Atom-atom Correlations Research Articles

The N-atom laser below saturation: a density matrix approach without large-N scaling

The authors present a method of deriving a reduced density operator equation for a quantized field interacting with an arbitrary number of atoms that does not neglect atom-atom correlations. As a particular example they analyse a three-level laser operating well below saturation and solve the density matrix equations in steady state. For weak pumping the system is equivalent to the Scully-Lamb model (1966) and the corresponding equations are recovered. Using the saturation photon number as a (large) scaling parameter one can derive a Fokker-Planck equation for the Glauber-P-distribution. The stationary solution of the reduced density matrix equation is compared with the solution of the Fokker-Planck equation and-for the case of a single-atom laser-with a numerical solution of the total density matrix equation.

X-ray-absorption studies of zirconia polymorphs. III. Static distortion and thermal distortion.

Static and dynamic Debye-Waller factors for the Zr(Y)-O shell and the Zr(Y)-Zr(Y) shell have been determined for four zirconia polymorphs from 10 K to room temperature. The apparent Einstein frequencies for cation-O vibrations and the Debye frequencies for cation-cation vibrations have also been obtained from the analysis. The higher phase stability and the stabilizing effect of Y dopants are manifest in the higher apparent vibrational frequencies. For tetragonal zirconia these frequencies correlate well with Raman data, and for cubic zirconia the Y-O frequency coincides with the unique Raman frequency for fluorite-structure oxides. Similar bonding in monoclinic and cubic zirconia yields similar vibrational frequencies, while a larger bond distance generally leads to a lower frequency. Comparison of the Debye-Waller factors obtained from extended x-ray-absorption fine structure and from neutron diffraction has also revealed the different extent of atom-atom correlation in atomic thermal motion for different bonding.

Integral equations for conventional correlation functions of simple dimerizing fluids

An integral equation theory is proposed for the atom-atom correlation functions of a simple reacting fluid, namely one in which a dimerization reaction is occurring. For a model fluid composed of hard sphere monomers and rigid dumbbell dimers the integral equations are solved exactly in the Percus-Yevick approximation, and an explicit expression for the equilibrium constant is derived. Comparison is made with the relevant Monte Carlo simulation data.

Structure factor measurements of liquid Cl2at high temperatures

Neutron diffraction measurements have been performed on orthobaric liquid Cl2 at 393 K and 412 K. The intermolecular structure factor, D M(Q), and the atom-atom pair correlation function g(r) have been derived. The D M(Q) reveals the presence of strong orientational correlations also at these high temperatures and low densities. Furthermore, the analysis of g(r) shows that the structure of liquid Cl2 does not change appreciably along the coexistence curve from the triple point up to the critical. Comparison between the experimental g(r) and the results of molecular dynamics (MD) simulations, using the A2 intermolecular potential, clearly indicates some inadequacies of this potential model even though it is able to reproduce the main features of the experimental g(r).

Structure of the surfactant-water interface

The microscopic characteristics of the surfactant-water interface are studied using computer simulation. The water region near the flat surface formed by the -COOH polar head groups of surfactant molecules is considered. We calculate the density profile of water molecules and probability distributions for their orientations, distribution functions for pair interaction energies, and atom-atom and dipole-dipole pair correlation functions for the carboxylate head groups. The average number of nearest neighbours in the head group subsystem is four, two of which form linear hydrogen bonds with the central head group, so that their dipole moments are parallel to that of the central head group, while the other two, situated on each side of the central head group, are directed antiparallel to its dipole moment. The water molecules of the first hydration monolayer are squeezed into the spaces between head groups, and are built themselves into the surfactant monolayer structure. At a surface density for surfactant ...

Collapse and revival phenomena in the many-atom-jaynes-cummings model in the presence on initial fock- and coherent-state fields

New aspects of cooperative radiation inhibition effects appearing in the interaction of many two-level atoms with a resonant single-mode radiation field inside a lossless cavity are examined. It is shown that collapses and revivals of the envelopes of Rabi oscillations of atomic energy expectation value occur in the presence of initial strong Fock-state fields. In the case of initial coherent fields, a cooperative energy shift of the quasi-stationary energy expectation value is pointed out. Further it is found that all cooperative radiation effects are caused by strong atom-atom correlations.

Molecular dynamics simulation of the liquid mixture CCl4/CS2

All centre-centre and atom-atom pair correlation functions have been calculated from a molecular dynamics simulation of the mixture CCl4/CS2 at three mole fractions and at room temperature. The agreement between the intermolecular correlation functions obtained and the corresponding data from a neutron scattering is excellent. The results are discussed in terms of the changes of the local environment of the CCl4 and CS2 molecules with changing mole fractions.

THE MULTI-PHOTON QUANTUM STATITISCAL THEORY OF DRIVEN OPTICAL SYSTEMS (II)——BAD CAVITY CASE

In this paper, the multi-photon FPE of driven optical systems are treated for bad cavity case. The semi-classical linear stability analysis are performed. The non-classical effects are discussed, and it is shown that in two-photon case the atom-atom correlation enhances the non-clasical effects. This is in opposite to the single-photon case, and different from the good cavity case. The two-photon spectrum of transmitted light and resonance fluorescense are obtained, where the Rabi frequency Ω∝y2 (y is the incident field).

A Monte Carlo simulation study of liquid chlorine

The results of Monte Carlo simulations to study liquid Cl2 using the Price and Stone potential are reported. We discuss the orientational correlations together with the atom-atom correlation functions, and compare our results with those obtained using a two Lennard-Jones centres plus quadrupole model. The main results of this comparison show that the atom-atom distribution functions are practically the same for the two potential models, whereas the angular configurations set up by the interactions are very different. At short distances the Price-Stone potential increases the weight of the cross configurations, giving an orientational order closer to the one characteristic of a two Lennard-Jones centres model without a quadrupole. On the contrary, the addition of a point quadrupolar interaction has the effect of increasing the fraction of ‘T’ configurations.

Atomic correlations in driven optical systems.

We consider the one-mode quantum-statistical model of optical bistability, and show that atom-atom correlations are negligible in the good-cavity limit, in all effects that can be described by a linearized treatment. In the light of this result, we discuss the concept of ``atomic cooperation'' in quantum optical systems. In the purely absorptive case, the atomic polarization exhibits a squeezing effect which arises both in the good- and in the bad-cavity limit. This phenomenon has the same origin of the squeezing effect in resonance fluorescence.

Neutron diffraction study of liquid fluorine at 77K

Measurements of the neutron scattering static structure factor S(Q) are reported for orthobaric liquid fluorine at 77K for an incident wavelength of 1·2Å. The observed S(Q) and the atom-atom correlation function are discussed and compared with those of other halogens and oxygen. From the d(r) pair distribution function it is shown that liquid fluorine has a coordination number of first neighbours more similar to liquid oxygen than halogens. The number of atoms in the first and second coordination shell is in good agreement with a close-packed arrangement of atoms.

The structure of liquid bromine

We report neutron diffraction measurements of liquid bromine at T = 298 K and T = 473 K and orthobaric densities. The structure factor, S(Q), in the range 0·8–15Å-1 and the non-bonded bromine atom-atom correlation function, g(r), are discussed and compared with previous results on Br2 and Cl2. Monte Carlo (MC) computer simulations using the two-centre Lennard-Jones interaction model with idealized point quadrupole were performed at the higher temperature. This effective pair potential turns out to be unable to reproduce the Br2 structure.

Summation of four-operator perturbation series: Application to atom-atom intensity-dependent correlations.

It is shown how certain classes of problems dealing with the interaction of radiation with atoms can be formulated in terms of four-operator perturbation series. The case of an isolated atom coupled to a single-mode field is discussed in detail within the resolvent formalism. The process where no photon is effectively absorbed by the atom is described, to all orders, in terms of a series involving four operators which simultaneously increase and/or decrease the photon number and the orbital quantum number. This series is exactly summed and the summation technique is generalized to single-atom, two-field and to two-atom, single-field systems exhibiting zero, one, and two net photon absorptions or emissions. The theory is applied to induced emission of a single photon from a pair of two-level atoms coupled to a monomode radiation field. The energy diagrams, the time dependence of the probability, and the resonance curves are discussed for systems where (i) both atoms are in the upper state and (ii) atom 1 is in the upper state and atom 2 is in the lower state at t=0. In comparing these results to the ones obtained with a single atom, we find that the important intensity-dependent correlations give rise to trapping effects even when the atoms are initially in the upper state.

Thermoelectric power minimum and electrical resistivity of liquid Hg-based alloys containing Li

The electrical resistivity rho and the thermoelectric power Q of binary liquid Hg-Li alloys have been measured. The resistivity decreases with the addition of Li. This behaviour shows a systematic variation of rho with the addition of solute alkali elements to liquid mercury alloys. As for the other akali amalgams, Q shows a minimum at 5 at.% Li in the curve plotted as a function of the Li concentration at constant temperature. The variation of rho with the addition of alkali elements (including Li) can be well described by the Faber-Ziman theory (1965) based on the nearly free electron model, while the minimum in Q cannot. In order to understand the origin of the minimum in Q of liquid H-Li alloys, higher-order atom-atom correlation function effects seem to be very important, as stressed previously by the present authors for other alkali amalgams such as Hg-Cs alloys. The 'modified Miedema plot' appears to reveal that this higher-order correlation effect is caused by charge transfer from the solute to the Hg atom.

Higher-order correlation effects on thermodynamic and electronic properties of liquid alloys

The higher-order atom-atom correlation function effect, which has been recently revealed to be related to the origin of the minimum in the thermoelectric power Q of liquid Hg alloys, is discussed in some detail. New experimental results of the electrical resistivity ϱ and Q of liquid HgLi alloys are included in this discussion. The relation between the higher order correlation function effects and the thermodynamic function of liquid Hg alloys (the heat of mixing ΔH M) is stressed. The charge transfer effect, which can been clarified by the modified Miedema's plot, seems to produce the local structural change which can be seen as the higher order correlation effect.

Fluctuation theory in quantum-optical systems

We show that the most complete and accurate description of fluctuations in quantum-optical systems is that obtained using the generalized Wigner distribution for the macroscopic observables of the system. The smallness of the inverse of the saturation photon number entitles us to neglect the terms with derivatives of order higher than second order in the time-evolution equation for the quasiprobability distribution. This treatment allows us to also describe correctly nonclassical effects such as photon antibunching or "squeezing," which are maltreated or even destroyed if one neglects the atom-atom correlations. We derive and analyze the Fokker-Planck equation for the Wigner function in the case of the usual laser and compare the results with those following from other approaches. In the region very high above threshold we find a small antibunching effect, which was not discovered in previous treatments due to the neglect of atom-atom correlations.

Interaction site models for molecular fluids

A detailed study is made of the atom-atom (i.e. site-site) correlation functions—especially the direct correlation function—for the interaction site model (ISM) of Andersen and Chandler. The work is based on the observation of Høye and Stell that the site-site Ornstein-Zernike-like equation of Chandler and Andersen can be regarded as a rewritten version of the usual Ornstein-Zernike equation for particle-particle correlations, where the particles are identified with the atoms that constitute the ISM molecules. Our new results include (i) new compressibility theorems in terms of the site-site direct correlation functions, and (ii) for ISM diatomics (both polar and non-polar) full asymptotic (i.e. large-r) characterization of the site-site direct correlation function based on the assumption that the corresponding particle-particle direct correlation function behaves asymptotically like the particle-particle potential times -1/k B T (k B = Boltzmann's constant and T = absolute temperature). Further asymptotic results are also given for a wider class of ISMs, in particular for triatomics. All our asymptotic results (except those for two classes of homonuclear symmetric n-atomics) are in fundamental disagreement with assumptions of the reference interaction site approximation (RISA) and the more general interaction site approximation (ISA), both originally proposed by Chandler and Andersen, as well as with all subsequently proposed approximations of which we are aware. (iii) A characterization is given of a family of ISMs containing point charges that is solvable in a class of linear approximations, including the ISA, as well as an approximation that is asymptotically faithful to the results noted in the preceding item. The family of ISMs considered includes models that have heretofore lacked analytic solution. (iv) The relation between the exact analytic solution of the Chandler-Andersen RISA and its approximate solution according to the widely-used Lowden-Chandler ansatz is examined on the basis of the particle-particle picture. It is pointed out how the relatively good liquid density agreement and the relatively poor low density agreement between the two solutions can be easily understood within this framework.

Reaction field simulation of water

Two molecular dynamics simulations of 216 molecules interacting by the ST2 water potential were carried out. Apart from technical improvements, the first simulation was identical to that reported by Stillinger and Rahman [4]. In the second, however, the reaction field method was applied and the influence of long range interactions was carefully studied. 7500 time steps (= 7·5 ps) were generated. The temperature given by the average kinetic energy was 120°C. The atom-atom pair correlation functions and the average dipole energy are rather insensitive to the reaction field. The average cosine between two molecular dipoles, however, is strongly influenced and corresponding curves are of different sign in the second and third coordination shell. For the integral of the average cosine, namely the Kirkwood g-factor g K, the situation is even worse : Large errors occur if the long range interactions are neglected. On the other hand, a convergence of g K was achieved by the inclusion of the reaction field. The pr...

EXAFS as a probe of atom-atom interaction potentials: AgI and CuI

The extended fine structure on the X-ray absorption cross section (EXAFS) depends sensitively upon the details of the nearest-neighbour peak in the atom-atom pair correlation function. It follows that EXAFS data can be helpful in determining the short-range portion of atom-atom pair interaction potentials such as are the starting point for molecular dynamics (MD) calculations. The cation-anion pair correlation functions g(r) obtained from MD calculations on superionic AgI and CuI are compared with EXAFS data. The nearest-neighbour peak in the MD g(r) begins at too short a cation-anion separation and is too broad to be consistent with the data. The causes and ramifications of this are discussed.

Analytical and numerical results for the steady state in cooperative resonance fluorescence

The cooperative resonance fluorescence steady state is discussed within the context of an operator master equation which conserves total pseudospin. Emphasis throughout is on quantum fluctuations and their significance in relation to a background of factorised dynamics. Atom-atom correlations are shown to play a fundamental role for systems driven beyond the linear regime. Use of the atomic coherent state representation yields a Fokker-Planck description closely allied to the dynamics for a classical angular momentum oscillator. For intense incident fields the quantum-mechanical steady state is understood in terms of diffusion both around and between classical trajectories on the Bloch sphere. In the limit of infinite systems simple closed-form expressions for steady-state features are derived. Coherent and incoherent fluorescent intensities are obtained together with the second-order correlation function for fluorescent light. Specific features are illustrated by numerical results for systems of from two to fifty atoms.