Neutral Atomic Systems Research Articles

Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently understood about QAOA's performance beyond its lowest-depth variant. An essential but missing ingredient for understanding and deploying QAOA is a constructive approach to carry out the outer-loop classical optimization. We provide an in-depth study of the performance of QAOA on MaxCut problems by developing an efficient parameter-optimization procedure and revealing its ability to exploit non-adiabatic operations. Building on observed patterns in optimal parameters, we propose heuristic strategies for initializing optimizations to find quasi-optimal $p$-level QAOA parameters in $O(\text{poly}(p))$ time, whereas the standard strategy of random initialization requires $2^{O(p)}$ optimization runs to achieve similar performance. We then benchmark QAOA and compare it with quantum annealing, especially on difficult instances where adiabatic quantum annealing fails due to small spectral gaps. The comparison reveals that QAOA can learn via optimization to utilize non-adiabatic mechanisms to circumvent the challenges associated with vanishing spectral gaps. Finally, we provide a realistic resource analysis on the experimental implementation of QAOA. When quantum fluctuations in measurements are accounted for, we illustrate that optimization will be important only for problem sizes beyond numerical simulations, but accessible on near-term devices. We propose a feasible implementation of large MaxCut problems with a few hundred vertices in a system of 2D neutral atoms, reaching the regime to challenge the best classical algorithms.

A boost to Rydberg quantum computing

Systems of neutral atoms are gradually gaining currency as a promising candidate for realizing large-scale quantum computing. The achievement of a record-high fidelity in quantum operation with alkaline-earth Rydberg atoms is a case in point.

Many-body physics with individually controlled Rydberg atoms

Over the last decade, systems of individually-controlled neutral atoms, interacting with each other when excited to Rydberg states, have emerged as a promising platform for quantum simulation of many-body problems, in particular spin systems. Here, we review the techniques underlying quantum gas microscopes and arrays of optical tweezers used in these experiments, explain how the different types of interactions between Rydberg atoms allow a natural mapping onto various quantum spin models, and describe recent results that were obtained with this platform to study quantum many-body physics.

Attoclock setup with negative ions: A possibility for experimental validation

The presumed connection in attoclock setups between the electron tunneling time and its asymptotic momentum has triggered vigorous debates. In neutral atomic systems investigated so far, the action of the long-range Coulomb potential on the electron momentum hinders extracting the effect of the tunneling process on the offset angle of the asymptotic electron momentum. We propose and investigate an attoclock experiment using ${\mathrm{F}}^{\ensuremath{-}}$ or ${\mathrm{Cl}}^{\ensuremath{-}}$ to circumvent this difficulty. Our calculations, performed with realistic laser parameters in the tunneling regime, could be checked directly against experiment and predict essentially a ``zero'' offset angle with no detectable effect of polarization.

Experimental progress of quantum computation based on trapped single neutral atoms

As an important candidate for quantum simulation and quantum computation, a microscopic array of single atoms confined in optical dipole traps is advantageous in controlled interaction, long coherence time, and scalability of providing thousands of qubits in a small footprint of less than 1 mm<sup>2</sup>. Recently, several breakthroughs have greatly advanced the applications of neutral atom system in quantum simulation and quantum computation, such as atom-by-atom assembling of defect-free arbitrary atomic arrays, single qubit addressing and manipulating in two-dimensional and three-dimensional arrays, extending coherence time of atomic qubits, controlled-NOT (C-NOT) gate based on Rydberg interactions, high fidelity readout, etc.In this paper, the experimental progress of quantum computation based on trapped single neutral atoms is reviewed, along with two contributions done by single atom group in Wuhan Institute of Physics and Mathematics of Chinese Academy of Sciences. First, a magic-intensity trapping technique is developed and used to mitigate the detrimental decoherence effects which are induced by light shift and substantially enhance the coherence time to 225 ms which is 100 times as large as our previous coherence time thus amplifying the ratio between coherence time and single qubit operation time to 10<sup>5</sup>. Second, the difference in resonant frequency between the two atoms of different isotopes is used to avoid crosstalking between individually addressing and manipulating nearby atoms. Based on this heteronuclear single atom system, the heteronuclear C-NOT quantum gate and entanglement of an Rb-85 atom and an Rb-87 atom are demonstrated via Rydberg blockade for the first time. These results will trigger the quests for new protocols and schemes to use the double species for quantum computation with neutral atoms. In the end, the challenge and outlook for further developing the neutral atom system in quantum simulation and quantum computation are also reviewed.

W-state preparation and entanglement dynamics in Rydberg atomic system based on the collective excitation enhancement

We present a theoretical scheme to realize the highly entangled W state in the neutral atomic system by using the Rydberg blockade effect. Considering three neutral atoms trapped in an optical lattice with an equilateral triangle geometric configuration, we show that only one atom can be excited to the Rydberg excite state due to the Rydberg blockade effect. By choosing a non-zero detuning from the exact two-photon resonance in order to compensate for the blockade error caused by the finite interaction energy, we show that the three atoms W state can be generated. Moreover, we show that three atoms are entangled when W state is achieved with high fidelity.

K -matrix formulation of two-particle scattering in a waveguide in the presence of one-dimensional spin-orbit coupling

The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two atoms confined by a wave guide in the presence of spin-orbit coupling terms within a K-matrix scattering framework. The tunability of resonances, induced by the interplay of the external wave guide geometry, the interactions, and the spin-orbit coupling terms, is demonstrated. Our results for the K-matrix elements as well as partial and total reflection coefficients for two identical fermions interacting through a finite-range interaction potential in the singlet channel only are compared with those obtained for a strictly one-dimensional effective low- energy Hamiltonian, which uses the effective coupling constant derived in Zhang et al. [Scientific Reports 4, 1 (2014)] and Zhang et al. [Phys. Rev. A 88, 053605 (2013)] as input. In the regime where the effective Hamiltonian is applicable, good agreement is obtained, provided the energy- dependence of the coupling constant is accounted for. Our approach naturally describes the energy regime in which the bands associated with excited transverse modes lie below a subset of the bands associated with the lowest transverse modes. The threshold behavior is discussed and scattering observables are linked to bound state properties.

Energy barriers between metastable states in first-order quantum phase transitions

A system of neutral atoms trapped in an optical lattice and dispersively coupled to the field of an optical cavity can realize a variation of the Bose-Hubbard model with infinite-range interactions. This model exhibits a first order quantum phase transition between a Mott insulator and a charge density wave, with spontaneous symmetry breaking between even and odd sites, as was recently observed experimentally [Landig \emph{et. al.}, Nature {\bf 532} (2016)]. In the present paper we approach the analysis of this transition using a variational model which allows us to establish the notion of an energy barrier separating the two phases. Using a discrete WKB method we then show that the local tunneling of atoms between adjacent sites lowers this energy barrier and hence facilitates the transition. Within our simplified description, we are thus able to increment the phase diagram of the model with information concerning the height of the barrier separating the metastable minima from the global minimum in each phase, which is an essential aspect for the understanding of the reconfiguration dynamics induced by a quench across a quantum critical point.

Engineering steady Knill-Laflamme-Milburn state of Rydberg atoms by dissipation.

The Knill-Laflamme-Milburn (KLM) states have been proved to be a useful resource for quantum information processing [Nature409, 46 (2001)]. For atomic KLM states, several schemes have been put forward based on the time-dependent unitary dynamics, but the dissipative generation of these states has not been reported. This work discusses the possibility for creating different forms of bipartite KLM states in neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the Rydberg antiblockade mechanism, is actively exploited to engineer a steady KLM state from an arbitrary initial state. The numerical simulation of the master equation signifies that a fidelity above 99% is available with the current experimental parameters.

Interactions propel a magnetic dance

A combination of leading-edge techniques has enabled interaction-induced magnetic motion to be observed for pairs of ultracold atoms — a breakthrough in the development of models of complex quantum behaviour. See Letter p.519 Simulating topological band structures, the corresponding edge states, and the quantum Hall effect with neutral atoms requires the introduction of artificial gauge fields. Although challenging, various groups have recently demonstrated artificial gauge fields in ultracold neutral-atom systems. However, up to now, these simulations have been limited to single-particle effects, meaning that many fascinating condensed-matter phenomena, such as the fractional quantum Hall effect, could not be studied. Here, the authors subject a two-dimensional Bose–Einstein condensate of rubidium-87 atoms to an artificial gauge field and use a quantum gas microscope to investigate how two-body interactions affect the chiral dynamics. If extended to many-body interactions, this strategy could enable the simulation of the interplay between many-body interactions and topology in condensed-matter physics.

Microscopy of the interacting Harper-Hofstadter model in the two-body limit.

The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement. Although these phases were discovered in a solid-state setting, recent innovations in systems of ultracold neutral atoms-uncharged atoms that do not naturally experience a Lorentz force-allow the synthesis of artificial magnetic, or gauge, fields. This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in cold-atom systems. However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated many-body states. Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a two-body system with a chiral band structure. We observe and explain the way in which interparticle interactions induce chirality in the propagation dynamics of particles in a ladder-like, real-space lattice governed by the interacting Harper-Hofstadter model, which describes lattice-confined, coherently mobile particles in the presence of a magnetic field. We use a bottom-up strategy to prepare interacting chiral quantum states, thus circumventing the challenges of a top-down approach that begins with a many-body system, the size of which can hinder the preparation of controlled states. Our experimental platform combines all of the necessary components for investigating highly entangled topological states, and our observations provide a benchmark for future experiments in the fractional quantum Hall regime.

Screening of nucleon electric dipole moments in nuclei

A partial screening of nucleon electric dipole moments (EDMs) in nuclear systems, which is related to the Schiff mechanism known for neutral atomic systems, is discussed. It is shown that the direct contribution from the neutron EDM to the deuteron EDM is partially screened by about 1% in a zero-range approximation calculation.

Excitation and charge transfer in low-energy hydrogen-atom collisions with neutral atoms: Theory, comparisons, and application to Ca

A theoretical method for the estimation of cross sections and rates for excitation and charge transfer processes in low-energy hydrogen atom collisions with neutral atoms, based on an asymptotic two-electron model of ionic-covalent interactions in the neutral atom-hydrogen atom system, is presented. The calculation of potentials and non-adiabatic radial couplings using the method is demonstrated. The potentials are used together with the multi-channel Landau-Zener model to calculate cross sections and rate coefficients. The main feature of the method is that it employs asymptotically exact atomic wavefunctions, which can be determined from known atomic parameters. The method is applied to Li+H, Na+H, and Mg+H collisions, and the results compare well with existing detailed full-quantum calculations. The method is applied to the astrophysically important problem of Ca+H collisions, and rate coefficients are calculated for temperatures in the range 1000-20000 K.

ADVANCED RELATIVISTIC ENERGY APPROACH TO RADIATION DECAY PROCESSES IN ATOMIC SYSTEMS

We consider the fundamental aspects of the advanced generalized energy approach to relativistic calculation of the radiative decay (transitions) probabilities in heavy neutral atomic systems and multicharged ions. The approach is based on the Gell-Mann and Low S-matrix formalism and the relativistic many-body perturbation theory (PT) with using the optimized one-quasiparticle representation and an accurate account of the relativistic and correlation. In relativistic case the Gell-Mann and Low formula expresses an energy shift through the electrodynamical scattering matrix including the interaction with as the laser field as the photon vacuum field. The last case is corresponding to definition of the traditional radiative transitions probabilities for atoms and ions.

Parallel implementation of the time-evolving block decimation algorithm for the Bose–Hubbard model

A system of ultracold atoms in an optical lattice represents a powerful experimental setup for testing the fundamentals of quantum mechanics. While its microscopic interaction mechanisms are well understood, the system behavior for a moderate number of particles is difficult to simulate due to a high dimension of its many-body space. This article presents TEBDOL, a parallel implementation of the time-evolving block decimation (TEBD) algorithm that can efficiently simulate time evolution of a one-dimensional chain of atoms in optical lattices. We investigate the parallelization strategy and the strong and weak scaling with the number of processes. Program summaryProgram title: TEBDOLCatalogue identifier: AEYN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License v3.0No. of lines in distributed program, including test data, etc.: 9060No. of bytes in distributed program, including test data, etc.: 54338Distribution format: tar.gzProgramming language: Common Lisp.Computer: x86-64.Operating system: Linux.Has the code been vectorized or parallelized?: Parallelized using MPIRAM: 1–64 GBClassification: 7.7.External routines: Basic Linear Algebra Subprograms (BLAS), Linear Algebra Package (LAPACK), Message Passing Interface (MPI)Nature of problem: A system of neutral atoms in an optical lattice is a many-body quantum system that can be described using the Bose–Hubbard model. Hilbert space dimensions of many-body quantum models grow exponentially with the number of particles. Simulating time evolution in the Bose–Hubbard model is therefore a hard problem even in case of a moderate number of particles.Solution method: A system state is represented by a tensor network. Its time evolution is then simulated using the time-evolving block decimation (TEBD) algorithm.Restrictions: TEBDOL is limited to one-dimensional systems. The times accessible in the simulations are restricted by the growth of entanglement in the system.Unusual features: Tensor networks in TEBDOL support a global Abelian symmetry, i.e., the program conserves the total number of particles. Models with multiple particle species are supported as well. TEBDOL is implemented in Common Lisp and can run in parallel on a computer cluster.Running time: Running time depends on the lattice size, on the number of particles, and on the maximal allowed tensor dimensions. Simulations of simple models take a few seconds on a single CPU while simulations of large and complex models can take up to a week on a cluster with hundreds of CPUs.

De Haas-van Alphen effect of a two-dimensional ultracold atomic gas

In this paper, we show how the ultracold atom analogue of the two-dimensional de Haas-van Alphen effect in electronic condensed matter systems can be induced by optical fields in a neutral atomic system. The interaction between the suitable spatially varying laser fields and tripod-type trapped atoms generates a synthetic magnetic field which leads the particles to organize themselves in Landau levels. Initially, with the atomic gas in a regime of lowest Landau level, we display the oscillatory behaviour of the atomic energy and its derivative with respect to the effective magnetic field (B) as a function of 1B. Furthermore, we estimate the area of the Fermi circle of the two-dimensional atomic gas.

Coherence lengths in attractively interacting Fermi gases with spin-orbit coupling

Extensive research has been lavished on effects of spin-orbit couplings (SOC) in attractively interacting Fermi systems in both neutral cold atom systems and condensed matter systems. Recently, it was suggested that a SOC drives a new class of BCS to BEC crossover which is different than the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a new BCS to BEC crossover and their experimental detections. We extend the concepts of the pairing length and "Cooper-pair size" in the absence of SOC to Fermi systems with SOC. We investigate the dependence of chemical potential, pairing length, "Cooper-pair size" on the SOC strength and the scattering length at $ 3d $ (the bound state energy at $ 2d $) for three attractively interacting Fermi gases with 3 dimensional (3d) Rashba, 3d Weyl and 2d Rashba SOC respectively. We show that only the pairing length can be used to characterize this new BCS to BEC crossover. Furthermore, it is the only length which can be directly measured by radio-frequency dissociation spectra type of experiments. We stress crucial differences among the pairing length, "Cooper-pair size " and the two-body bound state size. Our results provide the fundamental and global picture of the new BCS to BEC crossover and its experimental detections in various cold atom and condensed matter systems.

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

The coupling between the spin degrees of freedom and the orbital angular momentum has a profound effect on the properties of nuclei, atoms and condensed matter systems. Recently, synthetic gauge fields have been realized experimentally in neutral cold atom systems, giving rise to a spin-orbit coupling term with "strength" $k_{\text{so}}$. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body $s$-wave interaction for cold atoms under external confinement. Specifically, we consider two different harmonically trapped two-atom systems. The first system consists of an atom with spin-orbit coupling that interacts with a structureless particle through a short-range two-body potential. The second system consists of two atoms that both feel the spin-orbit coupling term and that interact through a short-range two-body potential. Treating the spin-orbit term perturbatively, we determine the correction to the ground state energy for various generic parameter combinations. Selected excited states are also treated. An important aspect of our study is that the perturbative treatment is not limited to small $s$-wave scattering lengths but provides insights into the system behavior over a wide range of scattering lengths, including the strongly-interacting unitary regime. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.

Methods of local interstellar medium investigation

The question of the Sun's motion relative to the local interstellar medium (LISM) is examined. Results from Russian, US, and French satellites and space probes observing scattered solar radiation in hydrogen Lyman-alpha and helium lines are presented. Data are briefly discussed on the direct registration inside the Solar System of neutral helium atoms, picked-up helium ions, and fast neutral hydrogen atoms entering from the LISM. The fast neutral hydrogen atoms arise in the region of solar wind–LISM interaction.

Correlation energies beyond the random-phase approximation: Inhomogeneous Singwi-Tosi-Land-Sjolander functional applied to spherical atoms and ions

The inhomogeneous Singwi, Tosi, Land and Sjolander (ISTLS) correlation energy functional of Dobson, Wang and Gould [PRB {\bf 66} 081108(R) (2008)] has proved to be excellent at predicting correlation energies in semi-homogeneous systems, showing promise as a robust `next step' fifth-rung functional by using dynamic correlation to go beyond the limitations of the direct random-phase approximation (dRPA), but with similar numerical scaling with system size. In this work we test the functional on fourteen spherically symmetric, neutral and charged atomic systems and find it gives excellent results (within 2mHa/$e^-$ except Be) for the absolute correlation energies of the neutral atoms tested, and good results for the ions (within 4mHa/$e^-$). In all cases it performs better than the dRPA. When combined with the previous successes, these new results point to the ISTLS functional being a prime contender for high-accuracy, benchmark DFT correlation energy calculations.