Critical Number Of Atoms Research Articles

Electrochemistry of Copper(I) Oxide in the 66.7–33.3 mol % Urea–Choline Chloride Room-Temperature Eutectic Melt

The electrochemistry of Cu(I) oxide was examined in the 66.7–33.3% mole fraction (m/o) urea–choline chloride melt. Electrochemical parameters that were measured include the standard heterogeneous rate constant and transfer coefficient of the Cu(I)/Cu(II) reaction and the Cu(I) diffusion coefficient. Data about the density, equivalent conductance, and absolute viscosity of this melt were obtained over the temperature range of 298–353 K. The conductivity and viscosity exhibited the non-Arrhenius behavior typical of glass-forming liquids. Overall, the physicochemical properties of the urea–choline chloride melt are comparable to those of common room-temperature ionic liquids. The electrodeposition of Cu was examined on glassy carbon and platinum electrodes by using potential-step techniques. The critical number of atoms required for the formation of a stable nucleus on glassy carbon was , indicating that active sites on the electrode surface served as critical nuclei. Cu deposits on Ni substrates were dense, nodular, and compact.

Effects of three-body atomic interaction and optical lattice on solitons in quasi-one-dimensional Bose-Einstein condensate

We make use of a coordinate-free approach to implement Vakhitov-Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter-wave bright solitons formed in Bose-Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of √1 − bg3 with g3 the coupling constant of the lattice potential and b = 0.7301.

The trapped two-dimensional Bose gas: from Bose–Einstein condensation to Berezinskii–Kosterlitz–Thouless physics

We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional (2D) geometry. In this experiment a well-defined critical point was identified, which separates the high-temperature normal state characterized by a single component density distribution, and the low-temperature state characterized by a bimodal density distribution and the emergence of high-contrast interference between independent 2D clouds. We first show that this transition cannot be explained in terms of conventional Bose–Einstein condensation of the trapped ideal Bose gas. Using the local density approximation (LDA), we then combine the mean-field (MF) Hartree–Fock theory with the prediction for the Berezinskii–Kosterlitz–Thouless (BKT) transition in an infinite uniform system. If the gas is treated as a strictly 2D system, the MF predictions for the spatial density profiles significantly deviate from those of a recent quantum Monte Carlo (QMC) analysis. However, when the residual thermal excitation of the strongly confined degree of freedom is taken into account, excellent agreement is reached between the MF and the QMC approaches. For the interaction strength corresponding to the experiment, we predict a strong correction to the critical atom number with respect to the ideal gas theory (factor ∼2). Quantitative agreement between theory and experiment is reached concerning the critical atom number if the predicted density profiles are used for temperature calibration.

Upper bound for the success probability of cavity-mediated adiabatic transfer in the presence of dissipation

The cavity-mediated adiabatic transfer (CMAT), which is the physical basis of several implementations of two-qubit gates, is investigated analytically. An upper bound for the success probability of CMAT in the presence of atomic spontaneous emission and cavity photon loss is given by a simple function of only the so-called critical atom number. Moreover, a situation which realizes the upper bound is found, and this is verified by numerical simulation. It also turns out from numerical simulation that standard Gaussian pulses can achieve the success probability close to the upper bound. That is, the standard Gaussian pulses are almost optimal for CMAT.

Buckling behaviors of single-walled carbon nanotubes filled with metal atoms

Molecular dynamics method is employed to investigate the buckling deformations of single-walled carbon nanotubes (SWCNTs) filled with nickel (Ni), copper (Cu), and platinum (Pt) atoms under axial compression. The critical buckling strains of filled tubes decrease linearly before a critical number of metal atoms and then increase linearly when more atoms are encapsulated. For SWCNT completely filled with metals, its critical strain is larger than that of the hollow tube. Furthermore, the critical strain of SWCNT completely filled with Ni atoms is larger than that of the tube fully filled with Cu or Pt atoms.

Critical Point of an Interacting Two-Dimensional Atomic Bose Gas

We have measured the critical atom number in an array of harmonically trapped two-dimensional (2D) Bose gases of rubidium atoms at different temperatures. We found this number to be about 5 times higher than predicted by the semiclassical theory of Bose-Einstein condensation (BEC) in the ideal gas. This demonstrates that the conventional BEC picture is inapplicable in an interacting 2D atomic gas, in sharp contrast to the three-dimensional case. A simple heuristic model based on the Berezinskii-Kosterlitz-Thouless theory of 2D superfluidity and the local density approximation accounts well for our experimental results.

Formation of Bright Matter-Wave Solitons during the Collapse of Attractive Bose-Einstein Condensates

We observe bright matter-wave solitons form during the collapse of (85)Rb condensates in a three-dimensional (3D) magnetic trap. The collapse is induced by using a Feshbach resonance to suddenly switch the atomic interactions from repulsive to attractive. Remnant condensates containing several times the critical number of atoms for the onset of instability are observed to survive the collapse. Under these conditions a highly robust configuration of 3D solitons forms such that each soliton satisfies the condition for stability and neighboring solitons exhibit repulsive interactions.

Spontaneous Symmetry Breaking of Population in a Nonadiabatically Driven Atomic Trap: An Ising-Class Phase Transition

We have observed spontaneous symmetry breaking of the population of Brownian particles between two moving potentials in the spatiotemporally symmetric system. Cold atoms preferentially occupy one of the dynamic double-well potentials, produced in the parametrically driven dissipative magneto-optical trap far from equilibrium, above a critical number of atoms. We find that the population asymmetry, which may be interpreted as the biased Brownian motion, can be qualitatively described by the mean-field Ising-class phase transition. This in situ study may be useful for investigation of dynamic phase transition or temporal behavior of critical phenomena.

Quantum-dot nucleation in strained-layer epitaxy: Minimum-energy pathway in the stress-driven two-dimensional to three-dimensional transformation

The transformation of monolayer islands into bilayer islands as a first step of the overall two-dimensional to three-dimensional (2D-3D) transformation in the coherent Stranski-Krastanov mode of growth is studied for the cases of expanded and compressed overlayers. Compressed overlayers display a nucleation-like behavior: the energy accompanying the transformation process displays a maximum at some critical number of atoms, which is small for large enough values of the misfit, and then decreases gradually down to the completion of the transformation, non-monotonically due to the atomistics of the process. On the contrary, the energy change in expanded overlayers increases up to close to the completion of the transformation and then abruptly collapses with the disappearance of the monoatomic steps to produce low-energy facets. This kind of transformation takes place only in materials with strong interatomic bonding. Softer materials under tensile stress are expected to grow predominantly with a planar morphology until misfit dislocations are introduced, or to transform into 3D islands by a different mechanism. It is concluded that the coherent Stranski-Krastanov growth in expanded overlayers is much less probable than in compressed ones for kinetic reasons.

Ultrahigh-Qtoroidal microresonators for cavity quantum electrodynamics

We investigate the suitability of toroidal microcavities for strong-coupling cavity quantum electrodynamics (QED). Numerical modeling of the optical modes demonstrate a significant reduction of modal volume with respect to the whispering gallery modes of dielectric spheres, while retaining the high quality factors representative of spherical cavities. The extra degree of freedom of toroid microcavities can be used to achieve improved cavity QED characteristics. Numerical results for atom-cavity coupling strength, critical atom number N_0 and critical photon number n_0 for cesium are calculated and shown to exceed values currently possible using Fabry-Perot cavities. Modeling predicts coupling rates g/(2*pi) exceeding 700 MHz and critical atom numbers approaching 10^{-7} in optimized structures. Furthermore, preliminary experimental measurements of toroidal cavities at a wavelength of 852 nm indicate that quality factors in excess of 100 million can be obtained in a 50 micron principal diameter cavity, which would result in strong coupling values of (g/(2*pi),n_0,N_0)=(86 MHz,4.6*10^{-4},1.0*10^{-3}).

Tunnelling induced collapse of an atomic Bose–Einstein condensate in a double-well potential

The stability of a low-temperature Bose–Einstein condensate with attractive interactions in one- and three-dimensional double-well potentials is discussed. In particular, the tunnelling dynamics of a condensate under the influence of a time-dependent potential gradient is investigated. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. The sensitivity of this tunnelling-induced collapse could provide a useful tool in the study of condensates with attractive interactions.

Collective excitations in circular atomic configurations and single-photon traps

Correlated excitations in a plane circular configuration of identical atoms with parallel dipole moments are investigated. The collective energy eigenstates, which are formally identical to Frenkel excitons, can be computed together with their level shifts and decay rates by decomposing the atomic state space into carrier spaces for the irreducible representations of the symmetry group Z{sub N} of the circle. It is shown that the index p of these representations can be used as a quantum number analogously to the orbital angular momentum quantum number l in hydrogenlike systems. Just as the hydrogen s states are the only electronic wave functions which can occupy the central region of the Coulomb potential, the quasiparticle corresponding to a collective excitation of the atoms in the circle can occupy the central atom only for vanishing Z{sub N} quantum number p. If a central atom is present, the p=0 state splits into two and shows level crossing at certain radii; in the regions between these radii, damped quantum beats between two 'extreme' p=0 configurations occur. The physical mechanisms behind super- and subradiance at a given radius are discussed. It is shown that, beyond a certain critical number of atoms in the circle, the lifetimemore » of the maximally subradiant state increases exponentially with the number of atoms in the configuration, making the system a natural candidate for a single-photon trap.« less

Atom-photon entanglement generation and distribution

We extend an earlier model by Law {\it et al.} \cite{law} for a cavity QED based single-photon-gun to atom-photon entanglement generation and distribution. We illuminate the importance of a small critical atom number on the fidelity of the proposed operation in the strong coupling limit. Our result points to a promisingly high purity and efficiency using currently available cavity QED parameters, and sheds new light on constructing quantum computing and communication devices with trapped atoms and high Q optical cavities.

The critical number of atoms in an attractive Bose–Einstein condensate on opticalplus harmonic traps

The stability of an attractive Bose–Einstein condensate on a joint one-dimensionaloptical lattice and an axially symmetrical harmonic trap is studied using thenumerical solution of the time-dependent mean-field Gross–Pitaevskii equationand the critical number of atoms for a stable condensate is calculated. We alsocalculate this critical number of atoms in a double-well potential which isalways greater than that in an axially symmetrical harmonic trap. Thecritical number of atoms in an optical trap can be made smaller or largerthan the corresponding number in the absence of the optical trap bymoving a node of the optical lattice potential in the axial direction of theharmonic trap. This variation of the critical number of atoms can beobserved experimentally and compared with the present calculations.

Optimal sizes of dielectric microspheres for cavity QED with strong coupling

The whispering gallery modes (WGMs) of quartz microspheres are investigated for the purpose of strong coupling between single photons and atoms in cavity quantum electrodynamics (cavity QED). Within our current understanding of the loss mechanisms of the WGMs, the saturation photon number ${n}_{0}$ and critical atom number ${N}_{0}$ cannot be minimized simultaneously, so that an ``optimal'' sphere size is taken to be the radius for which the geometric mean $\sqrt{{n}_{0}{N}_{0}},$ is minimized. While a general treatment is given for the dimensionless parameters used to characterize the atom-cavity system, detailed consideration is given to the ${D}_{2}$ transition in atomic cesium at ${\ensuremath{\lambda}}_{0}=852\mathrm{nm}$ using fused-silica microspheres, for which the maximum coupling coefficient ${g}_{a}/(2\ensuremath{\pi})\ensuremath{\approx}750\mathrm{MHz}$ occurs for a sphere radius $a=3.63\ensuremath{\mu}\mathrm{m}$ corresponding to the minimum for ${n}_{0}\ensuremath{\approx}6.06\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ By contrast, the minimum for ${N}_{0}\ensuremath{\approx}9.00\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ occurs for a sphere radius of $a=8.12\ensuremath{\mu}\mathrm{m},$ while the optimal sphere size for which $\sqrt{{n}_{0}{N}_{0}}$ is minimized occurs at $a=7.83\ensuremath{\mu}\mathrm{m}.$ On an experimental front, we have fabricated fused-silica microspheres with radii $a\ensuremath{\sim}10\ensuremath{\mu}\mathrm{m}$ and consistently observed quality factors $Q>~0.8\ifmmode\times\else\texttimes\fi{}{10}^{7}.$ These results for the WGMs are compared with corresponding parameters achieved in Fabry-Perot cavities to demonstrate the significant potential of microspheres as a tool for cavity QED with strong coupling.

Bose-Einstein condensate collapse: A comparison between theory and experiment

We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed at JILA with Bose-Einstein condensates of Rb-85, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. Besides the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally. Quantum field effects, such as fragmentation, that might account for these discrepancies are discussed.

Critical numbers of attractive Bose-Einstein condensed atoms in asymmetric traps

The recent Bose-Einstein condensation of ultracold atoms with attractive interactions led us to consider the possibility of probing the stability of its ground state in arbitrary three-dimensional harmonic traps. We performed a quantitative analysis of the critical number of atoms through a full numerical solution of the mean-field Gross-Pitaevskii equation. Characteristic limits are obtained for reductions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones.

Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap.

The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the vortex state but tends to saturate for large L.

Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

We calculated, within the Gross-Pitaevskii formalism, the critical number of atoms for Bose-Einstein condensates with two-body attractive interactions in cylindrical traps with different frequency ratios. In particular, by using the trap geometries considered by Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)], we show that the theoretical maximum critical numbers are given approximately by ${N}_{c}{=0.55(l}_{0}/|a|).$ Our results also show that, by exchanging the frequencies ${\ensuremath{\omega}}_{z}$ and ${\ensuremath{\omega}}_{\ensuremath{\rho}},$ the geometry with ${\ensuremath{\omega}}_{\ensuremath{\rho}}<{\ensuremath{\omega}}_{z}$ favors the condensation of larger number of particles. We also simulate the time evolution of the condensate when changing the ground state from $a=0$ to $a<0$ using a 200 ms ramp. A conjecture on higher-order nonlinear effects is also added in our analysis with an experimental proposal to determine its signal and strength.

Enhanced yield of photoinduced electrons in doped silver halide crystals

The conventional photographic process1,2,3 involves several steps: the photogeneration of electron–hole pairs in crystals of a silver halide; the reduction of silver cations to atoms by some fraction of these electrons; the subsequent build up of atoms to give clusters (the ‘latent image’); and the complete reduction by a developer of crystallites having more than a critical number of silver atoms per cluster. The effective quantum yield, Φeff, of photoinduced electron–hole pairs produced per photon absorbed is less than the theoretical limit (Φtheory = 1), because of the fast recombination of some fraction of the pairs1,2,3,4,5,6. Here we describe an approach for enhancing the yield of useful photogenerated electrons, in which the silver halide is doped with formate ions, HCO-2. The dopant ions act as hole scavengers, thus enhancing the escape of electrons from pair recombination. Moreover, the resulting CO˙-2 radical can itself transfer an electron to another silver cation, so raising the theoretical yield to two silver atoms per photon absorbed. This photoinduced bielectronic transfer mechanism is strictly proportional to the light quanta absorbed—the dopant ions do not induce spontaneous reduction of silver cations in the dark—and appears to be close to the theoretical limit of efficiency. The efficiency is constant at all illumination levels and applies to both dye-sensitized and unsensitized crystals. We suggest that this approach is a promising route for improving the performance of photographic emulsions7.