Publications

Order by: publication date number of citations

• Phase-space methods for simulating the dissipative many-body dynamics of collective spin systems

  Julian Huber, Peter Kirton, Peter Rabl

  SciPost Phys. 10, 045 (2021) · published 22 February 2021 | Toggle abstract · pdf

  We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses an extension of the truncated Wigner approximation to map the exact open system dynamics onto stochastic differential equations for the corresponding phase space distribution. This approach is most effective in the limit of very large spin quantum numbers, where exact numerical simulations and other approximation methods are no longer applicable. We benchmark this numerical technique for known superradiant decay and spin-squeezing processes and illustrate its application for the simulation of non-equilibrium phase transitions in dissipative spin lattice models.

  29 citations

• Tangent-space methods for truncating uniform MPS

  Bram Vanhecke, Maarten Van Damme, Jutho Haegeman, Laurens Vanderstraeten, Frank Verstraete

  SciPost Phys. Core 4, 004 (2021) · published 19 February 2021 | Toggle abstract · pdf

  A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projected entangled pair states. We formulate a tangent-space based variational algorithm to achieve this for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.

  14 citations

• Shape of a sound wave in a weakly-perturbed Bose gas

  Oleksandr V. Marchukov, Artem G. Volosniev

  SciPost Phys. 10, 025 (2021) · published 3 February 2021 | Toggle abstract · pdf

  We employ the Gross-Pitaevskii equation to study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wave lengths, and argue that it is possible to extract properties of the impurity by observing this shape. We illustrate here this possibility for a Bose gas with a trapped impurity atom -- an example of a relevant experimental setup. Presented results are general for all one-dimensional systems described by the nonlinear Schr\"odinger equation and can also be used in nonatomic systems, e.g., to analyze light propagation in nonlinear optical media. Finally, we calculate the shape of the sound-wave packet for a three-dimensional Bose gas assuming a spherically symmetric perturbation.

  4 citations

• On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension

  Mario Collura, Luca Dell'Anna, Timo Felser, Simone Montangero

  SciPost Phys. Core 4, 001 (2021) · published 2 February 2021 | Toggle abstract · pdf

  In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the ground state of short-range Hamiltonians. We show that when mapping a neural network, the resulting tensor network is highly constrained and thus the neural network states do in general not deliver the naive expected drastic improvement against the state-of-the-art tensor network methods. We explicitly show this result in two paradigmatic examples, the 1D ferromagnetic Ising model and the 2D antiferromagnetic Heisenberg model, addressing the lack of a detailed comparison of the expressiveness of these increasingly popular, variational ans\"atze.

  8 citations

• Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

  Milan Radonjić, Axel Pelster

  SciPost Phys. 10, 008 (2021) · published 14 January 2021 | Toggle abstract · pdf

  We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially equilibrated Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part, that actually corresponds to adiabatic switching on the disorder, and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. We also present an appropriate generalization to inhomogeneous trapped condensates. Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.

  2 citations

• Periodically and quasi-periodically driven dynamics of Bose-Einstein condensates

  Pengfei Zhang, Yingfei Gu

  SciPost Phys. 9, 079 (2020) · published 23 November 2020 | Toggle abstract · pdf

  We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

  11 citations

• Emergence of PT-symmetry breaking in open quantum systems

  Julian Huber, Peter Kirton, Stefan Rotter, Peter Rabl

  SciPost Phys. 9, 052 (2020) · published 19 October 2020 | Toggle abstract · pdf

  The effect of PT-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. Here we generalize the definition of PT symmetry to finite-dimensional open quantum systems, which are described by a Markovian master equation. Specifically, we show that the invariance of this master equation under a certain symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected PT-symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe PT-symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.

  49 citations

• Geometry of variational methods: dynamics of closed quantum systems

  Lucas Hackl, Tommaso Guaita, Tao Shi, Jutho Haegeman, Eugene Demler, J. Ignacio Cirac

  SciPost Phys. 9, 048 (2020) · published 8 October 2020 | Toggle abstract · pdf

  We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: K\"ahler and non-K\"ahler. Traditional variational methods typically require the variational family to be a K\"ahler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-K\"ahler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

  73 citations

• The influence of spacetime curvature on quantum emission in optical analogues to gravity

  Maxime J. Jacquet, Friedrich Koenig

  SciPost Phys. Core 3, 005 (2020) · published 30 September 2020 | Toggle abstract · pdf

  Quantum fluctuations on curved spacetimes cause the emission of pairs of particles from the quantum vacuum, as in the Hawking effect from black holes. We use an optical analogue to gravity to investigate the influence of the curvature on quantum emission. Due to dispersion, the spacetime curvature varies with frequency here. We analytically calculate for all frequencies the particle flux, correlations and entanglement. We find that horizons increase the flux with a characteristic spectral shape. The photon number correlations transition from multi- to two-mode, with close to maximal entanglement. The quantum state is a diagnostic for the mode conversion in laboratory tests of quantum field theory on curved spacetimes.

  17 citations

• Beyond Lee-Huang-Yang description of self-bound Bose mixtures

  Miki Ota, Grigori E. Astrakharchik

  SciPost Phys. 9, 020 (2020) · published 18 August 2020 | Toggle abstract · pdf

  We investigate the properties of self-bound ultradilute Bose-Bose mixtures, beyond the Lee-Huang-Yang description. Our approach is based on the determination of the beyond mean-field corrections to the phonon modes of the mixture in a self-consistent way and calculation of the associated equation of state. The newly obtained ground state energies show excellent agreement with recent quantum Monte Carlo calculations, providing a simple and accurate description of the self-bound mixtures with contact type interaction. We further show numerical results for the equilibrium properties of the finite size droplet, by adjusting the Gross-Pitaevskii equation. Our analysis is extended to the one-dimensional mixtures where an excellent agreement with quantum Monte Carlo predictions is found for the equilibrium densities. Finally, we discuss the effects of temperature on the stability of the liquid phase.

  57 citations