By exploiting a symmetric scheme for coupling $N$ spin-$1∕2$ constituents (the physical qubits) to states with total angular momentum $N∕2-1$, we construct rotationally invariant logical qudits of dimension $d=N-1$. One can encode all qudit states, and realize all qudit measurements, by this construction. The rotational invariance of all relevant objects enables one to transmit quantum information without having aligned reference frames between the parties that exchange the qudits. We illustrate the method by explicit constructions of reference-frame-free qubits and qutrits and, for the qubit case, comment on possible experimental implementations.

We report on calculated outer-shell photodetachment cross sections from the metastable $\left[\text{core}\right]nsn{p}^2{}^{4}P^e$ states in ${\mathrm{Mg}}^{-}$ $(n=3)$ and ${\mathrm{Ca}}^{-}$ $(n=4)$ negative ions in the photon energy range $\omega =0–10\mathrm{eV}$. Double-ionization thresholds for $\mathrm{Mg}\mathrm{II}$ and $\mathrm{Ca}\mathrm{II}$ as well as doubly excited thresholds of the residual atoms $\mathrm{Mg}\mathrm{I}$ and $\mathrm{Ca}\mathrm{I}$ are located within the photon energy range considered and thus doubly and triply excited states of both ${\mathrm{Mg}}^{-}$ and ${\mathrm{Ca}}^{-}$ are reached. We use a complex scaled configuration interaction (CSCI) method for the three active electrons supplemented with a sophisticated model potential as developed by Laughlin [Phys. Scr. 45, 238 (1992)] to account for core-valence interactions. The CI calculations are based on ${\mathrm{Mg}}^{+}$ and ${\mathrm{Ca}}^{+}$ one-electron orbitals expanded in terms of $B$-spline basis set. We compare our cross sections with the only calculation available up to a photon energy $0.25\mathrm{Ry}$ $(\omega \sim 3.4\mathrm{eV})$ [Zeng et al., Phys. Rev. A 62, 022713 (2000)] performed by using the $R$-matrix method, in which only one ${}^{4}P^o$ resonance for ${\mathrm{Mg}}^{-}$ and two (${}^{4}P^o$ and ${}^{4}D^o$) for ${\mathrm{Ca}}^{-}$ were predicted. In this work, by analyzing both the cross sections and the locations of the $\mathcal{S}$-matrix poles in the complex plane, we are able to predict six ${}^{4}P^o$, four ${}^{4}D^o$, and four ${}^{4}S^o$ resonant states for ${\mathrm{Mg}}^{-}$, and three ${}^{4}P^o$ and two ${}^{4}D^o$ resonant states in ${\mathrm{Ca}}^{-}$.

We investigate amplitude and phase control of the components of the spinor order parameter of a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. By modeling the interaction of the multilevel atomic system with a pair of Raman-detuned laser pulses, we show that it is possible to construct a pulse-sequence protocol for producing a desired state change within a single Zeeman manifold. We present several successful elementary tests of this protocol in both the $F=1$ and $F=2$ Zeeman manifolds of ${}^{87}\mathrm{Rb}$ using the $D_1$ transitions. We describe specific features of the interaction, which are important for multimode, spatially varying field configurations, including the role of state-dependent, light-induced potentials.

We use supercomputer simulations to show that interatomic interactions can strongly affect the phase evolution of Bose-Einstein condensates that are diffracted from atom chips, thereby explaining recent experiments. Interactions broaden and depopulate noncentral diffraction orders and so, counterintuitively, they actually reduce the spatial width of the diffracted cloud. This means that the experiments cannot be fully described by noninteracting theories and, consequently, interferometers that use many interacting atoms to enhance sensitivity require complex calibration. We identify device geometries required to approximate noninteracting behavior.

The problem with the construction of the Gross-Pitaevskii (GP) equation and related wave functions in a medium is associated with the necessity to begin with a description of the configuration space and proceed to a description of the physical space. We show that the balance equations of the number of particles and momentum immediately follow from the multiparticle Schrödinger equation. From the obtained set of balance equations, the equation for the wave function in the medium coincides in form with the GP equation, where we can restrict ourselves only by the first-order terms of the interaction radius of the stress tensor of bosons, for dilute gases. As a generalization of the GP equation, we made allowance for the contribution of the third-order terms of the interaction radius to the stress tensor of bosons. For a system of particles that comprises an ultracold mixture of bosons and fermions, a two-kind quantum hydrodynamics is constructed for the third-order terms of the interaction radius. The spectrum of eigenmodes involves additional information on the interparticle interaction as a correction to the Bogoliubov spectrum.

We experimentally demonstrate that an atom-optics kicked rotor can remove the interference signal due to chosen interferometer paths in a four-pulse de Broglie wave atom interferometer. The interferometer output is dominated by two degenerate spatial loops: the nonreciprocal “trapezoid” loop and the reciprocal “figure-8” loop. By applying the kicked rotor sequence at a particular time we suppressed the contribution of the “trapezoid” loop to the interferometer signal while preserving the contribution due to the “figure-8” loop. When the degeneracy is present, the interferometer is sensitive to both rotation and linear acceleration. When the degeneracy is lifted the interferometer is insensitive to linear acceleration, but still sensitive to rotation. The suppression of nonreciprocal loops in an atom interferometer is valuable for rotation sensing.

We have measured the hyperfine energy level structure of the $X_1$ and $A$ states of ${}^{207}\mathrm{Pb}{}^{19}\mathrm{F}$ and found it to be in disagreement with previous predictions. Specifically, we find our data are reproduced by the hyperfine parameters $A_{\perp ,X_1}=7200\pm 150\mathrm{MHz}$, $A_{\parallel ,X_1}=10300\pm 800\mathrm{MHz}$, $A_{\perp ,A}=1200\pm 300\mathrm{MHz}$, and $A_{\parallel ,A}=3000\pm 2500\mathrm{MHz}$. The hyperfine structure may also be reproduced with $A_{\perp ,X_1}=-7200\pm 150\mathrm{MHz}$ and $A_{\perp ,A}=-1200\pm 300\mathrm{MHz}$. These negative hyperfine constants would, however, require a reinterpretation of the parity assignments of both the $X_1$ and $A$ states of the PbF molecule.

We propose a scenario used for controlling molecular orientation with an infrared laser pulse and a delayed half-cycle pulse, with LiH molecules as an example. The infrared laser pulse excites the molecules in a thermally initial state to a specific rovibrational state, and the half-cycle pulse orients the molecules by rotational excitation. Numerical calculation shows that an efficient field-free time-dependent orientation can be realized even at room temperatures. The feasibility has been analyzed for LiH molecules under present experimental conditions.

Within the framework of quantum memory channels we introduce the notion of repeatability of quantum channels. In particular, a quantum channel is called repeatable if there exists a memory device implementing the same channel on each individual input. We show that random unitary channels can be implemented in a repeatable fashion, whereas the nonunital channels cannot.

We consider the simulation of interacting high-dimensional systems using pairwise interacting qubits. The main tool in this context is the generation of effective many-body interactions, and we examine a number of different protocols for obtaining them. These methods include the usage of higher-order processes (commutator method), unitary conjugation or graph state encoding, as well as teleportation-based approaches. We illustrate and compare these methods in detail and analyze the time cost for simulation. In the second part of the paper, we investigate the influence of noise on the simulation process. We concentrate on errors in the interaction Hamiltonians and consider two generic noise models: (i) timing errors in pairwise interactions and (ii) noisy pairwise interactions described by Master equations of Lindblad form. We analyze and compare the effect of noise for the different simulation methods and propose a way to significantly reduce the influence of noise by making use of entanglement purification together with a teleportation-based protocol.

Measurements play an important role in quantum computing (QC), either by providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with one-qubit gates, are universal for quantum computing. Here we generalize parity gates by using a higher-dimensional (qudit) ancilla. This enables us to go beyond the stabilizer or graph state formalism and prepare other types of multiparticle entangled states. The generalized parity module introduced here can prepare in one shot, heralded by the outcome of the ancilla, a large class of entangled states, including Greenberger-Home-Zeilinger states ${\mathrm{GHZ}}_n$, ${\mathrm{W}}_n$, Dicke states ${\mathcal{D}}_{n,k}$, and, more generally, certain sums of Dicke states, like $G_n$ states used in secret sharing. For ${\mathrm{W}}_n$ states it provides an exponential gain compared to linear-optics-based methods.

We have performed very accurate quantum-mechanical calculations for the two lowest $S$ states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading ${\alpha }^2$ relativistic correction ($\alpha$ is the fine-structure constant) and the ${\alpha }^3$ QED correction. We also estimated the ${\alpha }^4$ QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions.

Electron-impact ionization cross sections are calculated for the ground and metastable states of ${\mathrm{C}}^{+}$. Comparisons between perturbative distorted-wave and nonperturbative time-dependent close-coupling calculations find reductions in the peak direct ionization cross sections due to electron coupling effects of approximately 5% for ground state ${\mathrm{C}}^{+}$ and approximately 15% for metastable state ${\mathrm{C}}^{+}$. Fairly small excitation-autoionization contributions are found for ground state ${\mathrm{C}}^{+}$, while larger excitation-autoionization contributions are found for metastable state ${\mathrm{C}}^{+}$. Comparisons between perturbative distorted-wave and nonperturbative $R$-matrix with pseudostates calculations find reductions in the peak total ionization cross sections due to electron coupling effects of approximately 15–20 % for ground state ${\mathrm{C}}^{+}$ and approximately 25–35 % for metastable state ${\mathrm{C}}^{+}$. Finally, comparisons between theory and experiment find that present and previous ${\mathrm{C}}^{+}$ crossed-beam measurements are in excellent agreement with ground state nonperturbative $R$-matrix with pseudostates calculations for total ionization cross sections. Combined with previous non-perturbative calculations for C, ${\mathrm{C}}^{2+}$, and ${\mathrm{C}}^{3+}$, accurate ionization cross sections and rate coefficients are now available for the ground and metastable states of all carbon ion stages.

We have calculated long-range molecular potentials of the $0_g^{+}$, $0_u^{-}$, and $1_u$ symmetries between highly excited rubidium atoms. Strong $np+np$ potentials characterized by these symmetries are important in describing interaction-induced phenomena in the excitation spectra of high $np$ Rydberg states. Long-range molecular resonances are one such phenomenon and they were first reported in S. M. Farooqi et al., Phys. Rev. Lett. 91, 183002 (2003). One class of these resonances occurs at energies corresponding to excited atom pairs $(n-1)d+ns$. Such resonances are attributed to $\mathcal{l}$-mixing due to Rydberg-Rydberg interactions so that otherwise forbidden molecular transitions become allowed. We calculate molecular potentials in Hund’s case (c), use them to find the resonance line shape, and compare to experimental results.

We present a theory of x-ray diffraction from an ensemble of symmetric-top molecules aligned by a short intense optical laser pulse at finite rotational temperature. Employing quantum electrodynamics, we describe the x-ray–molecule interaction as an electronically elastic one-photon scattering process. We treat the short x-ray pulse as a multimode radiation field and examine the effect of its coherence properties. In the practically important case that the x-ray pulse is quasimonochromatic and its coherence time is much shorter than the time scale of molecular rotational dynamics in the laser field, there is a simple connection between the rotational wave-packet dynamics and the diffraction pattern obtained. Our theory thus opens up a new perspective for quantum molecular imaging using x-ray radiation. An illustrative application to ${\mathrm{Br}}_2$ is presented.

By generalizing the definition of fidelity for the nonlinear system, we investigate the dynamics and adiabaticity of the population transfer for atom-molecule three-level $\Lambda$ system on a stimulated Raman adiabatic passage (STIRAP). We find that the adiabatic fidelity for the coherent population trapping state or dark state, as the function of the adiabatic parameter, approaches to unit in a power law. The power exponent, however, is much less than the prediction of the linear adiabatic theorem. We further discuss how to achieve higher adiabatic fidelity for the dark state through optimizing the external parameters of the STIRAP.

We investigate the static and dynamic properties of bosonic lattice systems in which condensed and Mott insulating phases coexist due to the presence of a spatially varying potential. We formulate a description of these inhomogeneous systems and calculate the bulk energy at and near equilibrium. We derive the explicit form of the Josephson coupling between disjoint superfluid regions separated by Mott insulating regions. We obtain detailed estimates for the case of alternating superfluid and Mott insulating spherical shells in a radially symmetric parabolically confined cold atom system.

We present an exact many-body theory of ultracold fermionic gases for the Bose-Einstein condensation (BEC) regime of the BEC-BCS crossover. This is a purely fermionic approach which treats explicitly and systematically the dimers formed in the BEC regime as made of two fermions. We consider specifically the zero temperature case and calculate the first terms of the expansion of the chemical potential in powers of the density $n$. We derive first the mean-field contribution, which has the expected standard expression when it is written in terms of the dimer-dimer scattering length $a_M$. We go next in the expansion to the Lee-Huang-Yang order, proportional to $n^{3∕2}$. We find the far less obvious result that it retains also the same expression in terms of $a_M$ as for elementary bosons. The composite nature of the dimers appears only in the next term proportional to $n^2$.

We propose a microscopic approach describing the interaction of an ideal gas of hydrogenlike atoms with a weak electromagnetic field. This approach is based on the Green-function formalism and an approximate formulation of the method of second quantization for quantum many-particle systems in the presence of bound states of particles. The dependencies of the propagation velocity and damping rate of electromagnetic pulses on the microscopic characteristics of the system are studied for a gas of hydrogenlike atoms. For a Bose-Einstein condensate of alkali-metal atoms we find the conditions when the electromagnetic waves of both the optical and microwave regions are slowed. In the framework of the proposed approach, the influence of an external homogeneous and static magnetic field on the slowing phenomenon is studied.