A perturbative series is derived for the systematic construction of a dynamical invariant (Lewis invariant) for a time-dependent Hamiltonian which is characterized by a time-scale parameter $\tau$, as appears in the usual formulation of the adiabatic theorem. The derivations make efficient use of the quantum averaging method, and the perturbative series obtained permits the construction of the invariant in successive orders in $ϵ\sim 1/\tau$, corresponding to high-order adiabatic approximations. The series can be considered and resummed analytically to all orders, yielding an exact invariant for an harmonic oscillator linearly driven by an external field. For a nondegenerate two-level system, approximate invariants have been obtained up to the fifth order and illustrate how the adiabatic approximations of increasing orders successively approach the exact dynamics. The construct is applicable also to Floquet Hamiltonians and, in this context, it furnishes high-order adiabatic representations for the time evolution of Floquet states associated with a material system in an aperiodic laser pulse. We illustrate in particular how an exact Floquet dynamical invariant, defining exact adiabatic transports of Floquet states, is obtained for a laser-driven harmonic vibrational mode.

The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach is not justified. We apply a recently proposed correlated projection superoperator technique to the model of a central spin coupled to a spin bath via full Heisenberg interaction. Analytical solutions to both the Nakajima-Zwanzig and the time-convolutionless master equation are determined and compared with the results of the exact solution. The correlated projection operator technique significantly improves the standard methods and can be applied to many physical problems such as the hyperfine interaction in a quantum dot.

Isotropic $XX$ models of one-dimensional spin-1/2 chains are investigated with the aim to elucidate the formal structure and the physical properties that allow these systems to act as channels for long-distance, high-fidelity quantum teleportation. We introduce two types of models: (i) open, dimerized $XX$ chains, and (ii) open $XX$ chains with small end bonds. For both models we obtain the exact expressions for the end-to-end correlations and the scaling of the energy gap with the length of the chain. We determine the end-to-end concurrence and show that model (i) supports true long-distance entanglement at zero temperature, while model (ii) supports “quasi-long-distance” entanglement that slowly falls off with the size of the chain. Due to the different scalings of the gaps, respectively exponential for model (i) and algebraic in model (ii), we demonstrate that the latter allows for efficient qubit teleportation with high fidelity in sufficiently long chains even at moderately low temperatures.

Stark shifts of potassium and rubidium $D1$ lines have been measured with high precision by Miller et al. [Phys. Rev. A 49, 5128 (1994)]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the $4p_j\text{−}3d_{j^{\prime }}$ transitions in K and the $5p_j\text{−}4d_{j^{\prime }}$ transitions in Rb to high precision. The $4p_{1/2}\text{−}3d_{3/2}$ and $5p_{1/2}\text{−}4d_{3/2}$ transitions contribute on the order of 90% to the respective polarizabilities of the $n{p}_{1/2}$ states in K and Rb, and the remaining 10% can be accurately calculated using the relativistic all-order method. Therefore, the combination of the experimental data and theoretical calculations allows us to determine the $np\text{−}\left(n-1\right)d$ matrix elements and their uncertainties. We compare these values with our all-order calculations of the $np\text{−}\left(n-1\right)d$ matrix elements in K and Rb for a benchmark test of the accuracy of the all-order method for transitions involving $nd$ states. Such matrix elements are of special interest for many applications, such as determination of “magic” wavelengths in alkali-metal atoms for state-insensitive cooling and trapping, and determination of blackbody radiation shifts in optical frequency standards with ions.

The increasing interest in the Müller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock (HF) functional, but with a modified exchange term in which the square of the density matrix $\gamma (\mathbf{x},{\mathbf{x}}^{\prime })$ is replaced by the square of ${\gamma }^{1∕2}(\mathbf{x},{\mathbf{x}}^{\prime })$. After an extensive introductory discussion of density-matrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing $\gamma$’s have unique densities $\rho \left(\mathbf{r}\right)$, which is a physically desirable property often absent in HF theory. We show that minimizers exist if $N\le Z$, and derive various properties of the minimal energy and the corresponding minimizers. We also give a precise statement about the equation for the orbitals of $\gamma$, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.

A functional renormalization-group study for the Bose-Einstein condensate (BEC)-BCS crossover for ultracold gases of fermionic atoms is presented. We discuss the fixed point which is at the origin of universality for broad Feshbach resonances. All macroscopic quantities depend only on one relevant parameter, the concentration $a{k}_{\mathrm{F}}$, besides their dependence on the temperature in units of the Fermi energy. In particular, we compute the universal ratio between molecular and atomic scattering length in vacuum. We also present an estimate to which level of accuracy universality holds for gases of Li and K atoms.

We study the vortex pinning effect in a Bose-Einstein condensate in the presence of a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. We consider a triangular lattice potential created by blue-detuned laser beams. By rotating the lattice potential, we observe a structural phase transition from the Abrikosov vortex lattice to the pinned vortex lattice. We investigate the transition of the vortex lattice structure by changing conditions such as angular velocity, strength, and lattice constant of a rotating lattice potential. Our simulation results clearly show that the lattice potential has a strong vortex pinning effect when the vortex density coincides with the density of the pinning points.

We performed extensive measurements on the scattering efficiency of atomic Bragg scattering on a standing light wave up to sixth order and developed a two-state Demkov model to explain the results. Using an effective $2N$-photon coupling between the original and the reflected momentum states and the assumption of a mostly adiabatic transfer we derived the scattering probability. This probability has two factors: an oscillating part which represents the well-known Pendellösung oscillation and a part that is peaked in the energy difference between the two momentum states. This last part describes the tolerance on the Bragg condition for angular misalignment. Comparison of the measurements and numerical simulations with this model shows good agreement.

Refractive index control and its relevance to the velocity-selective effect generated by the propagation direction of the incoherent pumping field are studied in an open V-type atomic system. The velocity-selective effect on electromagnetically-induced transparency (EIT) is presented in theory and verified in the experiment. It shows that, in contrast to the case of copropagation, counter-propagation of the incoherent pumping field has an absolutely opposite effect on the dispersion of the V-type EIT system. The experimental results are in good agreement with the theoretical analysis.

We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10–50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.

We consider a Fabry-Perot resonance (a transmission band edge resonance) in periodic layered structures involving birefringent layers. In a previous publication [Phys. Rev. E 72, 036619 (2005)] we have shown that the presence of birefringent layers with misaligned in-plane anisotropy can dramatically enhance the performance of the photonic-crystal resonator. It allows us to reduce its size by an order of magnitude without compromising on its performance. The key characteristic of the enhanced slow-wave resonator is that the Bloch dispersion relation $\omega \left(k\right)$ of the periodic structure displays a degenerate photonic band edge, in the vicinity of which the dispersion curve can be approximated as $\mathrm{\Delta }\omega \sim (\mathrm{\Delta }k{)}^4$, rather than $\mathrm{\Delta }\omega \sim (\mathrm{\Delta }k{)}^2$. Such a situation can be realized in specially arranged stacks of misaligned anisotropic layers. On the down side, the presence of birefringent layers results in the slow-wave resonance being coupled only with one (elliptic) polarization component of the incident wave, while the other polarization component is reflected back to space. In this paper we show how a small modification of the periodic layered array can solve the above fundamental problem and provide a perfect impedance match regardless of the incident wave polarization, while preserving the giant slow-wave resonance characteristic of a degenerate photonic band edge. Both features are of critical importance for many practical applications, such as the enhancement of various light-matter interactions, light amplification and lasing, optical and microwave filters, antennas, etc.

In a pair of related papers, Wang et al. [Phys. Rev. A 75, 013813 (2007); 75, 042105 (2007)] claim to present evidence, based on quantum field theory, for the superluminality of evanescent modes in undersized waveguides. Here we show that the conclusion of the authors is false and is based on an error: they mistake a nonzero propagator for a nonzero commutator. The commutator of the field operator at two points separated by a spacelike interval is strictly zero, which makes true superluminality impossible.

We consider the possibility of performing linear optical quantum computations making use of extra photonic degrees of freedom. In particular, we focus on the case where we use photons as quadbits, four-dimensional photonic qudits. The basic 2-quadbit cluster state is a hyperentangled state across polarization and two spatial mode degrees of freedom. We examine the nondeterministic methods whereby such states can be created from single photons and/or Bell pairs and then give some mechanisms for performing higher-dimensional fusion gates.

We analyze the fidelity of a quantum simulation and we show that it displays fractal fluctuations if and only if the simulated dynamics is chaotic. This analysis allows us to investigate a given simulated dynamics without any prior knowledge. In the case of integrable dynamics, the appearance of fidelity fractal fluctuations is a signal of a highly corrupted simulation. We conjecture that fidelity fractal fluctuations are a signature of the appearance of quantum chaos. Our analysis can be realized already by a few-qubit quantum processor.

We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear $N$-body density matrix. The body-fixed frame transformation is carried out in order to achieve an electron density that reflects the internal symmetry of the system. We discuss the implications of this body-fixed frame transformation and establish a Runge-Gross-type theorem and derive Kohn-Sham equations for the electrons and nuclei. We illustrate the formalism by performing calculations on a one-dimensional diatomic molecule for which the many-body Schrödinger equation can be solved numerically. These benchmark results are then compared to the solution of the time-dependent Kohn-Sham equations in the Hartree approximation. Furthermore, we analyze the excitation energies obtained from the linear response formalism in the single pole approximation. We find that there is a clear need for improved functionals that go beyond the simple Hartree approximation.

The dielectric response to an inhomogeneous electric field has been investigated for Ba and ${\text{Ba}}_2$ within a molecular beam experiment. The ratio of the polarizabilities per atom of ${\text{Ba}}_2$ and Ba is determined to be $1.30\pm 0.13$. The experimental result is compared to a high level ab initio quantum chemical coupled cluster calculation with an energy-consistent scalar relativistic small-core pseudopotential for Ba. For the barium atom a polarizability of $40.82{\text{Å}}^3$ is obtained and the isotropic value of the polarizability calculated for ${\text{Ba}}_2$ is $97.88{\text{Å}}^3$, which is in good agreement with the experimental results, demonstrating that a quantitative understanding of the interaction between two closed-shell heavy element metal atoms has been achieved.

Previous calculations of low-temperature cross sections for collisions between spin-polarized metastable hydrogen atoms are improved to include nonadiabatic radial and angular coupling at large interatomic separations. The electrostatic dipole-quadrupole interaction produces nonadiabatic radial coupling between $\left(2s,2p\right)$ and $\left(2p,2p\right)$ states, while the Coriolis interaction produces nonadiabatic angular coupling. Both of these long-range contributions are handled in a space-fixed atomic gauge that is particularly convenient for a spin-polarized system. The improved theoretical results are compared with an existing experiment.

We observe velocity-selective two-photon resonances in a cold atom cloud in the presence of a magnetic field. We use these resonances to demonstrate a simple magnetometer with sub-mG resolution. The technique is particularly useful for zeroing the magnetic field and does not require any additional laser frequencies than are already used for standard magneto-optical traps. We verify the effects using Faraday rotation spectroscopy.

We calculate the low-energy elementary excitations of a Bose-Einstein condensate in an effective magnetic field. The field is created by the interplay between light beams carrying orbital angular momentum and the trapped atoms [G. Juzeliūnas et al., Phys. Rev. A 71, 053614 (2005)]. We examine the role of the homogeneous magnetic field, familiar from studies of rotating condensates, and also investigate spectra for vector potentials with a more general radial dependence. We discuss the instabilities which arise and how these may be manifested.

Ordinary intelligent states (OISs) hold equality in the Heisenberg uncertainty relation involving two noncommuting observables $\{A,B\}$, whereas generalized intelligent states (GISs) do so in the more generalized uncertainty relation, the Schrödinger-Robertson inequality. In general, OISs form a subset of GISs. However, if there exists a unitary evolution $U$ that transforms the operators $\{A,B\}$ to a new pair of operators in a rotation form, it is shown that an arbitrary GIS can be generated by applying the rotation operator $U$ to a certain OIS. In this sense, the set of OISs is unitarily equivalent to the set of GISs. It is the case, for example, with the su(2) and the su(1,1) algebras which have been extensively studied, particularly in quantum optics. When these algebras are represented by two bosonic operators (nondegenerate case), or by a single bosonic operator (degenerate case), the rotation, or pseudorotation, operator $U$ corresponds to phase shift, beam splitting, or parametric amplification, depending on two observables $\{A,B\}$.