We propose to produce five-partite entanglement via cascaded four-wave mixing in a high-$Q$ microresonator that may become a key to future one-way quantum computation on chip. A theoretical model is presented for the underlying continuous-variable entanglement among the generated comb modes that is expansible to more complicated scenarios. We analyze the entanglement condition when the van Loock and Furusawa criteria are violated and discuss the device parameters for potential experimental realization that may be utilized to build an integrated compact five-partite entanglement generator. The proposed approach exhibits great potential for future large-scale integrated full optical quantum computation on chip.

Calculations of low-energy collisions of antiprotons $\overline{p}$ with helium atoms in the ground $(1{}^1\mathit{S})$ and metastable $(2{}^3\mathit{S}$ and $2{}^1\mathit{S})$ states are carried out by using a semiclassical method and by further assuming that one of the two electrons is passive. Antiproton capture to form antiprotonic helium $\left(\to \overline{p}{\mathrm{He}}^{+}+e\right)$ and breakup ionization $\left(\to \overline{p}+{\mathrm{He}}^{+}+e\right)$ are investigated. The energy dependence of the capture and ionization cross sections and the distributions of the product states are presented and compared with previous theoretical calculations. For the metastable helium targets, most of the $\overline{p}{\mathrm{He}}^{+}$ atoms produced in the capture have long lifetimes against subsequent Auger decays and can be observed experimentally. For the ground-state targets, however, the formation of such long-lived states is rather a rare event at low collision energies.

We propose a method for isotope-selective dissociation of diatomic molecules in the gas phase by using two kinds of terahertz-pulse fields. The first field consists of a train of pulses, composing a frequency comb, which excites only the selected isotope into a highly rotationally-excited state. The second field dissociates the excited molecules by further rovibrational excitations. We numerically demonstrate the applicability of the proposed scheme by molecular wave-packet computations using the lithium chlorides ${}^7\mathrm{Li}{}^{35}\mathrm{Cl}$ and ${}^7\mathrm{Li}{}^{37}\mathrm{Cl}$. Nearly 20% of the ${}^7\mathrm{Li}{}^{37}\mathrm{Cl}$ in the lowest rovibrational state is dissociated in a single interaction of the designed terahertz fields, while the dissociation probability is negligible in ${}^7\mathrm{Li}{}^{35}\mathrm{Cl}$. This scheme is expected to be applicable to the molecular ensemble whose rotational states spread in energy.

We propose a detailed experimental procedure for preparing relativistic vortices, governed by the nonlinear Dirac equation, in a two-dimensional Bose-Einstein condensate (BEC) in a honeycomb optical lattice. Our setup contains Dirac points, in direct analogy to graphene. We determine a range of practical values for all relevant physical parameters needed to realize relativistic vortices in a BEC of ${}^{87}\mathrm{Rb}$ atoms. Seven distinct vortex types, including Anderson-Toulouse and Mermin-Ho skyrmion textures and half-quantum vortices, are obtained, and their discrete spectra and stability properties are calculated in a weak harmonic trap. We predict that most vortices are stable, with a lifetime between 1 and 10 s.

We study a few Fermi atoms interacting through attractive contact forces in a one-dimensional trap by means of numerical exact diagonalization. From the combined analysis of energies and wave functions of correlated ground and excited states we find evidence of BCS-like pairing even for very few atoms. For moderate interaction strength, we reproduce the even-odd oscillation of the separation energy observed in Zürn, Wenz, Murmann, Bergschneider, Lompe, and Jochim, Phys. Rev. Lett. 111, 175302 (2013). For strong interatomic attraction the arrangement of dimers in the trap differs from the homogeneous case as a consequence of Pauli blockade in real space.

We investigate the procedures of loading and detecting three-dimensional fermionic quantum gases in a one-dimensional optical superlattice potential subjected to a trapping potential. Additionally, we consider the relaxation dynamics after a sudden change of the superlattice potential. We numerically simulate the time-dependent evolution of the continuous system using exact diagonalization of noninteracting fermions. During the loading procedure we analyze the occupation of the instantaneous energy levels and compare the situation in a homogeneous system with the trapped one. Strong differences are found in particular in the evolution of excitations which we trace back to the distinct global density distribution. Starting from an imbalanced state in the superlattice potential, we consider the relaxation dynamics of fermions after a slow change of the superlattice potential and find a bimodal distribution of excitations. To be able to compare with the experimental results we also simulate the measurement sequence of the even and odd local density and find a strong dependence of the outcome on the actual ramp procedure. We suggest how the loading and detecting procedure can be optimized.

We use a BCS-type variational wave function to study attractively interacting quasi-one-dimensional fermionic atomic gases, motivated by cold-atom experiments that access the one-dimensional regime using an anisotropic harmonic trapping potential (with trapping frequencies ${\omega }_x={\omega }_y\gg {\omega }_z$) that confines the gas to a cigar-shaped geometry. To handle the presence of the trap along the $z$ direction, we construct our variational wave function from the harmonic oscillator Hermite functions, which are the eigenstates of the single-particle problem. Using an analytic determination of the effective interaction among harmonic oscillator states along with a numerical solution of the resulting variational equations, we make specific experimental predictions for how pairing correlations would be revealed in experimental probes, such as the local density and the momentum correlation function.

Using light to control the movement of nanostructured objects is a great challenge. This challenge involves fields like optical tweezing, Casimir forces, integrated optics, biophysics, and many others. However, when the complexity of the light-activated devices increases, disorder unavoidably occurs and induces a number of effects, such as multiple-scattering, diffusion, and the localization of light. We show that these effects radically enhance the mechanical effect of light. We determine theoretically the link between optical pressure and the light diffusion coefficient and unveil that optical forces and their statistical fluctuations reach a maximum at the onset of the photon localization. Disorder may thus be exploited for increasing the mechanical action of light on complex objects.

We study the characteristics of the light generated by a few emitters in a cavity at strong light-matter coupling. By means of the Glauber $g^{\left(2\right)}$ function we can identify clearly distinguished parameter regimes with super-Poissonian and sub-Poissonian photon statistics. We establish a relation between the emission characteristics for one and multiple emitters and explain its origin in terms of the photon-dressed emitter states. Cooperative effects lead to the generation of nonclassical light already at reduced light-matter coupling if the number of emitters is increased. Our results are obtained with a full input-output formalism and master equation valid also at strong light-matter coupling. We compare the behavior obtained with and without counterrotating light-matter-interaction terms in the Hamiltonian and find that the generation of nonclassical light is robust against such modifications. Finally, we contrast our findings with the predictions of the quantum optical master equation and find that it fails entirely at predicting regimes with different photon statistics.

We theoretically investigate the propagation of surface plasmon polaritons in an amplifying plasmonic coupler (metal–amplifying dielectric–metal). We study the loss-compensated nonlinear stationary modes of the system by deriving coupled-mode equations for the optical amplitudes, predicting the existence of a mode with broken symmetry for gain values higher than a characteristic threshold. We analyze the stability of symmetric, antisymmetric, and nonsymmetric modes by solving the linearized system for small perturbations and by numerically integrating coupled-mode equations in propagation. We find that, while the antisymmetric mode stays always stable or marginally stable, the stability of symmetric and nonsymmetric modes is more involved.

Every measurement that can be implemented by local quantum operations and classical communication (LOCC) using an infinite number of rounds is the limit of a sequence of measurements, where each measurement in the sequence requires only a finite number of rounds. This rather obvious and well-known fact is nonetheless of interest as it shows that these infinite-round measurements can be approximated arbitrarily closely simply by using more and more rounds of communication. Here we demonstrate the perhaps less obvious result that (at least) for bipartite systems, the reverse relationship also holds. Specifically, we show that every finite-round bipartite LOCC measurement is the limit of a continuous sequence of LOCC measurements, where each measurement in that sequence can be implemented by LOCC, but only with the use of an infinite number of rounds. Thus, the set of LOCC measurements that require an infinite number of rounds is dense in the entirety of LOCC, as is the set of finite-round LOCC measurements. This means there exist measurements that can only be implemented by LOCC by using an infinite number of rounds, but can nonetheless be approximated closely by using one round of communication, and actually in some cases, no communication is needed at all. These results follow from a necessary condition presented here for finite-round LOCC, which is extremely simple to check, is very easy to prove, and which can be violated by utilizing an infinite number of rounds.

Quasiprobability distributions emerging in the stochastic wave-function method of Carusotto et al. [Phys. Rev. A 63, 023606 (2001)] are investigated. We show that there are actually two types of quasiprobabilities. The first one, the “diagonal Hartree-Fock state projection” representation, is useful in representing the initial conditions for stochastic simulation in the most compact form. It defines antinormally ordered expansion of the density operator and normally ordered mapping of the observables to be averaged. We completely characterize the equivalence classes of this phase-space representation. The second quasiprobability distribution, the “nondiagonal Hartree-Fock state projection” representation, extends the first one in order to achieve stochastic representation of the quantum dynamics. We demonstrate how the differential identities of the stochastic ansatz generate the automorphisms of this phase-space representation. These automorphisms turn the stochastic representation into a gauge theory. The gauge transformations of the quasiprobability master equation are described. In particular, it is the analyticity of the stochastic ansatz that allows one to transform the master equation into the genuine Fokker-Planck equation. We demonstrate how the different variants of the stochastic wave-function method can be constructed, first by choosing a certain optimality criteria or constraints, and then by satisfying these criteria with a suitable choice of gauge. The problem of boundary terms is considered. It is demonstrated that the simple scheme with Fock states of Carusotto et al. is not subjected to this problem.

By combining a squeezed propagating microwave field and an unsqueezed vacuum field on a hybrid (microwave beam splitter), we generate entanglement between the two output modes. We verify that we have generated entangled states by making independent and efficient single-quadrature measurements of the two output modes. We observe the entanglement witness $E_{\mathrm{W}}=-0.{263}_{-0.036}^{+0.001}$ and the negativity $N=0.{0824}_{-0.0004}^{+0.01}$ with measurement efficiencies at least $26\pm 0.1\%$ and $41\pm 0.2\%$ for channels 1 and 2, respectively. These measurements show that the output two-mode state violates the separability criterion and therefore demonstrates entanglement. This shared entanglement between propagating microwaves provides an important resource for building quantum networks with superconducting microwave systems.

Oblivious transfer protocol is a basic building block in cryptography and is used to transfer information from a sender to a receiver in such a way that, at the end of the protocol, the sender does not know if the receiver got the message or not. Since Shor's quantum algorithm appeared, the security of most of the classical cryptographic schemes has been compromised, as they rely on the fact that factoring is infeasible. To overcome this, quantum mechanics has been used intensively in the past decades, and alternatives resistant to quantum attacks have been developed in order to fulfill the (potential) lack of security of a significant number of classical schemes. In this paper, we present a quantum computationally secure protocol for bit-string oblivious transfer between two parties, under the assumption of quantum hardness of state distinguishability and the constraint of performing at most few-qubit measurements (leaving open the question of general attacks performed on all qubits involved). The protocol is feasible, in the sense that it is implementable in polynomial time.

We propose a design for a quantum microwave-optical photonic interface using electron spins in crystals to adiabatically swap the quantum states between a flux qubit and optical cavity that can achieve a transfer fidelity in excess of $90\%$. Following detailed modeling, we show that our protocol is robust against inhomogeneous broadening of the microwave and optical transitions, phase mismatch between the microwave and optical fields, and has the advantage that we can dynamically control the overall microwave-optical coupling strength in time. Using these capabilities we show how to coherently transport quantum information between two distant superconducting chips optically with a fidelity exceeding $90\%$.

We derive the necessary and sufficient conditions for the local unitary (LU) equivalence of two general (pure or mixed) $n$-qubit states and determine the local unitary operators connecting them. Almost all relevant information is contained in the one-qubit reduced matrices of the multiqubit states under investigation. Our technique relies on identifying ab initio all local symmetries and the corresponding local cyclic unitary operators. To derive the above conditions we use the reference forms of the multiqubit states whose definition requires the diagonalization of the one-qubit reduced matrices. Based on those conditions, we propose a straightforward protocol to decide whether or not two $n$-qubit states are LU equivalent.

A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify the nonclassicality of a single qubit, defined by the vacuum and single-photon states, by applying the following four well-known measures of nonclassicality: (1) the nonclassical depth, $\tau$, related to the minimal amount of Gaussian noise which changes a nonpositive $P$ function into a positive one; (2) the nonclassical distance $D$, defined as the Bures distance of a given state to the closest classical state, which is the vacuum for the single-qubit Hilbert space; together with (3) the negativity potential (NP), and (4) concurrence potential, which are the nonclassicality measures corresponding to the entanglement measures (i.e., the negativity and concurrence, respectively) for the state generated by mixing a single-qubit state with the vacuum on a balanced beam splitter. We show that complete statistical mixtures of the vacuum and single-photon states are the most nonclassical single-qubit states regarding the distance $D$ for a fixed value of both the depth $\tau$ and NP in the whole range $[0,1]$ of their values, as well as the NP for a given value of $\tau$ such that $\tau >0.3154$. Conversely, pure states are the most nonclassical single-qubit states with respect to $\tau$ for a given $D$, NP versus $D$, and $\tau$ versus NP. We also show the “relativity” of these nonclassicality measures by comparing pairs of single-qubit states: if a state is less nonclassical than another state according to some measure then it might be more nonclassical according to another measure. Moreover, we find that the concurrence potential is equal to the nonclassical distance for single-qubit states. This implies an operational interpretation of the nonclassical distance as the potential for the entanglement of formation.

Low-dimensional behavior of two ultracold atoms trapped in two- and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used, allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement-induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with those of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known resonances are used to illustrate the bound-state properties.

We demonstrate that the dynamic information and the spatial structure of a Rydberg wave packet formed by two neighboring Rydberg states can be simultaneously probed by harmonic spectra in a few-cycle laser pulse, where the Rydberg wave packet is produced by a pump laser field. By controlling the time delay of the pump-probe laser pulses, the harmonic spectra present a periodic variation, which directly illustrates the electron oscillation between the two neighboring Rydberg states. Specifically, by taking advantage of the periodic variation of the harmonic efficiency and the dip structure in the spectrum, one can detect the spatial characteristics and the dynamic information of the initial Rydberg wave packet.

Ultracold atomic gases are, to a very good approximation, described by pairwise zero-range interactions. This paper demonstrates that $N$-body systems with two-body zero-range interactions can be treated reliably and efficiently by the finite-temperature and ground-state path-integral Monte Carlo approaches, using the exact two-body propagator for zero-range interactions in the pair product approximation. Harmonically trapped one- and three-dimensional systems are considered. A propagator for the harmonically trapped two-body system with infinitely strong zero-range interaction, which may also have applications in real time evolution schemes, is presented.