arXiv subjects

S. Groth

Publications and source records attributed to S. Groth.

18 recordsLinked to original sources

arXiv2020

Restricted configuration path integral Monte Carlo

Quantum Monte Carlo belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong degeneracy. The situation changed with the development of configuration path integral Monte Carlo (CPIMC) by Schoof \textit{et al.} [T. Schoof \textit{et al.}, Contrib. Plasma Phys. \textbf{51}, 687 (2011)] that allowed for the first \textit{ab initio} simulations for dense quantum plasmas. CPIMC also has a sign problem that occurs when the density is lowered, i.e. in a parameter range that is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC simulations for the warm dense electron gas are limited to small values of the Brueckner parameter -- the ratio of the interparticle distance to the Bohr radius -- $r_s=\bar{r}/a_B \lesssim 1$. In order to reach the regime of stronger coupling (lower density) with CPIMC, here we investigate additional restrictions on the Monte Carlo procedure. In particular, we introduce two different versions of "restricted CPIMC" where certain sign changing Monte Carlo updates are being omitted. Interestingly, one of the methods (RCPIMC) has no sign problem at all, but it is less accurate than RCPIMC+ which neglects only a smaller class of the Monte Carlo steps. Here we report extensive simulations for the ferromagnetic uniform electron gas with which we investigate the properties and accuracy of RCPIMC and RCPIMC+. Further, we establish the parameter range in the density-temperature plane where these simulations are both feasible and accurate. The conclusion is that RCPIMC and RCPIMC+ work best at temperatures in the range of $Θ\sim 0.1\dots 0.5$ allowing to reach density parameters up to $r_s \sim 3\dots 5$, thereby partially filling a gap left open by existing \textit{ab initio} QMC methods.

physics.comp-ph↗

arXiv2019

Dynamical structure factor of strongly coupled ions in a dense quantum plasma

The dynamical structure factor (DSF) of strongly coupled ions in dense plasmas with partially and strongly degenerate electrons is investigated. The main focus is on the impact of electronic correlations (non-ideality) on the ionic DSF. The latter is computed by carrying out molecular dynamics (MD) simulations with a screened ion-ion interaction potential. The electronic screening is taken into account by invoking the Singwi-Tosi-Land-Sjölander approximation, and compared to the MD simulation data obtained considering the electronic screening in the random phase approximation and using the Yukawa potential. %This allows us to gain insight into the impact of the electronic non-ideality on the ionic DSF. We find that electronic correlations lead to lower values of the ion-acoustic mode frequencies and to an extension of the applicability limit with respect to the wave-number of a hydrodynamic description. Moreover, we show that even in the limit of weak electronic coupling, electronic correlations have a non-negligible impact on the ionic longitudinal sound speed. Additionally, the applicability of the Yukawa potential with an adjustable screening parameter is discussed, which will be of interest, e.g., for the interpretation of experimental results for the ionic DSF of dense plasmas.

physics.plasm-ph↗

arXiv2018

\textit{Ab Initio} Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter

The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor $S(\mathbf{q},ω)$ constitutes a key quantity as it is directly measured in X-ray Thomson (XRTS) scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first \textit{ab initio} results for $S(\mathbf{q},ω)$ by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction $G(\mathbf{q},ω)$. In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for $S(\mathbf{q},ω)$ over substantial parts of the warm dense matter regime.

physics.plasm-ph↗

arXiv2018

Structural characteristics of strongly coupled ions in a dense quantum plasma

The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential. Special focus is put on the description of the electronic screening in the Singwi-Tosi-Land-Sjoelander (STLS) approximation. Different crosschecks and analyses using ion potentials obtained from ground-state quantum Monte Carlo data, the random phase approximation (RPA), and existing analytical models are presented for the computation of the structural properties, such as the pair distribution and the static structure factor, of strongly coupled ions. The results are highly sensitive to the features of the screened pair interaction potential. This effect is particularly visible in the static structure factor. The applicability range of the screened potential computed from STLS is identified in terms of density and temperature of the electrons. It is demonstrated that at r_s > 1, where rs is the ratio of the mean inter-electronic distance to the Bohr radius, electronic correlations beyond RPA have a non-negligible effect on the structural properties. Additionally, the applicability of the hypernetted chain approximation for the calculation of the structural properties using the screened pair interaction potential is analyzed employing the effective coupling parameter approach.

physics.plasm-ph↗

arXiv2017

Ion Potential in Non-ideal Dense Quantum Plasmas

The screened ion potential in non-ideal dense quantum plasmas is investigated by invoking the Singwi-Tosi-Land-Sjölander approximation for the electronic local field correction at densities $r_s\lesssim 2$ and degeneracy parameters $θ\lesssim 1$, where $r_s$ is the ratio of the mean inter-particle distance to the first Bohr radius, and $θ$ is the ratio of the thermal energy to the Fermi energy of the electrons. Various cross-checks with ion potentials obtained from ground state quantum Monte-Carlo data, the random phase approximation, as well as with existing analytical models are presented. Further, the importance of the electronic correlation effects for the dynamics in strongly coupled ionic subsystems for $0.1\leq r_s\leq 2$ is discussed.

physics.plasm-ph↗

arXiv2016

Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes II: Unpolarized Case

In a recent publication [S. Groth \textit{et al.}, PRB (2016)], we have shown that the combination of two novel complementary quantum Monte Carlo approaches, namely configuration path integral Monte Carlo (CPIMC) [T. Schoof \textit{et al.}, PRL \textbf{115}, 130402 (2015)] and permutation blocking path integral Monte Carlo (PB-PIMC) [T. Dornheim \textit{et al.}, NJP \textbf{17}, 073017 (2015)], allows for the accurate computation of thermodynamic properties of the spin-polarized uniform electron gas (UEG) over a wide range of temperatures and densities without the fixed-node approximation. In the present work, we extend this concept to the unpolarized case, which requires non-trivial enhancements that we describe in detail. We compare our new simulation results with recent restricted path integral Monte Carlo data [E. Brown \textit{et al}., PRL \textbf{110}, 146405 (2013)] for different energy contributions and pair distribution functions and find, for the exchange correlation energy, overall better agreement than for the spin-polarized case, while the separate kinetic and potential contributions substantially deviate.

cond-mat.str-el↗

arXiv2015

Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes

The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in the warm dense matter regime, e.g. dense plasmas and laser excited solids. Also, the quality of density functional theory calculations crucially relies on the availability of accurate data for the exchange-correlation energy. Recently, new benchmark results for the N = 33 spin-polarized electrons at high density, r_s = r/a_B <= 4 and low temperature, have been obtained with the configuration path integral Monte Carlo (CPIMC) method [T. Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)]. To achieve these results, the original CPIMC algorithm [T. Schoof et al., Contrib. Plasma Phys. 51, 687 (2011)] had to be further optimized to cope with the fermion sign problem (FSP). It is the purpose of this paper to give detailed information on the manifestation of the FSP in CPIMC simulations of the UEG and to demonstrate how it can be turned into a controllable convergence problem. In addition, we present new thermodynamic results for higher temperatures. Finally, to overcome the limitations of CPIMC towards strong coupling, we invoke an independent method|the recently developed permutation blocking path integral Monte Carlo approach [T. Dornheim et al., accepted for publication in J. Chem Phys., arXiv:1508.03221]. The combination of both approaches is able to yield ab initio data for the UEG over the entire density range, above a temperature of about one half of the Fermi temperature. Comparison with restricted path integral Monte Carlo data [E. W. Brown et al., Phys. Rev. Lett. 110, 146405 (2013)] allows us to quantify the systematic error arising from the free particle nodes.

cond-mat.str-el↗

arXiv2015

Ab initio thermodynamic results for the degenerate electron gas at finite temperature

The uniform electron gas (UEG) at finite temperature is of key relevance for many applications in dense plasmas, warm dense matter, laser excited solids and much more. Accurate thermodynamic data for the UEG are an essential ingredient for many-body theories, in particular, density functional theory. Recently, first-principle restricted path integral Monte Carlo results became available which, however, due to the fermion sign problem, had to be restricted to moderate degeneracy, i.e. low to moderate densities with $r_s={\bar r}/a_B \gtrsim 1$. Here we present novel first-principle configuration PIMC results for electrons for $r_s \leq 1$. We also present quantum statistical data within the $e^4$-approximation that are in good agreement with the simulations at small to moderate $r_s$.

physics.plasm-ph↗

arXiv2014

Towards ab initio thermodynamics of the electron gas at strong degeneracy

Recently a number of theoretical studies of the uniform electron gas (UEG) at finite temperature have appeared that are of relevance for dense plasmas, warm dense matter and laser excited solids and thermodynamic density functional theory simulations. In particular, restricted path integral Monte Carlo (RPIMC) results became available which, however, due to the Fermion sign problem, are confined to moderate quantum degeneracy, i.e. low to moderate densities. We have recently developed an alternative approach---configuration PIMC [T. Schoof {\em et al.}, Contrib. Plasma Phys. {\bf 51}, 687 (2011)] that allows one to study the so far not accessible high degeneracy regime. Here we present the first step towards UEG simulations using CPIMC by studying implementation and performance of the method for the model case of $N=4$ particles. We also provide benchmark data for the total energy.

cond-mat.quant-gas↗

arXiv2014

Introduction to Configuration Path Integral Monte Carlo

In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most successful approaches to first-principle simulations of many-body quantum systems. In this chapter we present a recently developed method---the configuration path integral Monte Carlo (CPIMC) method for moderately coupled, highly degenerate fermions at finite temperatures. It is based on the second quantization representation of the $N$-particle density operator in a basis of (anti-)symmetrized $N$-particle states (configurations of occupation numbers) and allows to tread arbitrary pair interactions in a continuous space. We give a detailed description of the method and discuss the application to electrons or, more generally, Coulomb-interacting fermions. As a test case we consider a few quantum particles in a one-dimensional harmonic trap. Depending on the coupling parameter (ratio of the interaction energy to kinetic energy), the method strongly reduces the sign problem as compared to direct path integral Monte Carlo (DPIMC) simulations in the regime of strong degeneracy which is of particular importance for dense matter in laser plasmas or compact stars. In order to provide a self-contained introduction, the chapter includes a short introduction to Metropolis Monte Carlo methods and the second quantization of quantum mechanics.

cond-mat.stat-mech↗

arXiv2010

A single atom detector integrated on an atom chip: fabrication, characterization and application

We describe a robust and reliable fluorescence detector for single atoms that is fully integrated into an atom chip. The detector allows spectrally and spatially selective detection of atoms, reaching a single atom detection efficiency of 66%. It consists of a tapered lensed single-mode fiber for precise delivery of excitation light and a multi-mode fiber to collect the fluorescence. The fibers are mounted in lithographically defined holding structures on the atom chip. Neutral 87Rb atoms propagating freely in a magnetic guide are detected and the noise of their fluorescence emission is analyzed. The variance of the photon distribution allows to determine the number of detected photons / atom and from there the atom detection efficiency. The second order intensity correlation function of the fluorescence shows near-perfect photon anti-bunching and signs of damped Rabi-oscillations. With simple improvements one can boost the detection efficiency to > 95%.

cond-mat.quant-gas↗

arXiv2006

Detecting Neutral Atoms on an Atom Chip

Detecting single atoms (qubits) is a key requirement for implementing quantum information processing on an atom chip. The detector should ideally be integrated on the chip. Here we present and compare different methods capable of detecting neutral atoms on an atom chip. After a short introduction to fluorescence and absorption detection we discuss cavity enhanced detection of single atoms. In particular we concentrate on optical fiber based detectors such as fiber cavities and tapered fiber dipole traps. We discuss the various constraints in building such detectors in detail along with the current implementations on atom chips. Results from experimental tests of fiber integration are also described. In addition we present a pilot experiment for atom detection using a concentric cavity to verify the required scaling.

physics.atom-ph↗

arXiv2005

Sensing electric and magnetic fields with Bose-Einstein Condensates

We discuss the application of Bose-Einstein condensates (BECs) as sensors for magnetic and electric fields. In an experimental demonstration we have brought one-dimensional BECs close to micro-fabricated wires on an atom chip and thereby reached a sensitivity to potential variations of ~10e-14eV at 3 micron spatial resolution. We demonstrate the versatility of this sensor by measuring a two-dimensional magnetic field map 10 micron above a 100-micron-wide wire. We show how the transverse current-density component inside the wire can be reconstructed from such maps. The field sensitivity in dependence on the spatial resolution is discussed and further improvements utilizing Feshbach resonances are outlined.

cond-mat.other↗

arXiv2005

Matter-wave interferometry in a double well on an atom chip

Matter-wave interference experiments enable us to study matter at its most basic, quantum level and form the basis of high-precision sensors for applications such as inertial and gravitational field sensing. Success in both of these pursuits requires the development of atom-optical elements that can manipulate matter waves at the same time as preserving their coherence and phase. Here, we present an integrated interferometer based on a simple, coherent matter-wave beam splitter constructed on an atom chip. Through the use of radio-frequency-induced adiabatic double-well potentials, we demonstrate the splitting of Bose-Einstein condensates into two clouds separated by distances ranging from 3 to 80 microns, enabling access to both tunnelling and isolated regimes. Moreover, by analysing the interference patterns formed by combining two clouds of ultracold atoms originating from a single condensate, we measure the deterministic phase evolution throughout the splitting process. We show that we can control the relative phase between the two fully separated samples and that our beam splitter is phase-preserving.

quant-ph↗

arXiv2005

Disorder Potentials near Lithographically Fabricated Atom Chips

We show that previously observed large disorder potentials in magnetic microtraps for neutral atoms are reduced by about two orders of magnitude when using atom chips with lithographically fabricated high quality gold layers. Using one dimensional Bose-Einstein condensates, we probe the remaining magnetic field variations at surface distances down to a few microns. Measurements on a 100 um wide wire imply that residual variations of the current flow result from local properties of the wire.

cond-mat.other↗

arXiv2004

Atom Chips: Fabrication and Thermal Properties

Neutral atoms can be trapped and manipulated with surface mounted microscopic current carrying and charged structures. We present a lithographic fabrication process for such atom chips based on evaporated metal films. The size limit of this process is below 1$μ$m. At room temperature, thin wires can carry more than 10$^7$A/cm$^2$ current density and voltages of more than 500V. Extensive test measurements for different substrates and metal thicknesses (up to 5 $μ$m) are compared to models for the heating characteristics of the microscopic wires. Among the materials tested, we find that Si is the best suited substrate for atom chips.

cond-mat.mtrl-sci↗

arXiv2003

An atom fiber for guiding cold neutral atoms

We present an omnidirectional matter wave guide on an atom chip. The rotational symmetry of the guide is maintained by a combination of two current carrying wires and a bias field pointing perpendicular to the chip surface. We demonstrate guiding of thermal atoms around more than two complete turns along a spiral shaped 25mm long curved path (curve radii down to 200$μ$m) at various atom--surface distances (35-450$μ$m). An extension of the scheme for the guiding of Bose-Einstein condensates is outlined.

quant-ph↗

arXiv2003

Trapping and manipulating neutral atoms with electrostatic fields

We report on experiments with cold thermal $^7$Li atoms confined in combined magnetic and electric potentials. A novel type of three-dimensional trap was formed by modulating a magnetic guide using electrostatic fields. We observed atoms trapped in a string of up to six individual such traps, a controlled transport of an atomic cloud over a distance of 400$μ$m, and a dynamic splitting of a single trap into a double well potential. Applications for quantum information processing are discussed.

quant-ph↗