Exact quantum master equation is derived for dephasing of a two-level system, which is an homogeneous time-convolutionless equation even though there is an initial correlation between a two-level system and a thermal reservoir. The result is compared with the quantum master equation derived by means of the projection operator method. Furthermore, the effects of the initial correlation on the dephasing process are examined.

In this addendum to our paper [B. Van Schaeybroeck, Phys. Rev. A 78, 023624 (2008)] we present an exact solution of the interface tension of Bose-Einstein condensates in a particular parameter regime.

In a self-defocusing optical cavity, optical-field perturbations on a vortex background behave as sound waves in a $\left(2+1\right)$ rotating acoustic black-hole spacetime. Numerical integration of the associated Klein-Gordon equation using typical experimental parameters shows that optical perturbations in the appropriate frequency range are amplified through the mechanism of superradiance. These results suggest the possibility to observe this phenomenon in a common nonlinear optical system.

Dispersion and dissipation are inherent to electromagnetic wave propagation in metamaterials. We show that these inherent limitations can be overcome by a self-induced transparency pulse that stably propagates through a metamaterial sparsely doped with resonantly absorbing dopants. This pulse has the form of a hitherto unexplored backward soliton. We discuss the observable signature of this soliton.

To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For a class of models in which a two-state system and a dynamical environment interact through a Hamiltonian restricted to be a tensor product, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians of the environment share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics.

We present a scheme for realizing a steady entanglement state between two trapped atoms, without requiring the initialization of atom-cavity system nor fine time-controlling of evolution dynamics. We show that high-fidelity entanglement of atomic state can be obtained in a period of time equal to a few times the inverse of atomic’s spontaneous decay rate. The robustness against cavity decay $\kappa$ and cavity thermal field $n_T$ has also been examined.

We report measurements of the isotope shifts of the $3d^{6}4s^2$ $a{{}^{5}D}_4-3d^{6}4s4p$ $z{{}^{5}F}_5^o$ $\text{Fe}\text{I}$ resonance line at 372 nm between all four stable isotopes ${}^{54}\text{F}\text{e}$, ${}^{56}\text{F}\text{e}$, ${}^{57}\text{F}\text{e}$, and ${}^{58}\text{F}\text{e}$, as well as the complete hyperfine structure of that line for ${}^{57}\text{F}\text{e}$, the only stable isotope having a nonzero nuclear spin. The field and specific mass shift coefficients of the transition have been derived from the data, as well as the experimental value for the hyperfine structure magnetic dipole coupling constant $A$ of the excited state of the transition in ${}^{57}\text{F}\text{e}$: $A\left(3d^{6}4s4pz{{}^{5}F}_5^o\right)=81.69\left(86\right)\text{MHz}$. The measurements were carried out by means of high-resolution Doppler-free laser saturated absorption spectroscopy in a Fe-Ar hollow cathode discharge cell using both natural and enriched iron samples. The measured isotope shifts and hyperfine constants are reported with uncertainties at the percent level.

Parity and time invariance violating electric dipole moment of ${}^{205}\text{T}\text{l}$ is calculated using the relativistic Hartree-Fock and configuration interaction methods and the many-body perturbation theory. Contributions from the interaction of the electron electric dipole moments with internal electric field and scalar-pseudoscalar electron-nucleon $\left(T,P\right)$-odd interaction are considered. The results are $d\left({}^{205}\text{T}\text{l}\right)=-582\left(20\right)d_e$ or $d\left({}^{205}\text{T}\text{l}\right)=-7.0\left(2\right)\times {10}^{-18}{C}^{SP}e\text{cm}$. Interpretation of the measurements are discussed. The results of similar calculations for ${}^{133}\text{C}\text{s}$ are $d\left({}^{133}\text{C}\text{s}\right)=124\left(4\right)d_e$ or $d\left({}^{133}\text{C}\text{s}\right)=0.76\left(2\right)\times {10}^{-18}{C}^{SP}e\text{cm}$.

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with two $p$ electrons or a single $d$ electron have been derived and implemented. The Hamiltonian used in the approach was obtained by rigorously separating the center-of-mass motion and it explicitly depends on the finite mass of the nucleus. The approach was employed to perform test calculations on the isotopes of the carbon atom in their ground electronic states and to determine the finite-nuclear-mass corrections for these states.

We develop an ab initio procedure based on the driven Schrödinger equation formalism and the external complex scaling method for the determination of the multifold differential cross sections of the single and double ionization of molecular hydrogen by single photon and fast electron impact. We take advantage of the separability of the two-center Schrodinger equation in prolate spheroidal coordinates in the numerical calculation of the two-electron two-center wave function of the initial and final states of the target. After having verified our procedure by reproducing existing confirmed triple differential cross sections of the $\left(e,2e\right)$ ionization of ${\text{H}}_2$, we have extended our calculation to the double ionization of ${\text{H}}_2$. Our results on double photoionization agree with existing experimental results. We observe in the mean time a small difference with respect to the absolute results obtained by similar ab initio calculations using spherical bases. For the case of the double ionization by fast electron impact for which very few experimental results exist, our results confirm the existing disagreement between the theoretical results and the unique experimental one in the case of $\left(e,3\text{−}1e\right)$. This we think makes it clear that for $\left(e,3e\right)$ the introduction of the higher terms of the Born series for mean energy electron-impact regime is necessary.

We demonstrate that exterior complex scaling (ECS) can be used to impose outgoing wave boundary conditions exactly on solutions of the time-dependent Schrödinger equation for atoms in intense electromagnetic pulses using finite grid methods. The procedure is formally exact when applied in the appropriate gauge and is demonstrated in a calculation of high-harmonic generation in which multiphoton resonances are seen for long pulse durations. However, we also demonstrate that while the application of ECS in this way is formally exact, numerical error can appear for long-time propagations that can only be controlled by extending the finite grid. A mathematical analysis of the origins of that numerical error, illustrated with an analytically solvable model, is also given.

We investigate the finite temperature momentum distribution of bosonic noncondensate particles inside a uniform three-dimensional optical lattice near the superfluid-to-Mott-insulator transition point, treating quantum fluctuations and thermal fluctuations on equal footing. We explicitly address the different momentum $\left(\mathbf{q}\right)$ dependences of quasiparticle distribution resulted from thermal and quantum origins: the former scales as ${\left|\mathbf{q}\right|}^{-2}$ and hence is dominant in the small momentum region, while the later scales as ${\left|\mathbf{q}\right|}^{-1}$ and hence is dominant in the large momentum limit. Semianalytical results are derived and therefore can be applied to a further study of strongly interacting bosonic systems. Our results also agree with the scaling theory of a quantum $XY$ model near the transition point.

We show that the interaction of adjacent fiber-optic solitons can be reduced by the Raman self-frequency shift. As the frequency slides, the interaction periodically alternates between attraction and repulsion. If this happens sufficiently rapidly, the forces largely average out. We present a simplified analytical model and compare its predictions to numerical simulations.

In this paper we examine the $N$-photon absorption properties of maximally path-entangled number states ($N00N$ states). We consider two cases. The first involves the $N$-photon absorption properties of the ideal $N00N$ state, one that does not include spectral information. We study how the $N$-photon absorption probability of this state scales with $N$, confirming results presented by others in a previous paper by a different method. We compare this to the absorption probability of various other states. The second case is that of two-photon absorption for an $N=2$ $N00N$ state generated from a type-II spontaneous down-conversion event. In this situation we find that the absorption probability is both better than analogous coherent light (due to frequency entanglement) and highly dependent on the optical setup. We show that the poor production rates of quantum states of light may be partially mitigated by adjusting the spectral parameters to improve their two-photon absorption rates. This work has application to quantum imaging, particularly quantum lithography, where the $N$-photon absorbing process in the lithographic resist must be optimized for practical applications.

The effect of the counterrotating terms on the linear polarizability is investigated, which is responsible for the validity of the optical theorem in all frequency regions. A unitary transformation method [H. Zheng, S. -Y. Zhu, and M.S. Zubairy, Rev. Lett. 101, 200404 (2008)] is adopted to overcome the difficulty brought in by the counterrotating terms, which yields a rotating-wave-approximation-like Hamiltonian with modified coupling constant due to the counterrotating terms. A simple expression for the polarizability is obtained, which is a sum of resonant (minus sign) and antiresonant (plus sign) parts, and from which the role of the counterrotating terms and quantum interference between the counterrotating terms and rotating terms at far off-resonance are discussed.

We develop a diagrammatic theory for transport of waves in dilute disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and crossed diagrams for the average wave intensity. Then, we sum up the diagrammatic series completely, i.e., nonperturbatively in the strength of the nonlinearity, and thereby obtain integral equations describing both nonlinear diffusive transport and coherent backscattering of the average intensity. As main result, we find that the nonlinearity significantly influences the magnitude of the coherent backscattering effect. Depending on the type of nonlinearity, coherent backscattering is either enhanced or suppressed, as compared to the linear case.

A generalized reflection time which follows directly from the Schrödinger equation without approximation is obtained. By the Winger-Eisenbud approach, this reflection time is conceptually well defined and can be applied to arbitrary continuous potentials including both quantum tunneling and quantum reflection issue. A simple explanation for the quantum reflection phenomenon is proposed and the explicit expression of the difference between the quantum reflection time and the classical reflection time is also derived.

We show that when an electron or photon propagates in a cylindrically symmetric waveguide, its spin angular momentum (SAM) and its orbital angular momentum (OAM) interact. Remarkably, we find that the dynamics resulting from this spin-orbit interaction are quantitatively described by a single expression applying to both electrons and photons. This leads to the prediction of several rotational effects: the spatial or time evolution of either particle’s spin-polarization vector is controlled by its OAM quantum number or, conversely, its spatial wave function is controlled by its SAM. We show that the common origin of these effects in electrons and photons is a universal geometric phase. We demonstrate how these phenomena can be used to reversibly transfer entanglement between the SAM and OAM degrees of freedom of two-particle states.

An exact solution for the problem of interaction between whispering gallery modes of spherical microresonators and a single dipole is presented. It is predicted that experimentally observed spectral doublets associated with this interaction are a part of a triplet whose third component has yet to be observed. It is also shown that the interaction between the dipole and nonresonant whispering gallery modes results in a renormalization of the dipole’s polarizability and experimental manifestations of this effect are discussed.

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intrapair and interpair entanglement. The pairs are taken from a large many-body system where all the pairs are generally entangled with each other. Using an explicit example based on single mode entanglement and an ancillary Bose-Einstein condensate, we show that the Bell-inequality violation in such systems can display statistical properties that are remarkably different from those obtained using identically prepared independent pairs. In particular, one can have probabilistic violation of Bell’s inequalities in which a finite fraction of all the runs result in violation even though there could be no violation when averaging over all the runs. Whether or not a particular run of results will end up being local realistically explainable is “decided” by a sequence of quantum (random) outcomes.