Collective states in highly symmetric atomic configurations and single-photon traps

We study correlated states in circular and linear-chain configurations of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective behavior is mediated by exchange of transverse photons between the atoms. For a circular atomic configuration containing N atoms, the collective energy eigenstates can be determined by group-theoretical means making use of the fact that the configuration possesses a cyclic symmetry group Z _N . For these circular configurations, the carrier spaces of the various irreducible representations of the symmetry group are at most two-dimensional, so that the effective Hamiltonian on the radiationless subspace of the system can be diagonalized analytically. As a consequence, the radiationless energy eigenstates carry a Z _N quantum number p = 0, 1, …, N, which is analogous to the angular momentum quantum number l = 0, 1, … carried by particles propagating in a central potential, such as a hydrogen-like system. Just as the hydrogen s states are the only electronic wave functions that can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the circular atomic sample can occupy the central atom only for vanishing Z _N quantum number p. When a central atom is present, the p = 0 state splits into two, showing level crossing at certain radii; in the regions between these radii, damped oscillations between two “ extreme” p = 0 states occur, where the excitation occupies either the outer atoms or the central atom only. For large numbers of atoms in a maximally subradiant state, a critical interatomic distance of λ/2 emerges both in the linear-chain and in the circular configuration of atoms. The spontaneous decay rate of the linear configuration exhibits a jumplike “critical” behavior for next-neighbor distances close to a half-wavelength. Furthermore, both the linear-chain and the circular configurations exhibit exponential photon trapping once the next-neighbor distance becomes less than a half-wavelength, with the suppression of spontaneous decay being particularly pronounced in the circular system. In this way, circular configurations containing sufficiently many atoms may be natural candidates for single-photon traps.     

Quantification of Quantum Entanglement in a Multiparticle System of Two-Level Atoms Interacting with a Squeezed Vacuum State of the Radiation Field

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms.     

Refinement of the structure of hydrogen–vacancy complexes in titanium by the Rietveld method

The VT1-0 titanium alloy (phase α-Ti) with various hydrogen and hydrogen-vacancy concentrations has been studied. The stability of the 32-atom Ti–nV–mH supercell (n is the number of the V vacancies, and m is the number of hydrogen atoms H) with varying numbers of vacancies and hydrogen atoms has been calculated from the first principles. The structural state of the α-Ti phase has been identified by the Rietveld method based on the calculations of the supercell stability and the data on the defect concentration obtained using positron spectroscopy. The complete structural information on the considered states of the α-Ti phase (the lattice parameters, spatial distribution of titanium and hydrogen atoms and vacancies) has been obtained.     

Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators

To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3–10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.     

Quantummechanical solutions of the laser masterequation I

The masterequation for the statistical operatorW of a Laser mode andA active two-level atoms 1 is solved by using the coherent state representation 2 of the lightfield. The ansatz forW represents the most general symmetrical coupling of the light mode to all atoms and therefore contains the full influence of quantum fluctuations of the atomic system on the light mode. The system of equations can be solved practically exactly in the stationary case and leads to a photon number distribution in the laser valid for arbitrary pumping. This distribution agrees with that found by a Fokker-Planck equation 3 for not too high pumping and approaches the Poisson distribution for very high pumping. The smooth transition of the inversion from σ₀ (below threshold) to σ (above threshold) can also be calculated.     

Ionization of <Emphasis Type="Italic">nS</Emphasis>, <Emphasis Type="Italic">nP</Emphasis>, and <Emphasis Type="Italic">nD</Emphasis> lithium,potassium, and cesium Rydberg atoms by blackbody radiation

The results of theoretical calculations of the blackbody ionization rates of lithium, potassium, and cesium atoms residing in Rydberg states are presented. The calculations are performed for nS, nP, and nD states in a wide range of principal quantum numbers, n = 8?65, for blackbody radiation temperatures T = 77, 300, and 600 K. The calculations are performed using the known quasi-classical formulas for the photoionization cross sections and for the radial matrix elements of transitions in the discrete spectrum. The effect of the blackbody-radiation-induced population redistribution between Rydberg states on the blackbody ionization rates measured under laboratory conditions is quantitatively analyzed. Simple analytical formulas that approximate the numerical results and that can be used to estimate the blackbody ionization rates of Rydberg atoms are presented. For the S series of lithium, the rate of population of high-lying Rydberg levels by blackbody radiation is found to anomalously behave as a function of n. This anomaly is similar to the occurrence of the Cooper minimum in the discrete spectrum.     

Possibility of the use of the magnetic field for creating a quantum filter on the <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript><Superscript>87</Superscript>Rb line

The possibility of the use of the F = 2?F = 1 transition of the D ₁ absorption line of the ⁸⁷Rb atom for creating of a single-photon quantum filter based on coherent population trapping (CPT) has been analyzed. It has been shown that the external magnetic field is necessary for ensuring the creation of the quantum filter on boson isotopes of alkali atoms. The field strength should be enough for the manifestation of the splitting of the Zeeman CPT resonances that is much larger than their spectral widths. The splittings of the CPT resonances, which characterize the nonlinearity of the Zeeman effect, have been measured for the ⁸⁷Rb atom and the possibility of the use of this system for the quantum filter is concluded.     

Optimization of the Electromagnetic (EM) Perturbative Effects Produced by High-Frequency Gravitational Waves

For the relic gravitational waves in high frequency band, we survey the electromagnetic resonance effect generated from the high frequency gravitational waves, which can be described in the transverse perturbative photon fluxes. Under the fixed tensor-scalar ratio r = 0.2, spectral index n _t = 0 and running index α _t = 0.01, we discuss several properties and quantity changes of the transverse perturbative photon fluxes, which can be improved significantly through setting the longitudinal magnetic component of background EM field in the standard gaussian form, and wave impedance analysis on the transverse direction. Through the theoretical calculation, the transverse perturbative photon fluxes can reach up to 10³ s ^?1 with some optimal parameters such as waist of EM field W ₀ = 0.05m, initial stochastic phase of gravitational waves δ = (0.21 + n)π(n = 0,1,2...). Furthermore the interference of the background transverse photon fluxes can be removed completely through establishing a suitable wave impedance function.     

Sub- and super-Poissonian photon statistics of single-molecule fluorescence blinking

An analysis of intermittent fluorescence is presented for a single molecule driven by a continuous-wave laser field. The interruptions of fluorescence are caused by transition of the molecule to a triplet state. A method previously developed to calculate photon distribution for continuous-wave fluorescence is applied to analyze photon statistics of fluorescence blinking. The probability w _N (T) of counting N photons over a time interval T is derived for intermittent fluorescence. The photons counted over relatively short intervals are found to have a sub-Poissonian (narrower than Poisson) distribution. The photon distribution over intervals longer than the mean off time has a complicated form with two maxima; i.e., a super-Poissonian (wider than Poisson) distribution is obtained.     

Quantum-chemical study of the spectral properties of stilbene isomers

Calculations of absorption spectra of cis-and trans-forms of stilbene by the quantum-chemical method of intermediate neglect of differential overlap with spectroscopy parametrization were carried out. The electron structure of a stilbene molecule was studied and energy-level diagrams were drawn and analyzed. Rate constants of different photophysical processes occurring in a stilbene molecule after absorption of a photon were calculated in relation to the molecule conformation. On the basis of the obtained results, possible configurations of photoisomer molecules were considered and the most probable configurations of excited stilbene molecules were determined. It was shown how the change in the configurations of cis-and trans-forms of stilbene affects its spectral properties.     

Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

The hydrogen atom in two dimensions, described by a Schrödinger equation with a Chern-Simons potential, is numerically solved. Both its wavefunctions and eigenvalues were determined for small values of the principal quantum number n. The only possible states correspond to l = 0. How the result depends on the topological mass of the photon is also discussed. In the case n = 1, the energy of the fundamental state, corresponding to different choice for the photon mass scale, are found to be comprehended in the interval ?3.5 × 10^-3 eV ≤ E ≤ ?9.0 × 10^?2 eV, corresponding to a mean radius of the electron in the range (5.637 ± 0.005) × 10^?8 cm ≤ ?r? ≤ (48.87 ± 0.03) × 10^-8 cm. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction.     

Cluster <Emphasis Type="Italic">ab initio</Emphasis> modeling of local lattice instability in relaxor ferroelectrics

The possibility of a zigzag-type instability occurring for oxygen atoms in B-O-B, B-O-Nb, and Nb-O-Nb linear chains is examined in disordered mixed perovskite compounds Pb(B_1/3, Nb_2/3)O₃ (B=Mg, Zn, Cd). Local adiabatic potentials for oxygen atoms are studied using total energy calculations by the ab initio Hartree-Fock + MP2 method for many-atomic clusters with different oxygen surroundings of lead atoms. The effect of lattice relaxation along the chain on the shape of the local potential in the transverse direction for the central oxygen atom is considered.     

Universal temperature corrections to the free energy for the gravitational field

The temperature correction to the free energy of the gravitational field is considered which does not depend on the Planck energy physics. The leading correction may be interpreted in terms of the temperature-dependent effective gravitational constant G_eff. The temperature correction to appears to be valid for all temperatures T?E_Planck. It is universal since it is determined only by the number of fermionic and bosonic fields with masses m?T, does not contain the Planck energy scale E_Planck which determines the gravitational constant at T=0, and does not depend on whether or not the gravitational field obeys the Einstein equations. That is why this universal modification of the free energy for gravitational field can be used to study thermodynamics of quantum systems in condensed matter (such as quantum liquids superfluid ³He and ⁴He), where the effective gravity emerging for fermionic and/or bosonic quasiparticles in the low-energy corner is quite different from the Einstein gravity.     

Quantum information-holding single-photon router based on spontaneous emission

In this paper, we propose a single-photon router via the use of a four-level atom system coupled with two one-dimensional coupled-resonator waveguides. A single photon can be directed from one quantum channel into another by atomic spontaneous emission. The coherent resonance and the photonic bound states lead to the perfect reflection appearing in the incident channel. The fidelity of the atom is related to the magnitude of the coupling strength and can reach unit when the coupling strength matches g _a = g _b . This shows that the transfer of a single photon into another quantum channel has no influence on the fidelity at special points.     

Photon distribution functions of the fluorescence photons from a single nanoparticle in various photon counting methods

Simple expressions have been derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. In contrast to the previously derived expressions represented in the form of N multiple integrals, the new expressions contain only single or double integrals of Poisson functions, which makes it possible to easily perform the numerical calculation of the photon distribution. The simplest photon counting method corresponds to the lengthiest function w _N ^M (T); on the contrary, the simplest function w _N ^O (T) corresponds to the most complex photon counting method. The functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) are noticeably different in short time intervals T; however, the distributions calculated using these functions are almost indistinguishable from each other in long T intervals. This circumstance makes it possible to use the simplest function w _N ^O (T) to consider the photon statistics measured by the simplest method. This possibility is particularly important for investigating the fluorescence photon statistics, where the intensity fluctuates.     

Studying the possibility of deep laser cooling of <Superscript>24</Superscript>Mg atoms in an optical lattice: Two-level quantum model

The possible deep laser cooling of ²⁴Mg atoms in a deep optical lattice in the presence of an additional pumping field resonant to the narrow 3s3s¹S₀ → 3s3p³P₁ (λ = 457 nm) optical transition is studied. Two quantum models of the laser cooling of atoms in the optical trap are compared. One is based on the direct numerical solution to the kinetic quantum equation for an atomic density matrix; it considers both optical pumping and quantum recoil effects during interaction between the atoms and field photons. The second, simplified model is based on decomposing the states of the atoms over the levels of vibration in the optical trap and analyzing the evolution of these states. The comparison allows derivation of optical field parameters (pumping field intensity and detuning) that ensure cooling of the atoms to minimal energies. The conditions for fast laser cooling in an optical trap are found.     

Kinetic processes in a nonideal Rydberg matter

A kinetic model is developed to describe ultracold nonideal Rydberg plasmas, which allows all stages of the generation and decay of such a plasma to be sequentially traced. The plasma kinetics is considered on the basis of available experimental data corresponding to a nonideality parameter of γ ～ 1. The results of theoretical analysis are in good agreement with experiment. Calculations show evidence of a significantly decreased recombination rate and, hence, of the possible formation of a metastable structure in the plasma under consideration. The distribution of the number of excited atoms is determined for the plasma with N_e = N_i = 7 × 10⁵ and E_e = 9 K. The observed behavior of the number and density of particles as functions of the time and principal quantum number is explained. It is suggested that the distribution of excited atoms for the given parameters has a maximum for the state with k = 25.     

Quantenelektrodynamik bei nichtverschwindender Photonmasse

Quantum electrodynamics with non-vanishing photon mass is written down in interaction representation. To apply the Wick decomposition formalism of theS-matrix one can introduce an indefinite metricη, similar to that of Gupta-Bleuler's quantum electrodynamics with vanishing photon mass. It will be shown that the complementary photons can be eliminated from the formalism with the help of the subsidiary condition. By a succeeding unitary transformation allx-singularities (x=photon mass) can be removed. The limiting processx→0, which then becomes possible, leads to the well-known so-called ‘reduced’ theory of quantum electrodynamics. A physical interpretation of this limiting process will be tried using, as a simple example, the radiation of an electric dipole.     

Ionization of Rydberg atoms by the kicks of half-cycle pulses

We present a quantum mechanical model to study the ionization of quasione-dimensional Rydberg atoms interacting with half-cycle pulses (HCPs) and use it to demonstrate the inadequacy of semiclassical approaches to calculate ionization probabilities of such atoms subject to the impact of more than one HCP. For a single-kicked atom both models correctly reproduce the experimentally observed ‘s-curve’ as can be seen by plotting the ionization probability P as a function of momentum transfer q₁. We demonstrate that for a twice-kicked atom, the semiclassical model yields numbers for P which are not physically realizable. For fixed values of momentum transfers q₁ and q₂, in a twice-kicked atom, the ionization probability as a function of time delay between the kicks exhibits periodic decay and revival. The results of the semiclassical approach appear to agree with the quantum mechanical values at the times of revival of P, else these show considerable deviation. We attempt to provide a physical explanation for the limitation of the semiclassical approach.     

On the mechanisms of formation of excited hydrogen atoms in a decaying helium-hydrogen plasma

We spectroscopically studied the population of the excited hydrogen atomic states with the principal quantum numbers n=3 and 4 in a decaying plasma produced by a pulsed discharge in a mixture of helium (p=40.4 Torr) with a small amount of hydrogen ([H₂]≈10¹² cm^?3). Experiments on recording the response of the spectral line intensities to a short-duration electron temperature perturbation revealed the contribution of electron-ion recombination to the population of the H*(n=3) states in the early afterglow. The ions produced by collisions of hydrogen molecules with metastable He(2³ S ₁) atoms, whose density decreases relatively rapidly with time in the decaying plasma, were assumed to be involved in this process. No population of the H*(n=4) atomic levels due to electron-ion recombination was found. Our experimental results are consistent with the conclusions of previous studies that excitation transfer during collisions of metastable helium molecules with hydrogen molecules plays a major role in the population of the excited hydrogen atomic states both with n=3 and with n=4 during most of the afterglow.