Arbitrary Number Of Atoms Research Articles

Singly-excited resonant open quantum system Tavis-Cummings model with quantum circuit mapping

Tavis-Cummings (TC) cavity quantum electrodynamical effects, describing the interaction of N atoms with an optical resonator, are at the core of atomic, optical and solid state physics. The full numerical simulation of TC dynamics scales exponentially with the number of atoms. By restricting the open quantum system to a single excitation, typical of experimental realizations in quantum optics, we analytically solve the TC model with an arbitrary number of atoms with linear complexity. This solution allows us to devise the Quantum Mapping Algorithm of Resonator Interaction with N Atoms (Q-MARINA), an intuitive TC mapping to a quantum circuit with linear space and time scaling, whose N+1 qubits represent atoms and a lossy cavity, while the dynamics is encoded through 2N entangling gates. Finally, we benchmark the robustness of the algorithm on a quantum simulator and superconducting quantum processors against the quantum master equation solution on a classical computer.

State carving in a chirally-coupled atom-nanophotonic cavity

Coherent quantum control of multiqubit systems represents one of the challenging tasks in quantum science and quantum technology. Here we theoretically investigate the reflectivity spectrum in an atom-nanophotonic cavity with collective nonreciprocal couplings. In the strong-coupling regime with a high cooperativity, we theoretically predict distinct on-resonance spectral dips owing to destructive interferences of chiral couplings. Due to the well-separated multiple dips in the spectrum, a contrasted reflectivity suggests a new control knob over the desired entangled state preparation in the basis of coupled and uncoupled states from the atoms’ internal hyperfine ground states. We propose to utilize such atom-nanophotonic cavity to quantum engineer the atomic internal states via photon-mediated dipole–dipole interactions in the coupled state and the chirality of decay channels, where the atomic Bell state and W states for arbitrary number of atoms can be tailored and heralded by state carving in the single-photon reflection spectrum. Our results pave the way toward quantum engineering of multiqubit states and offer new opportunities for coherent and scalable multipartite entanglement transport in atoms coupled to nanophotonic devices.

About the connection of the electron binding energy of a single carbon anion with binding energies of an electron attached to carbon molecules

We demonstrate that the model of zero-range potentials can be successfully employed for the description of attached electrons in atomic and molecular anions, for example, negatively charged carbon clusters. To illustrate the capability of the model we calculate the energies of the attached electron for the family of carbon cluster anions consisting of two-, three- (equilateral triangle) and four (tetrahedron) carbon atoms equidistant from each other as well as for a C3 molecule having a chain structure. The considered approach can be easily extended to carbon clusters containing an arbitrary number of atoms arranged in an arbitrary configuration.

Tunable non-Markovian dynamics with a three-level atom mediated by the classical laser in a semi-infinite photonic waveguide

In this work, we investigate the non-Markovian (NM) dynamical evolution of a three-level atom coupled to a semi-infinite one-dimensional photonic waveguide and driven by a classical driving field. The single-end of waveguide behaves as a perfect mirror while light can pass through the opposite end with no backreflection. We derive the exact analytical expressions for the wave function of the driven three-level atom by solving a set of delay differential equations and give the conditions of atom-photon bound state formation that can inhibit the dissipation, which appears in the atom-mirror interspace in order to trap a considerable amount of initial atomic excitation. We show that when the evolution time of the system is shorter than the time delay taken by a photon to perform a round trip between the atom and mirror, the atomic dynamics exhibits Markovian properties, which depend on the driving strength and rescaled parameters. If the evolution time of the system exceeds the time delay, the photon can be reabsorbed by the atom with the photon emitted by the atom having completed the round trip, which exhibits NM memory effects, where the population eventually convergences to the finite-steady values. We also study the influence of the loss and dephasing on the formation of a bound state. Finally, the above results are extended to a more general quantum system involving single-end photonic waveguide coupled to an arbitrary number of noninteracting three-level atoms driven by the driving fields. The presented formalism might open a way to better understand exactly the NM dynamics of driven multilevel atoms coupled to a semi-infinite waveguide.

Helium-induced electronic transitions in photo-excited Ba+-Hen exciplexes.

The possibility for helium-induced electronic transitions in a photo-excited atom is investigated using Ba+ excited to the 6p 2P state as a prototypical example. A diabatization scheme has been designed to obtain the necessary potential energy surfaces and couplings for complexes of Ba+ with an arbitrary number of helium atoms. It involves computing new He-Ba+ electronic wave functions and expanding them in determinants of the non-interacting complex. The 6p 2P ← 6s 2S photodissociation spectrum of He⋯Ba+ calculated with this model shows very weak coupling for a single He atom. However, several electronic relaxation mechanisms are identified, which could potentially explain the expulsion of barium ions from helium nanodroplets observed experimentally upon Ba+ photoexcitation. For instance, an avoided crossing in the ring-shaped He7Ba+ structure is shown to provide an efficient pathway for fine structure relaxation. Symmetry breaking by either helium density fluctuations or vibrations can also induce efficient relaxation in these systems, e.g., bending vibrations in the linear He2Ba+ excimer. The identified relaxation mechanisms can provide insight into helium-induced non-adiabatic transitions observed in other systems.

Analytical Description of the H/D Exchange Kinetic of Macromolecule.

We present the accurate analytical solution obtained for the system of rate equations describing the isotope exchange process for molecules containing an arbitrary number of equivalent labile atoms. The exact solution was obtained using Mathematica 7.0 software, and this solution has the form of the time-dependent Gaussian distribution. For the case when forward exchange considerably overlaps the back exchange, it is possible to estimate the activation energy of the reaction by obtaining a temperature dependence of the reaction degree. Using a previously developed approach for performing H/D exchange directly in the ESI source, we have estimated the activation energies for ions with different functional groups and they were found to be in a range 0.04-0.3 eV. Since the value of the activation energy depends on the type of functional group, the developed approach can have potential analytical applications for determining types of functional groups in complex mixtures, such as petroleum, humic substances, bio-oil, and so on.

Dicke phase transition and collapse of superradiant phase in optomechanical cavity with arbitrary number of atoms

We in this paper derive the analytical expressions of ground-state energy, average photon-number, and the atomic population by means of the spin-coherent-state variational method for arbitrary number of atoms in an optomechanical cavity. It is found that the existence of mechanical oscillator does not affect the phase boundary between the normal and superradiant phases. However, the superradiant phase collapses by the resonant damping of the oscillator when the atom–field coupling increases to a so-called turning point. As a consequence the system undergoes at this point an additional phase transition from the superradiant phase to a new normal phase of the atomic population-inversion state. The region of superradiant phase decreases with the increase of photon–phonon coupling. It shrinks to zero at a critical value of the coupling and a direct atomic population transfer appears between two atom-levels. Moreover we find an unstable nonzero-photon state, which is the counterpart of the superradiant state. In the absence of oscillator our result reduces exactly to that of Dicke model. Particularly the ground-state energy for N=1 (i.e. the Rabi model) is in perfect agreement with the numerical diagonalization in a wide region of coupling constant for both red and blue detuning. The Dicke phase transition remains for the Rabi model in agreement with the recent observation.

An Effective Procedure for Analyzing Molecular Vibrations in Terms of Local Fragment Modes.

Normal mode analysis is nowadays routinely performed in most quantum chemistry codes as a valuable tool for studying molecular motions. In systems formed by several molecular units, such as noncovalently bound donor-acceptor systems, normal modes are frequently delocalized over the whole structure, leading to a complicated interpretation of vibrations. Here, we propose a simple procedure to localize normal modes, based on the definition of fragment Hessian submatrices that lead to legitimate local fragment modes. These fragment modes can be defined for any arbitrary number of atoms and fragments and form in general a complete basis that can be used to expand the total normal modes. We use this fragment basis to explore the molecular origin of the normal modes of benzene, and several peaks in the infrared spectrum of tetraalanine. Additionally, we propose a criteria to define breathing modes in noncovalently bound systems, based on the fact that motions of the center of mass of fragments are not translational and rotational invariant with respect to the total center of mass of the system. By using the Sayvetz-Eckart conditions of fragments, we can quantify the contribution of rotation and translation of the fragments center of mass on the normal modes of the total system.

Sparse coded image super-resolution using K-SVD trained dictionary based on regularized orthogonal matching pursuit.

Image super-resolution (SR) plays a vital role in medical imaging that allows a more efficient and effective diagnosis process. Usually, diagnosing is difficult and inaccurate from low-resolution (LR) and noisy images. Resolution enhancement through conventional interpolation methods strongly affects the precision of consequent processing steps, such as segmentation and registration. Therefore, we propose an efficient sparse coded image SR reconstruction technique using a trained dictionary. We apply a simple and efficient regularized version of orthogonal matching pursuit (ROMP) to seek the coefficients of sparse representation. ROMP has the transparency and greediness of OMP and the robustness of the L1-minization that enhance the dictionary learning process to capture feature descriptors such as oriented edges and contours from complex images like brain MRIs. The sparse coding part of the K-SVD dictionary training procedure is modified by substituting OMP with ROMP. The dictionary update stage allows simultaneously updating an arbitrary number of atoms and vectors of sparse coefficients. In SR reconstruction, ROMP is used to determine the vector of sparse coefficients for the underlying patch. The recovered representations are then applied to the trained dictionary, and finally, an optimization leads to high-resolution output of high-quality. Experimental results demonstrate that the super-resolution reconstruction quality of the proposed scheme is comparatively better than other state-of-the-art schemes.

A novel regularized K-SVD dictionary learning based medical image super-resolution algorithm

Recently sparse representations over learned dictionaries have been proven to be a very successful representation method for many image processing applications. In the medical image processing community, image super-resolution has been playing a vital role to make the computer based diagnosis more efficient and accurate. Resolution enhancement through conventional interpolation methods strongly affects the precision of consequent processing steps such as segmentation and registration. In this paper, we propose a novel regularized K-SVD dictionary learning based medical image super-resolution algorithm. First, the dictionary is trained using the modified version of the K-SVD dictionary learning procedure. The sparse coding phase of the K-SVD dictionary learning scheme is then enhanced incorporating a simple and an efficient regularized version of orthogonal matching pursuit. In addition, the dictionary update stage allows for an arbitrary number of atoms at the same time and sparse coefficient vector. In the SR reconstruction procedure, ROMP is adopted to find out for the vector of sparse representation coefficients for the underlying patch. In the final part, mathematical optimization finalizes the SR work effectively. The numerical analysis and experimental simulation prove the feasibility and robustness of our proposed methodology compared with other state-of-the-art algorithms.

Interference effects during the reradiation of ultrashort electromagnetic pulses by polyatomic systems

A theory of the reradiation of ultrashort electromagnetic pulses by arbitrary polyatomic systems of isolated complex atoms has been developed. The technique used allows the spatial inhomogeneity of the field of an ultrashort pulse and photon momenta in reradiation processes to be accurately taken into account. The angular distributions of the reradiation spectra have been obtained for an arbitrary number of atoms in the system. The processes of interference between the photon emission amplitudes are shown to give rise to characteristic “diffraction” maxima. We consider one-dimensional, two-dimensional, and three-dimensional rectangular lattices as examples as well as planar and cylindrical structures as models of planar nanosystems and nanotubes.

The Mott Problem in One Dimension

In the α decay of a nucleus, the tracks left in the medium by the α particle are linear, even though its initial wave function is spherically symmetric. Understanding this quantum phenomenon has been called “the Mott problem”, ever since Mott’s fundamental paper on the subject (Mott in Proc. R. Soc. London Ser. A 126:79 1929). Here we study a one dimensional version of the Mott problem. The particle emitted in the decay is represented as a superposition of waves, one traveling to the left, the other to the right. The atoms with which the particle interacts are modeled as two level systems. The wave equation obeyed by the particle is taken to be the massless Dirac equation. For a certain space-time structure for the particle-atom interaction, it is possible to derive an explicit space-time solution for the entire system, for an arbitrary number of atoms. In the one dimensional solution, the coherent superposition of right and left-moving wave packets leaves behind tracks of excited atoms. The Mott problem on the nature of the tracks left behind is addressed using the reduced density matrix, defined by taking the trace over all particle degrees of freedom. It is found that the reduced density matrix is the incoherent sum of two terms, one involving excited atoms only on the right; the other involving excited atoms only on the left, implying that tracks will show excited atoms on one side or the other. In one dimension, tracks which involve excited atoms exclusively on one side or the other are the analog of straight tracks in three dimensions.

Polarization bremsstrahlung at collisions of fast ions with multiatomic targets

The processes of polarization bremsstrahlung at collisions of fast ions with linear chains consisting of isolated atoms have been considered. The intensities and angular distributions of radiation spectra have been obtained for an arbitrary number of atoms in a chain. It has been shown that the interference of the photon emission amplitudes leads to a noticeable change in the spectral angular distributions of polarization bremsstrahlung as compared to the distributions at collisions with an isolated atom. The results allow standard generalization to the cases of polarization bremsstrahlung at channeling of fast ions over surfaces and in solid lattices.

Reemission spectra and interference effects at the interaction of multiatomic targets with ultrashort electromagnetic pulses

The processes of reemission of ultrashort electromagnetic pulses by linear chains consisting of isolated multielectron atoms have been considered. The developed method makes it possible to accurately take into account the spatial inhomogeneity of the field of an ultrashort pulse and the momenta of photons in reemission processes. The angular distributions of reemission spectra have been obtained for an arbitrary number of atoms in a chain. It has been shown that the interference of the photon emission amplitudes leads to the appearance of characteristic “diffraction” maxima. The results allow standard generalization to the cases of rescattering from two-dimensional (graphene-like) and three-dimensional lattices, as well as to the case of the inclusion of thermal vibrations of the atoms of lattices.

Construction of Myazawa's Equations for the Case of an Arbitrary Number of Junction Atoms

In an earlier paper, by the technique of incomplete mathematical induction, the algorithm of construction of Miyazawa's equations for an arbitrary number of “junction atoms” in macromolecular chains were “guessed.” In this paper, we describe the technique of complete mathematical induction to prove the correctness of this algorithm.

Direct calculation of the lattice Green function with arbitrary interactions for general crystals

Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces, and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic strain. Flexible boundary condition methods embed a defect in infinite harmonic bulk through the lattice Green function. We demonstrate an efficient and accurate calculation of the lattice Green function from the force-constant matrix for general crystals with an arbitrary basis by extending a method for Bravais lattices. New terms appear due to the presence of optical modes and the possible loss of inversion symmetry. By separately treating poles and discontinuities in reciprocal space, numerical accuracy is controlled at all distances. We compute the lattice Green function for a two-dimensional model with broken symmetry to elucidate the role of different coupling terms. The algorithm is generally applicable in two and three dimensions to crystals with arbitrary number of atoms in the unit cell, symmetry, and interactions.

Quantum theory of bright matter-wave solitons in harmonic confinement

This paper investigates bright quantum-matter-wave solitons beyond the Gross-Pitaevskii equation (GPE). As proposals for interferometry and creating nonlocal quantum superpositions have been formed, it has become necessary to investigate effects not present in mean-field models. We investigate the effect of harmonic confinement on the internal degrees of freedom, as the ratio of zero-point harmonic oscillator length to classical soliton length, for different numbers of atoms. We derive a first-order energy correction for the addition of a harmonic potential to the many-body wave function and use this to create a variational technique based on energy minimization of this wave function for an arbitrary number of atoms, and include numerics based on diagonalization of the Hamiltonian in a basis of harmonic oscillator Fock states. Finally we compare agreement between a Hartree product ground state and the Bethe ansatz solution with a Gaussian envelope localizing the center of mass and show a region of good agreement.

Generating coherence and entanglement with a finite-size atomic ensemble in a ring cavity

We propose a model to study the coherence and entanglement resulting from the interaction of a finite-size atomic ensemble with degenerate counter-propagating field modes of a high-Q ring cavity. Our approach applies to an arbitrary number of atoms N and includes the spatial variation of the field throughout the ensemble. We report several new interesting aspects of coherence and entangled behaviour that emerge when the size of the atomic ensemble is not taken to the thermodynamic limit of N→∞. Under such conditions, it is found that although in the thermodynamic limit the counter-propagating cavity modes are mutually incoherent and exhibit no one-photon interference, the modes can, however, be made mutually coherent and exhibit interference after interacting with a finite-size atomic ensemble. It is also found that the spatial redistribution of the atoms over a finite size results in non-orthogonality of the collective bosonic modes. This non-orthogonality leads to the super-bunching effect that the correlations of photons of the individual cavity modes and of different modes are stronger than those of a thermal field. We also investigate the spectral distributions of the logarithmic negativity and the variances of the output fields. These functions determine the entanglement properties of the output cavity fields and can be measured by a homodyne technique. We find that the entanglement is redistributed over several components of the spectrum and the finite-size effect is to concentrate the entanglement at the central component of the spectrum.

Vacuum Degeneracy of a Circuit QED System in the Ultrastrong Coupling Regime

We investigate theoretically the quantum vacuum properties of a chain of N superconducting Josephson atoms inductively coupled to a transmission line resonator. We derive the quantum field Hamiltonian for such a circuit QED system, showing that, due to the type and strength of the interaction, a quantum phase transition can occur with a twice degenerate quantum vacuum above a critical coupling. In the finite-size case, the degeneracy is lifted, with an energy splitting decreasing exponentially with increasing values of g{2}N{2}, where g is the dimensionless vacuum Rabi coupling per artificial atom. We determine analytically the ultrastrong coupling asymptotic expression of the two degenerate vacua for an arbitrary number of artificial atoms and of resonator modes. In the ultrastrong coupling regime the degeneracy is protected with respect to random fluctuations of the transition energies of the Josephson elements.

Variational cellular model of the energy bands of silicon

The recently proposed variational cellular method is formulated for application to three-dimensional periodic structures with an arbitrary number of atoms per unit cell. The method is used here to determine the electronic structure of silicon. The energy band calculations were carried out with the unit cell partitioned into four space-filling polyhedra. Interstitial cells were included in order to improve on the spherical cellular potentials. The calculations reported show that the method requires a small computational effort to obtain accurate and well-converged results.