In optically controlled quantum computers it may be favorable to address different qubits using light with different frequencies, since the optical diffraction does not then limit the distance between qubits. Using qubits that are close to each other enables qubit-qubit interactions and gate operations that are strong and fast in comparison to qubit-environment interactions and decoherence rates. However, as qubits are addressed in frequency space, great care has to be taken when designing the laser pulses, so that they perform the desired operation on one qubit, without affecting other qubits. Complex hyperbolic secant pulses have theoretically been shown to be excellent for such frequency-addressed quantum computing [I. Roos and K. Molmer, Phys. Rev. A 69, 022321 (2004)]—e.g., for use in quantum computers based on optical interactions in rare-earth-metal-ion-doped crystals. The optical transition lines of the rare-earth-metal-ions are inhomogeneously broadened and therefore the frequency of the excitation pulses can be used to selectively address qubit ions that are spatially separated by a distance much less than a wavelength. Here, frequency-selective transfer of qubit ions between qubit states using complex hyperbolic secant pulses is experimentally demonstrated. Transfer efficiencies better than 90% were obtained. Using the complex hyperbolic secant pulses it was also possible to create two groups of ions, absorbing at specific frequencies, where 85% of the ions at one of the frequencies was shifted out of resonance with the field when ions in the other frequency group were excited. This procedure of selecting interacting ions, called qubit distillation, was carried out in preparation for two-qubit gate operations in the rare-earth-metal-ion-doped crystals. The techniques for frequency-selective state-to-state transfer developed here may be also useful also for other quantum optics and quantum information experiments in these long-coherence-time solid-state systems.

The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy $S\left[\varrho \right]=-\mathrm{Tr}\left(\varrho \ln \varrho \right)$ of a density matrix ${\varrho }_{123}$ on the product of three Hilbert spaces satisfies $S\left[{\varrho }_{123}\right]-S\left[{\varrho }_{12}\right]⩽S\left[{\varrho }_{23}\right]-S\left[{\varrho }_2\right]$. We strengthen this to $S\left[{\varrho }_{123}\right]-S\left[{\varrho }_{12}\right]⩽{\sum }_{\alpha }{n}^{\alpha }(S\left[{\varrho }_{23}^{\alpha }\right]-S\left[{\varrho }_2^{\alpha }\right])$, where the $n^{\alpha }$ are weights and the ${\varrho }_{23}^{\alpha }$ are partitions of ${\varrho }_{23}$. Correspondingly, there is a strengthening of the theorem that the map $A\mapsto \mathrm{Tr}\exp [L+\ln A]$ is concave. As applications we prove some monotonicity and convexity properties of the Wehrl coherent state entropy and entropy inequalities for quantum gases.

The structure of the state spaces of bipartite $N\otimes N$ quantum systems which are invariant under product representations of the group SO(3) of three-dimensional proper rotations is analyzed. The subsystems represent particles of arbitrary spin $j$ which transform according to an irreducible representation of the rotation group. A positive map $\vartheta$ is introduced which describes the time reversal symmetry of the local states and which is unitarily equivalent to the transposition of matrices. It is shown that the partial time reversal transformation ${\vartheta }_2=I\otimes \vartheta$ acting on the composite system can be expressed in terms of the invariant $6\text{−}j$ symbols introduced by Wigner into the quantum theory of angular momentum. This fact enables a complete geometrical construction of the manifold of states with positive partial transposition and of the sets of separable and entangled states of $4\otimes 4$ systems. The separable states are shown to form a three-dimensional prism and a three-dimensional manifold of bound entangled states is identified. A positive map is obtained which yields, together with the time reversal, a necessary and sufficient condition for the separability of states of $4\otimes 4$ systems. The relations to the reduction criterion and to the recently proposed cross norm criterion for separability are discussed.

Measuring the amplitude and absolute (i.e., temporal and initial) phase of a monochromatic microwave field at a specific point of space and time has many potential applications, including precise qubit rotations and wavelength quantum teleportation. Here we show how such a measurement can indeed be made using resonant atomic probes via detection of incoherent fluorescence induced by a laser beam. This measurement is possible due to self-interference effects between the positive- and negative-frequency components of the field. In effect, the small cluster of atoms here act as a highly localized pickup coil, and the fluorescence channel acts as a transmission line.

We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean-field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean-field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three-dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean-field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents is easily within experimental reach.

The interaction of single cw laser (coupling) field with a four-level $\Lambda$ system containing two closely spaced upper levels ($a$ and $b$) is studied as a means to attain quantum control. By adjusting the coupling field Rabi frequency and detuning, it is possible to create target states of a prescribed admixture of states $a$ and $b$ within a dressed state representation. An electromagnetically induced transparency of an additional probe beam is also studied. The four-level $\Lambda$ system gives rise to generally two dark resonances for a given coupling field detuning. When the resonances are degenerate EIT is enhanced.

It is theoretically shown that the phenomenon of coherent destruction of tunneling in bistable quantum systems induced by an external driving field can be realized in a periodically curved optical waveguide coupler, the periodic bending of the coupler simulating the effect of the external field in the quantum system.

We study the effects of dynamical imperfections in quantum computers. By considering an explicit example, we identify different regimes ranging from the low-frequency case, where the imperfections can be considered as static but with renormalized parameters, to the high-frequency fluctuations, where the effects of imperfections are completely wiped out. We generalize our results by proving a theorem on the dynamical evolution of a system in the presence of dynamical perturbations.

The characteristic oscillations of the density-density correlation function and the resulting structure factor are studied for a hard-core Bose gas in a one-dimensional lattice. Their wavelength diverges as the system undergoes a continuous transition from an incommensurate to a Mott insulating phase. The transition is associated with a unit static structure factor and a vanishing sound velocity. The qualitative picture is unchanged when a weak confining potential is applied to the system.

We measure the lifetime of the $8s$ level of ${}^{210}\mathrm{Fr}$ atoms on a magneto-optically trapped sample with time-correlated single-photon counting. The $7P_{1∕2}$ state serves as the resonant intermediate level for two-step excitation of the $8s$ level completed with a $1.3\text{−}\mu \mathrm{m}$ laser. Analysis of the fluorescence decay through the $7P_{3∕2}$ level gives $53.30\pm 0.44\mathrm{ns}$ for the $8s$ level lifetime.

We derive a formalism for the computation of resonance-scattering polarization of hydrogen lines in the presence of simultaneous magnetic and electric fields, within a framework of the quantum theory of polarized line formation in the limit of complete frequency redistribution and of collisionless regime. Quantum interferences between fine-structure levels are included in this formalism. In the presence of a magnetic field, these interferences affect, together with the magnetic Hanle effect, the polarization of the atomic levels. In the presence of an electric field, interferences between distinct orbital configurations are also induced, further affecting the polarization of the hydrogen levels. In turn, the electric field is expected to affect the polarization of the atomic levels (electric Hanle effect), in a way analogous to the magnetic Hanle effect. We find that the simultaneous action of electric and magnetic fields give rise to complicated patterns of polarization and depolarization regimes, for varying geometries and field strengths.

Recently, it has been shown that the density per particle, or shape function, determines all the properties of molecules and, more generally, finite Coulomb systems (e.g., clusters). Here, we provide numerical evidence for this “existence” theorem, showing that atomic properties (specifically the kinetic energy and exchange energy) have simple approximate expressions in terms of the shape function. While the accuracy of our results is limited, this provides “proof-of-principle” evidence that shape-functional theory represents an alternative to density-functional theory for finite Coulomb systems.

Spectra of $L$ x rays emitted from Ho targets bombarded by 10 keV electrons and $6\mathrm{MeV}∕\mathrm{amu}$ C, Ne, Ar, Kr, and Xe ions were measured in high resolution using a curved crystal spectrometer. The spectra were analyzed in order to examine the systematic evolution of the $L$ x-ray satellite structure as a function of projectile atomic number. Scaling rules are established for the apparent average $M$-shell spectator vacancy fraction and apparent average double to single $L$-vacancy population ratio at the time of $L$ x-ray emission. The results are compared to those obtained for $K$-shell ionizing collisions and with predictions of the geometrical model.

We present a semianalytical treatment of both the elastic and inelastic collisional properties near a $p$-wave Feshbach resonance. Our model is based on a simple three-channel system that reproduces more elaborate coupled-channel calculations. We stress the main differences between $s$-wave and $p$-wave scattering. We show in particular that, for elastic and inelastic scattering close to a $p$-wave Feshbach resonance, resonant processes dominate over the low-energy behavior.

A mixture of spin-polarized light- and heavy-Fermionic atoms on a finite-size two-dimensional optical lattice is considered at various temperatures and values of the coupling between the two atomic species. In the case where the heavy atoms are immobile in comparison to the light atoms, this system can be seen as a correlated binary alloy related to the Falicov-Kimball model. The heavy atoms represent a scattering environment for the light atoms. The distributions of the binary alloy are discussed in terms of strong- and weak-coupling expansions. We further present numerical results for the intermediate interaction regime and for the density of states of the light particles. The numerical approach is based on a combination of a Monte Carlo simulation and an exact diagonalization method. We find that the scattering by the correlated heavy atoms can open a gap in the spectrum of the light atoms, either for strong interaction or small temperatures.

The center-of-mass dynamics of a vortex in the surface region of a Bose-Einstein condensate is investigated both analytically using a variational calculation and numerically by solving the time-dependent Gross-Pitaevskii equation. We find, in agreement with previous works, that away from the Thomas-Fermi surface, the vortex moves parallel to the surface of the condensate with a constant velocity. We obtain an expression for this velocity in terms of the distance of the vortex core from the Thomas-Fermi surface that fits accurately with the numerical results. We find also that, coupled to its motion parallel to the surface, the vortex oscillates along the direction normal to the surface around a minimum point of an effective potential.

Repulsive Bose-Einstein condensates immersed into a double-well trap potential are studied within the framework of the recently introduced mean-field approach which allows for bosons to reside in several different orthonormal orbitals. In the case of a one-orbital mean-field theory (Gross-Pitaevskii) the ground state of the system reveals a bifurcation scenario at some critical values of the interparticle interaction and/or the number of particles. At about the same values of the parameters the two-orbital mean field predicts that the system becomes twofold fragmented. By applying the three-orbital mean field we verify numerically that for the double-well external potential studied here the overall best mean field is achieved with two orbitals. The variational principle minimizes the energy at a vanishing population of the third orbital. To discuss the energies needed to remove a boson from and the energies gained by adding a boson to the condensate, we introduce boson ionization potentials and boson affinities and relate them to the chemical potentials. The impact of the finite number of bosons in the condensate on these quantities is analyzed. We recall that within the framework of the multiorbital mean-field theory each fragment is characterized by its own chemical potential. Finally, the stability of fragmented states is discussed in terms of the boson transfer energy which is the energy needed to transfer a boson from one fragment to another.

We study the dynamical Casimir effect for a scalar field satisfying the (generalized) Neumann boundary condition on a deforming mirror. The angular distribution and the spectrum of radiation is calculated to second order in the deformation amplitude. For a harmonic traveling wave on the surface, we find two cusps in the radiation spectrum. There are several regimes in which the radiation is restricted to particular directions. The position of the cusps and the radiation window at a certain frequency can be tuned by the mechanical deformation. The number of emitted photons is much larger than for the Dirichlet boundary condition.

We introduce a probability distribution for polarization of three-dimensional quantum light fields as a marginal of the quadrature $Q$ function for a three-mode field by removing the variables irrelevant for polarization (total intensity and global phase). The probability distribution turns out to be determined by projection on SU(3) coherent states. We introduce a degree of polarization as the distance between the polarization distribution and the uniform distribution associated with completely unpolarized light. We study the relation between two- and three-dimensional polarization by considering field states with a component in the vacuum state. We apply this formalism to some relevant field states.

We perform ab initio QED calculations of energy levels for the $n=1$ and $n=2$ states of He-like ions with the nuclear charge in the range $Z=12\text{–}100$. The complete set of two-electron QED corrections is evaluated to all orders in the parameter $\alpha Z$. Uncalculated contributions to energy levels come through orders ${\alpha }^3{\left(\alpha Z\right)}^2$, ${\alpha }^2{\left(\alpha Z\right)}^7$, and higher. A significant improvement in accuracy of theoretical predictions is achieved, especially in the high-$Z$ region.