We introduce a family of states, the fermionic projected entangled pair states (fPEPS), which describe fermionic systems on lattices in arbitrary spatial dimensions. It constitutes the natural extension of another family of states, the PEPS, which efficiently approximate ground and thermal states of spin systems with short-range interactions. We give an explicit mapping between those families, which allows us to extend previous simulation methods to fermionic systems. We also show that fPEPS naturally arise as exact ground states of certain fermionic Hamiltonians. We give an example of such a Hamiltonian, exhibiting criticality while obeying an area law.

We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the dimension of the state space. The witnesses can be measured successively; if all of them give an inconclusive result, one exploits their tomographic completeness for a reconstruction of the quantum state and can then determine its entanglement properties by data processing. There are witnesses that are optimal for this purpose. The optimized witness-based measurement can provide exponential improvement with respect to witness efficiency in high-dimensional Hilbert spaces, at the price of a reduction in the tomographic efficiency. We describe a systematic construction and illustrate the matter with the example of two qubits. For the case of two polarization qubits of photons, we show how existing technology can be used to implement the optimized witnesses in a very efficient way. Owing to the details of the implementation, which actually measures the eigenstate basis of the witness rather than solely determining the expectation value of the witness, one does not need to measure more than six witnesses in this example of a 16-dimensional state space.

We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.

We present a joint experimental and theoretical study of selective population of dressed states (SPODS) in a three-level system. Control is exerted by shaped intense femtosecond laser pulses generated by a generalized spectral phase-step modulation function. We show that both control parameters (i.e., the phase-step amplitude and position) can be used to switch population among each three dressed states with high selectivity. The dynamics of the system, and hence the resulting photoelectron signal is studied theoretically by analyzing the time evolution of the adiabatic dressed-state energies and populations.

We study the spontaneous symmetry breaking (SSB) of a superfluid Bose-Fermi (BF) mixture in a double-well potential (DWP). The mixture is described by the Gross-Pitaevskii equation (GPE) for the bosons, coupled to an equation for the order parameter of the Fermi superfluid, which is derived from the respective density functional in the unitarity limit (a similar model applies to the BCS regime, too). Straightforward SSB in the degenerate Fermi gas loaded into a DWP is impossible, as it requires an attractive self-interaction, and the intrinsic nonlinearity in the Fermi gas is repulsive. Nonetheless, we demonstrate that the symmetry breaking is possible in the mixture with attraction between fermions and bosons, like ${}^{40}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$. Numerical results are represented by dependencies of asymmetry parameters for both components on particle numbers of the mixture, $N_{\mathrm{F}}$ and $N_{\mathrm{B}}$, and by phase diagrams in the $(N_{\mathrm{F}},N_{\mathrm{B}})$ plane, which displays regions of symmetric and asymmetric ground states. The dynamical picture of the SSB, induced by a gradual transformation of the single-well potential into the DWP, is reported too. An analytical approximation is proposed for the case when the GPE for the boson wave function may be treated by means of the Thomas-Fermi (TF) approximation. Under a special linear relationship between $N_{\mathrm{F}}$ and $N_{\mathrm{B}}$, the TF approximation allows us to reduce the model to a single equation for the fermionic function, which includes competing repulsive and attractive nonlinear terms. The latter one directly displays the mechanism of the generation of the effective attraction in the Fermi superfluid, mediated by the bosonic component of the mixture.

We report the realization of a Bose-Einstein condensate of metastable helium-$4$ atoms (${}^4\mathrm{He}$${}^{*}$) in an all-optical potential. Up to $10$${}^5$ spin-polarized ${}^4\mathrm{He}$${}^{*}$ atoms are condensed in an optical dipole trap formed from a single, focused, vertically propagating far-off-resonance laser beam. The vertical trap geometry is chosen to best match the resolution characteristics of a delay-line anode microchannel plate detector capable of registering single He${}^{*}$ atoms. We also confirm the instability of certain spin-state combinations of ${}^4\mathrm{He}$${}^{*}$ to two-body inelastic processes, which necessarily affects the scope of future experiments using optically trapped spin mixtures. In order to better quantify this constraint, we measure spin-state-resolved two-body inelastic loss rate coefficients in the optical trap.

Propagation of an asymmetric Gaussian beam in a cubic-quintic absorbing medium is analyzed and compared with that of a symmetric beam in both lossless and lossy media. A “collective variable approach” technique, based on trial functions, is used for solution of the general nonlinear Schrödinger equation. Using this variational approach, we investigate the self-focusing and breathing of an intense asymmetric Gaussian beam, taking into account both linear and nonlinear absorption. For a lossless medium, we define regions of oscillatory and diffractive beam propagation, for both symmetric and asymmetric beams. In particular, for an asymmetric beam, we find that there is no sharp boundary between the oscillatory self-focusing and oscillatory diffractive regimes of propagation. In the oscillatory region, we detect an interesting phenomenon—“beats” of the amplitude and perpendicular widths of the beam. For a lossy medium, significant differences between the amplitudes, widths, and phases of the symmetric and asymmetric beams have been predicted.

The noisy-storage model allows the implementation of secure two-party protocols under the sole assumption that no large-scale reliable quantum storage is available to the cheating party. No quantum storage is thereby required for the honest parties. Examples of such protocols include bit commitment, oblivious transfer, and secure identification. Here, we provide a guideline for the practical implementation of such protocols. In particular, we analyze security in a practical setting where the honest parties themselves are unable to perform perfect operations and need to deal with practical problems such as errors during transmission and detector inefficiencies. We provide explicit security parameters for two different experimental setups using weak coherent, and parametric down-conversion sources. In addition, we analyze a modification of the protocols based on decoy states.

The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at $2.2$ eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the $e^{+}$-Cd system. The $s$-wave binding energy is estimated to be $126\pm 42$ meV, with a scattering length of $A_{\mathrm{scat}}=(14.2\pm 2.1)$$a_0$, while the threshold annihilation parameter, $Z_{\mathrm{eff}}$, was $93.9\pm 26.5$. The $p$-wave phase shift exhibits a weak shape resonance that results in a peak $Z_{\mathrm{eff}}$ of $91\pm 17$ at a collision energy of about $490\pm 50$ meV.

We study properties of the strongly repulsive Bose gas on one-dimensional incommensurate optical lattices with a harmonic trap, which can be dealt with by use of an exact numerical method through Bose-Fermi mapping. We first exploit the phase transition of hard-core bosons in optical lattices from the superfluid to the Bose-glass phase as the strength of the incommensurate potential increases. Then we study the dynamical properties of the system after suddenly switching off the harmonic trap. We calculate the one-particle density matrices, the momentum distributions, and the natural orbitals and their occupations for both the static and dynamic systems. Our results indicate that the Bose-glass and superfluid phases display quite different properties and expansion dynamics.

A standing-wave control field applied to a three-level atomic medium in a planar hollow-core photonic crystal waveguide creates periodic variations of linear and nonlinear refractive indexes of the medium. This property can be used for efficient steering of light. In this work, we study, both analytically and numerically, the dynamics of probe optical beams in such structures. By properly designing the spatial dependence of the nonlinearity, it is possible to induce long-living Bloch oscillations of spatial gap solitons, thus providing desirable change in the direction of the beam propagation without inducing appreciable diffraction. Due to the significant enhancement of the nonlinearity, such self-focusing of the probe beam can be reached at extremely weak light intensities.

The resonance-enhanced surface second-harmonic generation (SHG) from a suspension of polystyrene microspheres was investigated as a function of particle size in a range of the order of the fundamental wavelength for two different second-harmonic-enhancing dyes—malachite green and pyridine 1. The two dyes gave the same strongly modulated pattern of the forward second-harmonic scattering efficiency. Direct comparison to the nonlinear Rayleigh-Gans-Debye (NLRGD) and nonlinear Wentzel-Kramers-Brillouin (NLWKB) model predictions showed that the NLWKB model reproduces the overall trend in the size dependence but fails with respect to the strong modulations. The standard NLRGD model was found to fail altogether in the present particle size range, which was well beyond the observed upper particle size for which the NLRGD and NLWKB models give comparable results. A generalization of the NLRGD model to allow for dispersion and to use the particle refractive indices instead of those of the surrounding medium extended its applicability range by almost an order of magnitude in particle size. There is a pronounced maximal SHG efficiency for particles with a radius that is close to the fundamental wavelength inside the particle. The optically soft particle approximation is inadequate to describe the SHG in this particle size range, as refraction and reflection of the waves at the particle surface have a decisive influence. Dispersion of the media plays a negligible role for particle sizes up to about twice the optimal one for SHG.

We used a split-mirror setup attached to a reaction microscope at the free-electron laser in Hamburg (FLASH) to perform an XUV-pump–XUV-probe experiment by tracing the ultrafast nuclear wave-packet motion in the ${\mathrm{D}}_2$${}^{+}$$(1s{\sigma }_g$) with $<$$10$ fs time resolution. Comparison with time-dependent calculations shows excellent agreement with the measured vibrational period of $22\pm 4$ fs in ${\mathrm{D}}_2$${}^{+}$, points to the importance of accurately knowing the internuclear distance-dependent ionization probability, and paves the way to control sequential and nonsequential two-photon double-ionization contributions.

Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field interaction $g(t)$. By means of a time-reversal argument, we prove the stability of Bloch oscillations of breathing solitons that would be quasistatically unstable. Floquet theory shows that these breathing solitons can be more stable against certain experimental perturbations than rigid solitons or even noninteracting wave packets.

We demonstrate how the term describing the interaction between a single two-level atom and two cavity field modes may attain a Rashba form. As an outcome, cavity QED provides a testbed for studies of phenomena reminiscent of the spin-orbit induced anomalous Hall effect. The effective magnetic field, deriving from the non-Abelian gauge potentials rendered by the Rashba coupling, induces a transverse force acting on the phase space distributions. Thereby, the phase space distributions build up a transverse motion manifesting itself in spiral trajectories, rather than circular ones obtained for a zero magnetic field as one would acquire for the corresponding Abelian gauge potentials. Utilizing realistic experimental parameters, the phenomenon is numerically verified, ascertain that it should be realizable with current techniques.

We will show that when a neutral particle with permanent electric dipole moment interacts with a specific field configuration when the local reference frames of the observers are Fermi-Walker transported, the Landau quantization analog to the He-McKellar-Wilkens setup arises in the nonrelativistic quantum dynamics of the neutral particle due the noninertial effects of the Fermi-Walker reference frame. We show that the noninertial effects do not break the infinity degeneracy of the energy levels, but in this case, the cyclotron frequency depends on the angular velocity.

We study the entanglement preservation of two qubits locally interacting with their reservoirs. We show that the existence of a bound state of the qubit and its reservoir and the non-Markovian effect are two essential ingredients and their interplay plays a crucial role in preserving the entanglement in the steady state. When the non-Markovian effect is neglected, the entanglement sudden death (ESD) is reproduced. On the other hand, when the non-Markovian is significantly strong but the bound state is absent, the phenomenon of the ESD and its revival is recovered. Our formulation presents a unified picture about the entanglement preservation and provides a clear clue on how to preserve the entanglement in quantum information processing.

We show that a many-body system of single-electron quantum dots, whose orbital states are dressed by a global magnetic field, can be described by an effective Hamiltonian with an anisotropic $\mathit{XZ}$ spin-spin interaction which is proportional to the Zeeman splitting. We show that these interaction potentials give rise to spin-dependent Hubbard models with tunable nearest neighbor two-body and three-body interactions. The two-body interactions can even be switched off via the external electric field, and hence the three-body interaction plays a dominant role. The derivation of these effective interaction potentials follows from a well-controlled and systematic expansion into many-body interaction terms. Models of this type have appeared in the recent discussion of exotic quantum phases, in particular in the context of topological quantum phases and quantum computing, and we show that quantum dots can be regarded as a realistic experimental route which provides the basic building blocks and techniques toward the study of these phenomena. The main application of this derived model is to develop topological quantum computation.

We propose an efficient approach for deterministically generating scalable cluster states with photons. This approach involves unitary transformations performed on atoms coupled to optical cavities. Its operation cost scales linearly with the number of qubits in the cluster state, and photon qubits are encoded such that single-qubit operations can be easily implemented by using linear optics. Robust optical one-way quantum computation can be performed since cluster states can be stored in atoms and then transferred to photons that can be easily operated and measured. Therefore, this proposal could help in performing robust large-scale optical one-way quantum computation.

A secret-sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret-sharing schemes have been shown to be induced by matroids. Furthermore, access structures of such schemes can be characterized by an excluded minor relation. No such relations are known for quantum secret-sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum-secret-sharing schemes. In addition to providing a new perspective on quantum-secret-sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum-secret-sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum-secret-sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure-state quantum-secret-sharing scheme with information rate $1$.