz JPWs in cuprate superconductors can be parametrically amplified through the cubic tunneling nonlinearity. Parametric amplification is sensitive to the relative phase between pump and seed waves and may be optimized to achieve squeezing of the order parameter phase fluctuations or single terahertz-photon devices.

cond-mat.supr-con↗

arXiv2013

Quantifying the Nonclassicality of Operations

Deep insight can be gained into the nature of nonclassical correlations by studying the quantum operations that create them. Motivated by this we propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to quantify its commutativity with the completely dephasing operation. We show that our measure of nonclassicality is a sum of two independent contributions, the generating power -- its ability to produce nonclassical states out of classical ones, and the distinguishing power -- its usefulness to a classical observer for distinguishing between classical and nonclassical states. Each of these effects can be exploited individually in quantum protocols. We further show that our measure leads to an interpretation of quantum discord as the difference in superdense coding capacities between a quantum state and the best classical state when both are produced at a source that makes a classical error during transmission.

quant-ph↗

arXiv2012

Repulsively induced photon super-bunching in driven resonator arrays

We analyze the non-equilibrium behaviour of driven nonlinear photonic resonator arrays under the selective excitation of specific photonic many-body modes. Targeting the unit-filled ground state, we find a counter-intuitive `super bunching' in the emitted photon statistics in spite of relatively strong onsite repulsive interaction. We consider resonator arrays with Kerr nonlinearities described by the Bose Hubbard model, but also show that an analogous effect is observable in near-future experiments coupling resonators to two-level systems as described by the Jaynes Cummings Hubbard Hamiltonian. For the experimentally accessible case of a pair of coupled resonators forming a photonic molecule, we provide an analytical explanation for the nature of the effect.

quant-ph↗

arXiv2011

Categorical Tensor Network States

We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state S, we present a new and general method to factor S into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

quant-ph↗

arXiv2010

Decoherence of a quantum memory coupled to a collective spin bath

We study the quantum dynamics of a single qubit coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The spin bath is described by the Lipkin-Meshkov-Glick model and the bath spins are subjected to a transverse magnetic field. We investigate the qubit interacting via either an Ising- or an XY-type coupling term to subsets of bath spins of differing size. The large degree of symmetry of the bath allows us to find parameter regimes where the initial qubit state is revived at well defined times after the qubit preparation. These times may become independent of the bath size for large baths and thus enable faithful qubit storage even in the presence of strong coupling to a bath. We analyze a large range of parameters and identify those which are best suited for quantum memories. In general we find that a small number of links between qubit and bath spins leads to less decoherence and that systems with Ising coupling between qubit and bath spins are preferable.

quant-ph↗

arXiv2009

Density Matrix Renormalization Group in the Heisenberg Picture

In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing density matrix renormalization group calculations in the Heisenberg picture, as only the observable of interest but not the entire state is considered. In some non-trivial cases, this approach can even be exact for finite bond dimensions.

cond-mat.str-el↗

arXiv2007

Dynamics, dephasing and clustering of impurity atoms in Bose-Einstein condensates

We investigate the influence of a Bose-Einstein condensate (BEC) on the properties of immersed impurity atoms, which are trapped in an optical lattice. Assuming a weak coupling of the impurity atoms to the BEC, we derive a quantum master equation for the lattice system. In the special case of fixed impurities with two internal states the atoms represent a quantum register and the quantum master equation reproduces the exact evolution of the qubits. We characterise the qubit dephasing which is caused by the interspecies coupling and show that the effect of sub- and superdecoherence is observable for realistic experimental parameters. Furthermore, the BEC phonons mediate an attractive interaction between the impurities, which has an important impact on their spatial distribution. If the lattice atoms are allowed to move, there occurs a sharp transition with the impurities aggregating in a macroscopic cluster at experimentally achievable temperatures. We also investigate the impact of the BEC on the transport properties of the impurity atoms and show that a crossover from coherent to diffusive behaviour occurs with increasing interaction strength.

quant-ph↗

arXiv2007

Polaron Physics in Optical Lattices

We investigate the effects of a nearly uniform Bose-Einstein condensate (BEC) on the properties of immersed trapped impurity atoms. Using a weak-coupling expansion in the BEC-impurity interaction strength, we derive a model describing polarons, i.e., impurities dressed by a coherent state of Bogoliubov phonons, and apply it to ultracold bosonic atoms in an optical lattice. We show that, with increasing BEC temperature, the transport properties of the impurities change from coherent to diffusive. Furthermore, stable polaron clusters are formed via a phonon-mediated off-site attraction.

quant-ph↗