We experimentally demonstrate a programmable single-qubit quantum gate. This device applies a unitary phase shift operation to a data qubit with the value of the phase shift being fully determined by the state of a program qubit. Our linear optical implementation is based on the encoding of qubits into polarization states of single photons, two-photon interference on a polarizing beam splitter, and measurement on the output program qubit. We fully characterize the programmable gate by quantum process tomography. The achieved average quantum process fidelity exceeding 97% illustrates very good performance of the gate for all values of the encoded phase shift. We also show that by using a different set of program states the device can operate as a programmable partial polarization filter.

The entanglement properties of a class of topological stabilizer states, the so-called topological color codes defined on a two-dimensional lattice or 2-colex, are calculated. The topological entropy is used to measure the entanglement of different bipartitions of the 2-colex. The dependency of the ground-state degeneracy on the genus of the surface shows that the color code can support a topological order, and the contribution of the color in its structure makes it interesting to compare with Kitaev’s toric code. While a qubit is maximally entangled with the rest of the system, two qubits are no longer entangled showing that the color code is genuinely multipartite entangled. For a convex region, it is found that entanglement entropy depends only on the degrees of freedom living on the boundary of two subsystems. The boundary scaling of entropy is supplemented with a topological subleading term, which for a color code defined on a compact surface, is twice over the toric code. From the entanglement entropy we construct a set of bipartitions in which the diverging term arising from the boundary term is washed out, and the remaining nonvanishing term will have a topological nature. Besides the color code on the compact surface, we also analyze the entanglement properties of a version of color code with a border, i.e., triangular color code.

We show an efficient purification protocol in solid-state qubits by replacing the usual bilateral controlled-NOT gate by the bilateral $\mathrm{iSWAP}$ gate. We also show that this replacement can be applied to breeding and hashing protocols, which are useful for quantum state purification. These replacements reduce the number of fragile and cumbersome two-qubit operations, making more feasible quantum-information processing with solid-state qubits. As examples, we also present quantitative analyses for the required time to perform state purification using either superconducting or semiconducting qubits.

In this paper, we present results illustrating the power and flexibility of one-bit teleportations in quantum bus computation. We first show a scheme to perform a universal set of gates on continuous variable modes, which we call a quantum bus or qubus, using controlled phase-space rotations, homodyne detection, ancilla qubits, and single-qubit measurement. Within our comparison criteria, the resource usage for this scheme is lower than any previous scheme to date. We then illustrate how one-bit teleportations into a qubus can be used to encode qubit states into a quantum repetition code, which in turn can be used as an efficient method for producing Greenberger-Horne-Zeilinger states that can be used to create large cluster states. Each of these schemes can be modified so that teleportation measurements are post-selected to yield outputs with higher fidelity without changing the physical parameters of the system.

We present ideas for controlling quantum dynamics in a dissipative environment using short, intense laser pulses. The proposed algorithm is an extension of the well-established time-local pump-dump control scheme to the density matrix formalism, using time-dependent targets. This provides a natural framework for guiding the reaction along a desired path. As a test case, the selective photoexcitation of charge transfer and semi-charge-transfer states of the LiCN molecule in a strong dissipative environment is studied.

Radio-frequency (rf) fields in the MHz range are used to induce resonant energy transfer between cold Rydberg atoms in spatially separated volumes. After laser preparation of the Rydberg atoms, dipole-dipole coupling excites the $49s$ atoms in one cylinder to the $49p$ state while the $41d$ atoms in the second cylinder are transferred down to the $42p$ state. The energy exchanged between the atoms in this process is $33\mathrm{GHz}$. An external rf field brings this energy transfer into resonance. The strength of the interaction has been investigated as a function of amplitude $(0–1\mathrm{V}∕\mathrm{cm})$ and frequency $(1–30\mathrm{MHz})$ of the rf field and as a function of a static-field offset. Multiphoton transitions up to fifth order as well as selection rules prohibiting the process at certain fields have been observed. The width of the resonances has been reduced compared to earlier results by switching off external magnetic fields of the magneto-optical trap, making sub-MHz spectroscopy possible. All features are well reproduced by theoretical calculations taking the strong ac Stark shift due to the rf field into account.

Surface-electrode (SE) rf traps are a promising approach to manufacturing complex ion-trap networks suitable for large-scale quantum information processing. In this paper we present analytical methods for modeling SE traps in the gapless plane approximation, and apply these methods to two particular classes of SE traps. For the SE ring trap we derive analytical expressions for the trap geometry and strength, and also calculate the depth in the absence of control fields. For translationally symmetric multipole configurations (analogs of the linear Paul trap), we derive analytical expressions for electrode geometry and strength. Further, we provide arbitrarily good approximations of the trap depth in the absence of static fields and identify the requirements for obtaining maximal depth. Lastly, we show that the depth of SE multipoles can be greatly influenced by control fields.

We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D tubes) with spin imbalance, where strong intratube quantum fluctuations invalidate mean-field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against intertube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.

Previous work has shown that in a two-dimensional periodic medium under focusing or defocusing cubic nonlinearities, gap solitons in the form of low-amplitude and slowly modulated single-Bloch-wave packets can bifurcate out from the edges of Bloch bands. In this paper, linear stability properties of these gap solitons near band edges are determined both analytically and numerically. Through asymptotic analysis, it is shown that these gap solitons are linearly unstable if the slope of their power curve at the band edge has the opposite sign of nonlinearity (here focusing nonlinearity is said to have a positive sign, and defocusing nonlinearity to have a negative sign). An equivalent condition for linear instability is that the power of the gap solitons near the band edge is lower than the limit power value on the band edge. Through numerical computations of the power curves, it is found that this condition is always satisfied, thus two-dimensional gap solitons near band edges are linearly unstable. The analytical formula for the unstable eigenvalue of gap solitons near band edges is also asymptotically derived. It is shown that this unstable eigenvalue is proportional to the cubic power of the soliton’s amplitude, and it induces width instabilities of gap solitons. A comparison between this analytical eigenvalue formula and numerically computed eigenvalues shows excellent agreement.

A two-mode boson model, widely used for the physics of fast rotating nuclei and Bose-Einstein condensates, is studied in the context of entanglement control. We derive an analytical expression for the entanglement between the fields in this model as a function of time. We found that depending on the interaction strengths between boson modes and the nature of the initial boson states the dynamical evolution of the entanglement and the squeezing can occur independently.

We present a detailed analysis of the production efficiency of weakly bound heteronuclear ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ Feshbach molecules using radio-frequency association in a harmonic trap. The efficiency was measured in a wide range of temperatures, binding energies, and radio frequencies. A comprehensive analytical model is presented, explaining the observed asymmetric spectra and achieving good quantitative agreement with the measured production rates. This model provides a deep understanding of the molecule association process and paves the way for future experiments which rely on Feshbach molecules, e.g., for the production of deeply bound molecules.

We consider phase coherence collapse and revival in deep optical lattices, and calculate within the Bose-Hubbard model the revival amplitude damping incurred by a finite tunneling coupling of the lattice wells (after sweeping from the superfluid to the Mott phase). Deriving scaling laws for the corresponding decay of first-order coherence revival in terms of filling factor, final lattice depth, and number of tunneling coupling partners, we estimate whether revival damping related to tunneling between sites can be or even has already been observed in experiment.

A new criterion to detect the entanglement present in a hyperentangled state, based on the evaluation of an entanglement witness, is presented. We show how some witnesses recently introduced for graph states, measured by only two local settings, can be used in this case. We also define a new witness $W_3$ that improves the resistance to noise by increasing the number of local measurements.

We present a general procedure for constructing lattices of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions such that the ground state encodes a cluster state. We give specific details for lattices in one, two, and three dimensions, investigating both periodic and fixed boundary conditions, as well as present a proof for the applicability of this procedure to any graph. We determine the energy gap of these systems, which is shown to be independent of the size of the lattice but dependent on the type of lattice (in particular, the coordination number), and investigate the scaling of this gap in terms of the coupling constants of the Hamiltonian. We provide a comparative analysis of the different lattice types with respect to their usefulness for measurement-based quantum computation.

We report quantum secret sharing experiment in telecommunication fiber in five-party implementation. The quantum secret sharing experiment has been based on a single qubit protocol, which has opened the door to practical secret sharing implementation over fiber channels and in free space. The previous quantum secret sharing proposals were based on multiparticle entangled states, difficult in the practical implementation and not scalable. The secret sharing protocol has been implemented in an interferometric fiber optics setup with phase encoding and demonstrated for three, four, and five parties. The experimental setup measurements have shown feasibility and scalability of secure multiparty quantum communication over commercial telecom fiber networks.

Accurate ab initio calculations of the energy levels of the superheavy element $Z=112$ are presented. Relativistic Hartree-Fock and configuration interaction methods are combined with the many-body perturbation theory to construct the many-electron wave function for valence electrons and to include core-valence correlations. Two different approaches in which the element is treated as a system with two or twelve external electrons above closed shells are used and compared. Similar calculations for mercury are used to control the accuracy of the calculations. The results are compared with other calculations.

Two particles incident upon an external potential can combine to form one particle with two components, either by transmission past the potential or by reflection. An example is two atoms combining to form a molecule. The probability of forming a molecule depends sensitively on the strength of the external potential. Delta barrier potentials are shown to be good approximations to narrow Gaussian barriers. Multiple barriers can increase the probability of formation of a molecule up to about 0.5 for reflection and 0.25 for transmission.

Results are presented for the absolute bremsstrahlung yields at a backward angle of 135° from $53\mathrm{keV}$ electrons on gold targets of thickness ranging from $66\text{to}28976\mu \mathrm{g}∕{\mathrm{cm}}^2$. The target thicknesses range from thin enough for single collision conditions to apply to thick enough for the yield to be dominated by multiple interactions. The results for all thicknesses are found to be in very good agreement with the predictions of PENELOPE, a Monte Carlo program which is based on ordinary bremsstrahlung and does not include any contribution from polarization bremsstrahlung. Absolute doubly differential cross sections are computed for the thinnest targets. The results are compared with two theoretical free atom cross section models, one for ordinary bremsstrahlung only and the second, the stripping approximation, for total bremsstrahlung including a contribution from polarization bremsstrahlung. The results agree with the predictions of ordinary bremsstrahlung for radiated photon energies from $5\text{to}53\mathrm{keV}$ and do not agree with the predictions of the stripping approximation. The conclusion, in contrast with recent free gas atom results, is that the absolute yields from solid films are well described by ordinary bremsstrahlung and do not require any additional polarizational bremsstrahlung contribution.

Absolute integral cross sections have been measured for associative ionization reactions involving the ${\mathrm{C}}^{-}$ and ${\mathrm{C}}^{+}$, ${\mathrm{N}}^{+}$, and ${\mathrm{O}}^{+}$ reactants. These measurements, obtained using a merged-beam setup in the keV range, provide us with useful experimental information on the efficiency and mechanisms of molecular ion formation from ionic reactants. The relative magnitudes of the different cross sections are rationalized by considering the spin multiplicities of initial and final states, and the exothermicities of the detachment and transfer ionization channels. The very different production efficiencies of $\mathrm{C}{\mathrm{O}}^{+}$ ions via the ${\mathrm{O}}^{-}+{\mathrm{C}}^{+}$ and ${\mathrm{C}}^{-}+{\mathrm{O}}^{+}$ channels are explained by statistical and energetic considerations. The potential energy curves of CO and $\mathrm{C}{\mathrm{O}}^{+}$ have been calculated by quantum ab initio methods in order to characterize the reactive pathways leading to autoionization. Thermal rate coefficients are derived to serve the plasma physics community.

A method to generate a broadband isolated attosecond pulse with stable pulse duration and high signal-to-noise ratio is proposed. By adopting a few-cycle driving pulse combined with its second-harmonic field of which the polarization angle is $\pi ∕3$ with respect to the driving pulse, the short path is well selected and a smooth supercontinuum with the bandwidth of about $50\mathrm{eV}$ is observed, which leads to 100-as single attosecond pulse generation with high signal-to-noise ratio. More surprisingly, the intensity variation of the second-harmonic field can hardly affect the location and the bandwidth of the generated supercontinuum but only slightly reduce its phase-locking degree. For the intensity of the second-harmonic field higher than ${10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$, a pure isolated attosecond pulse with duration of about 100 as can be generated by directly filtering out a supercontinuum from $85–125\mathrm{eV}$, which facilitates the experimental implement of the isolated attosecond pulse generation.