An explicit unconditionally stable numerical method for solving damped nonlinear Schr\"{o}dinger equations with a focusing nonlinearity

This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schr\"{o}dinger equations (NLS). The method is explicit, unconditionally stable and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing nonlinear Schr\"{o}dinger equations in 2d with a linear, cubic or a quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter \dt is larger than a threshold value \dt_{\rm th}. We note that our method can also be applied to solve the 3d Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC).Comment: SIAM Journal on Numerical Analysis, to appea

Dissipation Induced Nonstationarity in a Quantum Gas

Non-stationary long-time dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, et al. arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in the thermodynamic limit and show that this system is always dynamically unstable -- even when mean-field theory predicts stability. Instabilities always occur in higher-order correlation functions leading to squeezing and entanglement induced by cavity dissipation. The dynamics may be understood as the formation of a dissipative time crystal. We use perturbation theory for finite system sizes to confirm the non-stationary behaviour.Comment: Main text: 5 pages, 3 figures and Supplemental material: 6 pages, 2 figures. Version as accepted by Phys. Rev. Let

Non-stationary coherent quantum many-body dynamics through dissipation

The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time-crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.Comment: Main text in MS Word (10 pages, 4 figures) and Supplementary material in TeX (10 pages, 2 figures). Main text PDF embedded in TeX. Version as accepted by Nature Communication

Simulating and detecting artificial magnetic fields in trapped atoms

A Bose-Einstein condensate exhibiting a nontrivial phase induces an artificial magnetic field in immersed impurity atoms trapped in a stationary, ring-shaped optical lattice. We present an effective Hamiltonian for the impurities for two condensate setups: the condensate in a rotating ring and in an excited rotational state in a stationary ring. We use Bogoliubov theory to derive analytical formulas for the induced artificial magnetic field and the hopping amplitude in the limit of low condensate temperature where the impurity dynamics is coherent. As methods for observing the artificial magnetic field we discuss time of flight imaging and mass current measurements. Moreover, we compare the analytical results of the effective model to numerical results of a corresponding two-species Bose-Hubbard model. We also study numerically the clustering properties of the impurities and the quantum chaotic behavior of the two-species Bose-Hubbard model.Comment: 14 pages, 9 figures. Published versio

A polynomial Ansatz for Norm-conserving Pseudopotentials

We show that efficient norm-conserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills the same smoothness conditions imposed by the Troullier-Martins method [Phys. Rev. B 43, 1993 (1991)] where pseudopotentials are represented by a polynomial of degree twenty-two. We compare our method to the Troullier-Martins approach in electronic structure calculations for diamond and iron in the bcc structure and find that the two methods perform equally well in calculations of the total energy. However, first and second derivatives of the total energy with respect to atomic coordinates converge significantly faster with the plane wave cutoff if the standard Troullier-Martins potentials are replaced by the pseudopotentials introduced here.Comment: 7 pages, 3 figure

Non-stationarity and Dissipative Time Crystals: Spectral Properties and Finite-Size Effects

We discuss the emergence of non-stationarity in open quantum many-body systems. This leads us to the definition of dissipative time crystals which display experimentally observable, persistent, time-periodic oscillations induced by noisy contact with an environment. We use the Loschmidt echo and local observables to indicate the presence of a finite sized dissipative time crystal. Starting from the closed Hubbard model we then provide examples of dissipation mechanisms that yield experimentally observable quantum periodic dynamics and allow analysis of the emergence of finite sized dissipative time crystals. For a disordered Hubbard model including two-particle loss and gain we find a dark Hamiltonian driving oscillations between GHZ states in the long-time limit. Finally, we discuss how the presented examples could be experimentally realized.Comment: 31 pages, 5 figures. Submitted to NJP: Focus on Time Crystal

Three-body bound states in dipole-dipole interacting Rydberg atoms

We show that the dipole-dipole interaction between three identical Rydberg atoms can give rise to bound trimer states. The microscopic origin of these states is fundamentally different from Efimov physics. Two stable trimer configurations exist where the atoms form the vertices of an equilateral triangle in a plane perpendicular to a static electric field. The triangle edge length typically exceeds $R\approx 2\,\mu\text{m}$, and each configuration is two-fold degenerate due to Kramers' degeneracy. The depth of the potential wells and the triangle edge length can be controlled by external parameters. We establish the Borromean nature of the trimer states, analyze the quantum dynamics in the potential wells and describe methods for their production and detection.Comment: 5 pages, 3 figures and supplementary material; to appear in PR

The isolated Heisenberg magnet as a quantum time crystal

We demonstrate analytically and numerically that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. We trace this phenomenon to the existence of extensive dynamical symmetries and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain. We discuss how the ensuing persistent oscillations that violate one of the most fundamental laws of physics could be observed experimentally and identify potential metrological applications.Comment: Main text: 5 pages, 2 figures; Supplementary: 4 pages, 1 figure. New version contains study of stability to integrability breakin

Cavity-mediated electron-photon superconductivity

We investigate electron paring in a two-dimensional electron system mediated by vacuum fluctuations inside a nanoplasmonic terahertz cavity. We show that the structured cavity vacuum can induce long-range attractive interactions between current fluctuations which lead to pairing in generic materials with critical temperatures in the low-Kelvin regime for realistic parameters. The induced state is a pair density wave superconductor which can show a transition from a fully gapped to a partially gapped phase - akin to the pseudogap phase in high-$T_c$ superconductors. Our findings provide a promising tool for engineering intrinsic electron interactions in two-dimensional materials.Comment: 11 page