Point-like Atoms Research Articles

A simple efficient algorithm for molecular simulations of constant potential electrodes.

Increasingly, society requires high power, high energy storage devices for applications ranging from electric vehicles to buffers on the electric grid. Supercapacitors are a promising contribution to meeting these demands, though there still remain unsolved practical problems. Molecular dynamics simulations can shed light on the relevant molecular level processes in electric double layer capacitors, but these simulations are computationally very demanding. Our focus here is on the algorithmic complexity of the constant potential method (CPM), which uses dedicated electrostatics solvers to maintain a fixed potential difference between two conducting electrodes. We show how any standard electrostatics solver-capable of calculating the energies and forces on all atoms-can be used to implement CPM with a minimum of coding. As an example, we compare our generalized implementation of CPM, based on invocations of the particle-particle-particle-mesh routine of the Large-scale Atomic/Molecular Massively Parallel Simulator, with a traditional implementation based on a dedicated re-implementation of Ewald summation. Both methods yield comparable results on four test systems, with the former achieving a substantial gain in speed and improved scalability. The step from dedicated electrostatic solvers to generic routines is made possible by noting that CPM's traditional narrow Gaussian point-spread of atomic charges on the electrodes effectively endows point-like atoms with chemical hardness, i.e., an intra-atomic energy quadratic in the charge.

The Effect of Internal Dynamics on the Motion of Cold Atoms in 2D Optical Lattices with Interfering Laser Beams

We show theoretically and numerically that cold two-level atoms demonstrate unexpectedly complicated motion in an absolutely rigid two-dimensional optical lattice with interfering laser beams. The point-like atoms can move there in a chaotic way resembling motion of particles in a random potential. Chaos arises if the laser frequency is close to the atomic transition frequency where one should take into account the excitation of internal atomic states by the laser field. After loading cold atoms to the lattice, their induced electric dipole moments interact with a spatially inhomogeneous electric field of the two-dimensional standing laser wave. We find the range of the atom–field detuning where the synchronized (with the laser field) component of the atomic dipole moment changes in a random-like manner just after crossing the nodal lines of the standing wave where the electric field is zero. It, in turn, causes irregular changes in the momentum of atoms, leading eventually to chaotic walking of cold atoms in a deterministic potential. We show that adjusting the single control parameter, the atom–field detuning, it is possible to switch between regular and chaotic regimes of motion.

Cooperative spontaneous decay of local excitation in a dense and disordered ensemble of point-like impurity atoms near a charged conductive surface

On the basis of the general quantum microscopic theory we study the process of spontaneous decay of an excited atom in a dense and disordered ensemble of point-like impurity atoms embedded into transparent dielectric and located near a charged perfectly conducting surface. We have analyzed the simultaneous influence of the modified spatial structure of field modes near the conductive surface and the electric field on the character of interatomic dipole-dipole interaction. This leads to the modification of the transition spectrum of an excited atom inside an ensemble and the spontaneous decay dynamics. We have shown that the electric field changes the cooperative Lamb shift, as well as the character of sub- and superradiant decay.

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

This paper is a review article on some aspects of quantum–classical correspondence in chaotic dynamics of cold atoms interacting with a standing-wave laser field forming an optical lattice. The problem is treated from both (semi)classical and quantum points of view. In both approaches, the interaction of an atomic electic dipole with the laser field is treated quantum mechanically. Translational motion is described, at first, classically (atoms are considered to be point-like objects) and then quantum mechanically as a propagation of matter waves. Semiclassical equations of motion are shown to be chaotic in the sense of classical dynamical chaos. Point-like atoms in an absolutely deterministic and rigid optical lattice can move in a random-like manner demonstrating a chaotic walking with typical features of classical chaos. This behavior is explained by random-like ‘jumps’ of one of the atomic internal variable when atoms cross nodes of the standing wave and occurs in a specific range of the atom-field detuning. When treating atoms as matter waves, we show that they can make nonadiabatic transitions when crossing the standing-wave nodes. The point is that atomic wave packets split at each node in the same range of the atom-field detuning where the classical chaos occurs. The key point is that the squared amplitude of those semiclassical ‘jumps’ equal to the quantum Landau–Zener parameter which defines the probability of nonadiabatic transitions at the nodes. Nonadiabatic atomic wave packets are much more complicated compared to adiabatic ones and may be called chaotic in this sense. A few possible experiments to observe some manifestations of classical and quantum chaos with cold atoms in horizontal and vertical optical lattices are proposed and discussed.

Long range correlations and folding angle with applications to α-helical proteins

The conformational complexity of chain-like macromolecules such as proteins and other linear polymers is much larger than that of point-like atoms and molecules. Unlike particles, chains can bend, twist, and even become knotted. Thus chains might also display a much richer phase structure. Unfortunately, it is not very easy to characterize the phase of a long chain. Essentially, the only known attribute is the radius of gyration. The way how it changes when the degree of polymerization becomes different, and how it evolves when the ambient temperature and solvent properties change, is commonly used to disclose the phase. But in any finite length chain there are corrections to scaling that complicate the detailed analysis of the phase structure. Here we introduce a quantity that we call the folding angle to identify and scrutinize the phase structure, as a complement to the radius of gyration. We argue for a mean-field level relationship between the folding angle and the scaling exponent in the radius of gyration. We then estimate the value of the folding angle in the case of crystallographic α-helical protein structures in the Protein Data Bank. We also show how the experimental value of the folding angle can be obtained computationally, using a semiclassical Born-Oppenheimer description of α-helical chiral chains.

Bose-Glass phases of ultracold atoms due to cavity backaction.

We determine the quantum ground-state properties of ultracold bosonic atoms interacting with the mode of a high-finesse resonator. The atoms are confined by an external optical lattice, whose period is incommensurate with the cavity mode wavelength, and are driven by a transverse laser, which is resonant with the cavity mode. While for pointlike atoms photon scattering into the cavity is suppressed, for sufficiently strong lasers quantum fluctuations can support the buildup of an intracavity field, which in turn amplifies quantum fluctuations. The dynamics is described by a Bose-Hubbard model where the coefficients due to the cavity field depend on the atomic density at all lattice sites. Quantum MonteCarlo simulations and mean-field calculations show that, for large parameter regions, cavity backaction forces the atoms into clusters with a checkerboard density distribution. Here, the ground state lacks superfluidity and possesses finite compressibility, typical of a Bose glass. This system constitutes a novel setting where quantum fluctuations give rise to effects usually associated with disorder.

Nonadiabatic quantum chaos in atom optics

Coherent dynamics of atomic matter waves in a standing-wave laser field is studied. In the dressed-state picture, wave packets of ballistic two-level atoms propagate simultaneously in two optical potentials. The probability to make a transition from one potential to another one is maximal when centroids of wave packets cross the field nodes and is given by a simple formula with the single exponent, the Landau–Zener parameter κ. If κ≫1, the motion is essentially adiabatic. If κ≪1, it is (almost) resonant and periodic. If κ≃1, atom makes nonadiabatic transitions with a splitting of its wave packet at each node and strong complexification of the wave function as compared to the two other cases. This effect is referred as nonadiabatic quantum chaos. Proliferation of wave packets at κ≃1 is shown to be connected closely with chaotic center-of-mass motion in the semiclassical theory of point-like atoms with positive values of the maximal Lyapunov exponent. The quantum–classical correspondence established is justified by the fact that the Landau–Zener parameter κ specifies the regime of the semiclassical dynamical chaos in the map simulating chaotic center-of-mass motion. Manifestations of nonadiabatic quantum chaos are found in the behavior of the momentum and position probabilities.

Matter-wave propagation in optical lattices

Coherent propagation of atomic-matter waves in a one-dimensional optical lattice is studied. Wave packets of cold two-level atoms propagate simultaneously in two optical potentials in a dressed-state basis. Three regimes of the wave-packet propagation are specified by the quantity Δ2/ωD, where Δ and ωD are the dimensionless atom–laser detuning and the Doppler shift, respectively. At Δ2/ωD ≫ 1, the propagation is essentially adiabatic, at Δ2/ωD ≪ 1, it is (almost) resonant, and at Δ2 ≃ ωD, the wave packets propagate nonadiabatically, splitting at each node of the standing wave. The latter means that the atom makes a transition from one potential to the other one when crossing each node, and the probability of that transition is given by a Landau–Zener-like formula. All the regimes of propagation are studied with δ-like and Gaussian wave packets in the momentum and position spaces. Varying the control parameters, we can create wave packets trapped in a well of optical potentials and moving ballistically in a given direction in close analogy with point-like atoms. Within some range of the parameters, we force the atom to move in a pure quamtum-mechanical manner in such a way that a part of the packet is trapped in a well, and the other part propagates ballistically. The propagation modes are found to be characterized by different types of time evolution of the uncertainty product and the Wigner function.

Spreading of atomic wave packets and semiclassical chaos

The correspondence between the statistical properties of the evolution of a quantum system and Lyapunov instability and the chaos of its semiclassical analog has been demonstrated. The results of the analyses of atomic motion in a laser field in the semiclassical approximation (dynamics is described by several nonlinear equations) and without this approximation (dynamics is described by an infinite system of linear equations) are compared. In the ranges of the parameters for which the semiclassical dynamics of point-like atoms is unstable, the fast “spreading” of quantized wave packets in the momentum space is observed. Thus, deterministic chaos “imitates” the statistics of the quantum nondeterministic effects, although the semiclassical and quantum solutions are fundamentally different.

Quantum chaos and fractals with atoms in cavities

We study the coupled translational, electronic, and field dynamics of the combined system “a two-level atom + a single-mode quantized field + a standing-wave ideal cavity”. In the semiclassical approximation with a point-like atom, interacting with the classical field, the dynamics is described by the Heisenberg equations for the atomic and field expectation values which are known to produce semiclassical chaos under appropriate conditions. We derive Hamilton–Schrödinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At exact resonance, the semiquantum dynamics is regular. At large values of detuning | δ|≫1, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler–Rabi resonance, deep Rabi oscillations that may occur at any large value of | δ| to be equal to | αp 0|, is found numerically and described analytically (with α to be the normalized recoil frequency and p 0 the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. It is shown that in the chaotic regime values of the population inversion z out, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion z in that the probability of detecting any value of z out in the admissible interval [−1,1] becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical with chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.

Space-time description of photon emission from an atom

Starting from the postulate that the electromagnetic field appearing in the transverse set of microscopic Maxwell-Lorentz equations governing field-matter interactions, properly normalized, can be looked upon as describing one-photon-emission and -absorption processes in space and time, a first-quantized initiation of photon emission by a single atom is presented. The wave function for the emerging photon is introduced as a six-vector object constructed from the complex analytical signals of the Riemann-Silberstein vectors belonging to opposite photon helicities. When the atom is no longer electrodynamically active, the emitted photon is described in first quantization by the so-called energy wave function well known for photons in free space. From the momentum representation of the emerging photon wave function a condition on the analytical part of the transverse atomic current density is established which ensures that precisely one photon is emitted. A propagator description of the emerged photon dynamics in the coordinate representation is established. The photon propagator is introduced as a two-component spinor, where upper and lower tensor components are constructed, respectively, from positive and negative helicity combinations of the propagators describing the time-space evolution of the transverse electric and magnetic fields. It is shown that the emission region for the photon coincides with the region in space where the transverse atomic current density is nonvanishing. For a photon emitted in an electric dipole transition the emission region essentially is the near-field zone of the atom, and this zone therefore determines the initial (and best) spatial confinement of the photon. The photon emerging from an atom active for a finite time necessarily is of the polychromatic sort and the associated wave packet essentially is confined between spherical shells moving outwards with the vacuum speed of light. To illustrate the main principles of the fundamental theory in a heuristic fashion we apply it to a study of the emission of a one-photon sinusoidal wavetrain from a pointlike atom. It is found that the atomic current density needed to create just one photon is independent of the oscillation period in the train and thus depends only on the number of periods in the wave train. An explicit expression for the one-photon energy is derived, and it is shown that only for extremely short pulse trains pronounced deviations from the textbook result, $E=\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0},$ occur. The radial energy flow in the coupled atom-photon system in the near-field zone of the atom is investigated, and the cycle-averaged outwards energy transport carried by the emerging photon in a given distance from the atom is determined.

The elastic behavior of entropic "fisherman's net”

A new formalism is used for a Monte Carlo determination of the elastic constants of a two-dimensional net of fixed connectivity. The net is composed of point-like atoms each of which is tethered to six neighbors by a bond limiting the distance between them to a certain maximal separation, but having zero energy at all smaller lengths. We measure the elastic constants for many values of the ratio $\gamma$ between the maximal and actual extensions of the net. When the net is very stretched ($\gamma\sim 1$), a simple transformation maps the system into a triangular hard disks solid, and we show that the elastic properties of both systems, coincide. We also show that the crossover to a Gaussian elastic behavior, expected for the non-stressed net, occurs when the net is more loose ($\gamma\sim 3$).

Ice-Like Melting of Flexible Line Crystals

Abstract A small number of crystalline materials composed of point-like atoms or molecules are known to contract upon melting into the liquid state. The most famous example is ice, which melts into a liquid which is denser than the coexisting solid phase. We discuss the conditions under which this unusual melting may be expected for collections of flexible directed lines with repulsive pairwise interactions arrayed in, say, a triangular lattice. Ice-like melting should occur generically for flexible lines with sufficiently long-range interactions.

The algebraic approach to solving the phase problem for crystals with point-like atoms

The algebraic approach to solving the phase problem for crystals with point-like atoms

THE TRIANGLE PATTERN — A NEW QUASIPERIODIC TILING WITH FIVEFOLD SYMMETRY

We introduce a quasiperiodic tiling with fivefold symmetry that is built from two types of triangles, an acute and an obtuse one. An easy to computerize construction algorithm based on the dualization scheme is presented that creates the pattern not pointwise but tile by tile directly. We present the vertex statistics, the inflation rule, and the Fourier analysis for selected decorations with pointlike atoms. A connection to the planar Penrose pattern and to the 3D icosahedral quasilattice is briefly discussed.

Lattice Dynamical Analysis of MgO

Abstract The lattice dynamical properties of MgO are studied using a model based on the Birman method, which is different from the conventional point-like atom model. The model includes three kinds of forces: the short-range, the long-range Coulomb, and the long-range polarization interactions. The long-range interactions are dependent on the magnitude of the expansion of the electron distribution. The degrees of the expansion for Mg and O (wMg and wO) are estimated from the X-ray data. The calculated phonon dispersion curves agree with the observed curves in the case of wMg=0.35 Å and wO=0.73 Å, which are nearly equal to the estimated values, 0.35 and 0.65 Å.