The complete $O\left({\alpha }^2\right)$ correction to the long-range interaction between neutral closed-shell atoms is obtained, the relation to the asymptotic expansion of the known short-range interaction at the atomic scale is presented and a general interaction potential that is valid in the whole range of the interatomic distances is constructed.

A self-consistent theory is derived to describe the BCS–Bose-Einstein-condensate crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper pairs and “bare” Feshbach molecules, has been included within a self-consistent $T$-matrix approximation, beyond the Nozières and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal-state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature $T_c$ increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor $Z_m$ of the molecule’s Green function and a complex effective mass have been determined to characterize the fraction and lifetime of Feshbach molecules at $T_c$. Our many-body calculations of $Z_m$ agree qualitatively well with recent measurments of the gas of ${}^6\mathrm{Li}$ atoms near the broad resonance at $834\mathrm{G}$. The crossover from narrow to broad resonances has also been studied.

We propose a general method of solving the Schrödinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schrödinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function ${\psi }_0$ and scaling $g$ function, and then the ICI method automatically generates the wave function that has the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke’s atom for the electron singularity case, and the helium atom for both cases.

We demonstrate how linear differential operators could be emulated by a quantum processor, should one ever be built, using the Abrams-Lloyd algorithm. Given a linear differential operator of order $2S$, acting on functions $\psi (x_1,x_2,\dots ,x_D)$ with $D$ arguments, the computational cost required to estimate a low order eigenvalue to accuracy $\Theta (1∕N^2)$ is $\Theta \left((2(S+1)(1+1∕\nu )+D)\ln N\right)$ qubits and $O\left(N^{2(S+1)(1+1∕\nu )}{\ln }^c{N}^D\right)$ gate operations, where $N$ is the number of points to which each argument is discretized, $\nu$ and $c$ are implementation dependent constants of $O\left(1\right)$. Optimal classical methods require $\Theta \left(N^D\right)$ bits and $\Omega \left(N^D\right)$ gate operations to perform the same eigenvalue estimation. The Abrams-Lloyd algorithm thereby leads to exponential reduction in memory and polynomial reduction in gate operations, provided the domain has sufficiently large dimension $D>2(S+1)(1+1∕\nu )$. In the case of Schrödinger’s equation, ground state energy estimation of two or more particles can in principle be performed with fewer quantum mechanical gates than classical gates.

The free iterative-complement-interaction (ICI) method based on the scaled Schrödinger equation proposed previously has been applied to the calculations of very accurate wave functions of the hydrogen molecule in an analytical expansion form. All the variables were determined with the variational principle by calculating the necessary integrals analytically. The initial wave function and the scaling function were changes to see the effects on the convergence speed of the ICI calculations. The free ICI wave functions that were generated automatically were different from the existing wave functions, and this difference was shown to be physically important. The best wave function reported in this paper seems to be the best worldwide in the literature from the variational point of view. The quality of the wave function was examined by calculating the nuclear and electron cusps.

Investigating the quantum phase transition in a ring from a uniform attractive Bose-Einstein condensate to a localized bright soliton we find that the soliton undergoes transverse collapse at a critical interaction strength, which depends on the ring dimensions. In addition, we predict the existence of other soliton configurations with many peaks, showing that they have a limited stability domain. Finally, we show that the phase diagram displays several new features when the toroidal trap is set in rotation.

We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions, respectively, and use these to reformulate Maxwell’s equations. These variables enable us to not only judge the effect and significance of backward-traveling field components, but also to discard them when appropriate. They thereby have the potential to simplify numerical simulations, leading to potential speed gains of up to 100% over standard finite difference time-domain (FDTD) or pseudospectral spatial-domain (PSSD) simulations. We present results for various illustrative situations, including an example application to second harmonic generation in periodically poled lithium niobate. These field variables are also used to derive both envelope equations useful for narrow-band pulse propagation, and a second order wave equation. Alternative definitions are also presented.

We propose a method to probe Landau and Beliaev processes in dilute trapped atomic condensates with a multiple-state structure using electromagnetically induced transparency configurations. Under certain conditions, damping rates from these collisional processes are directly proportional to the dephasing rates, making it possible to determine damping rates through measurement of the dephasing. In the systems we consider, Landau decay rates are enhanced at low momenta, which allows one to distinguish between Landau-dominated and Beliaev-dominated regimes at the same temperature. Furthermore, the enhancement of Landau rates potentially provides a way to measure low temperatures $(T⪡T_c)$ in dilute condensates more accurately than current methods permit.

We have experimentally observed switching between photon-photon correlations and anticorrelations between two orthogonally polarized laser beams in an electromagnetically induced transparency configuration in Rb vapor. The correlation and anticorrelation switching occurs at a specific magnetic field strength.

We present an eikonal model for electron excitation and loss from highly charged ionic projectiles colliding with atomic targets at relativistic collision energies. In this model the distortion of the target transition four-current by the strong field of the projectile nucleus is taken into account using the symmetric eikonal approximation. General expressions are derived for the eikonal transition amplitude in the case of collisions with one- and two-electron targets. The correspondence between the eikonal and first-order transition amplitudes is discussed. Relativistic features and the nonrelativistic limit of the eikonal transition amplitude are considered. It is shown that the higher-order terms in the projectile-target interaction, which are not accounted for by the first-order amplitude, may be of importance even for quite small values of $\nu =Z_p∕v$, where $Z_p$ is the charge of the projectile nucleus and $v$ the collision velocity.

We present detailed numerical results on the dynamics of a Bose-Einstein condensate in a tilted periodic optical lattice over many Bloch periods. We show that an increasing atom-atom interaction systematically affects coherent tunneling, and eventually destroys the resonant tunneling peaks.

Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.

We present a detailed numerical analysis of the lowest-order resonant modes of a hexagonal dielectric cavity. Our investigations include resonant wave numbers, linewidths, mode patterns, and their dependency on the refractive index. On the basis of our theoretical results, we are able to simulate the resonance spectra of individual hexagonal zinc oxide nanocavities without a free parameter. A superposition of Lorenzian resonance lines leads to perfect agreement with experimental data obtained from polarization-resolved micro-photoluminescence and cathodoluminescence spectroscopy. Series of radially higher-order modes are theoretically predicted and experimentally observed. Therefore, we present a consistent description of the resonance behavior of a hexagonal dielectric optical cavity on nanoscopic scale.

We reconsider the problem of entanglement of thermal equilibrium states of composite systems. We introduce characteristic, viz., critical, temperatures—and bounds for them—marking transitions from entanglement to separability, or vice versa. We present examples for the various possible thermal entanglement scenarios in bipartite qubit-qubit and qubit-qutrit systems.

The influence of the vibrational heating of a single cold ion trapped in a bimodal cavity under continuous excitation on the generation of two-mode squeezing and entanglement of the cavity field from the ion is discussed. It is found that the vibrational heating gives a strong limitation for the appearance of the two-mode squeezing, but the two cavity modes can develop into a robust entangled Gaussian state.

A general multistep linear state symmetrization device for photonic qubits is presented together with the experimental realizations of the $1\to 3$ and $2\to 3$ universal optimal quantum cloning machines and of a 3-qubit purification procedure. Since the present method exploits the bosonic nature of the photons, it can be applied to any particle obeying to the Bose statistics. On a technological perspective, the present protocol is expected to find relevant applications as a multiqubit symmetrization device to be used in modern quantum-information networks.

The Skornyakov–Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.

A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this long-standing problem, based on a universally applicable formalism for ensembles on configuration space. This approach overcomes difficulties arising in previous attempts and in particular allows for a back reaction on the classical ensemble, conservation of probability and energy, and the correct classical equations of motion in the limit of no interaction. Applications include automatic decoherence for quantum ensembles interacting with classical measurement apparatuses, a generalization of coherent states to hybrid harmonic oscillators, and an equation for describing the interaction of quantum matter fields with classical gravity, which implies that the radius of a Robertson-Walker universe containing a quantum massive scalar field can be sharply defined only for particular “quantized” values.

In several quantum information (QI) phenomena of large technological importance the information is carried by the phase of the quantum superposition states, or qubits. The phase-covariant cloning machine (PQCM) addresses precisely the problem of optimally copying these qubits with the largest attainable “fidelity.” We present a general scheme which realizes the $1\to 3$ phase covariant cloning process by a combination of three different QI processes: the universal cloning, the NOT gate, and the projection over the symmetric subspace of the output qubits. The experimental implementation of a PQCM for polarization encoded qubits, the first ever realized with photons, is reported.