We propose a deterministic implementation of weak cubic nonlinearity, which is a basic building block of a full-scale continuous-variable quantum computation. Our proposal relies on preparation of a specific ancillary state and transferring its nonlinear properties onto the desired target by means of deterministic Gaussian operations and feed forward. We show that, despite the imperfections arising from the deterministic nature of the operation, the weak quantum nonlinearity can be implemented and verified with the current level of technology.

In this work we report a quantum interference mediated control of the resonance profiles in a generic three-level system and investigate its effect on key quantum interference (QI) phenomena. Namely in a three-level configuration with doublets in the ground or excited states, we show control over enhancement and suppression of the emission (absorption) profiles. This is achieved by manipulation of the strength of QI and the energy spacing of the doublets. We analyze the application of such QI-induced control of the resonance profile in the framework of two limiting cases of lasing without inversion and photodetection.

The problem of the two-level laser is studied analytically. The steady-state solution is expressed as a continued fraction and allows for accurate approximation by rational functions. Moreover, we show that the abrupt change observed in the pump dependence of the steady-state population is directly connected to the transition to the lasing regime. The condition for a sharp transition to Poissonian statistics is expressed as a scaling limit of vanishing cavity loss and light-matter coupling, $\kappa \to 0$, $g\to 0$, such that $g^2/\kappa$ stays finite and $g^2/\kappa >2\gamma$, where $\gamma$ is the rate of nonradiative losses. The same scaling procedure is also shown to describe a similar change to the Poisson distribution in the Scully-Lamb laser model, suggesting that the low-$\kappa$, low-$g$ asymptotics is of more general significance for the laser transition.

Artificially structured metamaterials offer a means to enhance the weak optical nonlinearities of natural materials. The enhancement results from the inhomogeneous nature of the metamaterial unit cell, over which the local field distribution can likewise be strongly inhomogeneous, with highly localized and concentrated field regions. We investigate the nonlinear enhancement effect in metamaterials through a numerical study of four nonlinear metamaterial designs comprising arrays of metallic structures embedded in nonlinear dielectrics and operating around 10 THz. Through full-wave simulations and by employing an extended version of the transfer-matrix-based nonlinear parameter retrieval method, we confirm and quantify the enhanced nonlinearities, showing bulk quadratic nonlinear properties that are up to two orders of magnitude larger, and cubic nonlinear properties that are up to four orders of magnitude larger than the bulk nonlinear dielectric alone. Furthermore, the proposed nonlinear metamaterials support a variety of configurable nonlinear properties and regimes, including electric, magnetic, broadband, and low loss, depending on the particular geometry chosen. Finally, we use the retrieved parameters in a coupled-mode theory to predict the optimal crystal lengths and conversion efficiencies of these structures, displaying the possibility of efficient and subwavelength nonlinear devices based on metamaterials.

In contrast with entanglement, as measured by concurrence, in general, quantum discord does not possess the property of monogamy; that is, there is no tradeoff between the quantum discord shared by a pair of subsystems and the quantum discord that both of them can share with a third party. Here, we show that, as far as monogamy is considered, quantum discord of pure states is equivalent to the entanglement of formation. This result allows one to analytically prove that none of the pure three-qubit states belonging to the subclass of $W$ states is monogamous. A suitable physical interpretation of the meaning of the correlation information as a quantifier of monogamy for the total information is also given. Finally, we prove that, for rank 2 two-qubit states, discord and classical correlations are bounded from above by single-qubit von Neumann entropies.

The ground state of atoms from H to Ar was calculated using a self-interaction correction to local- and gradient-dependent density functionals. The correction can significantly improve the total energy and makes the orbital energies consistent with ionization energies. However, when the calculation is restricted to real orbitals, application of the self-interaction correction can give significantly higher total energy and worse results, as illustrated by the case of the Perdew-Burke-Ernzerhof gradient-dependent functional. This illustrates the importance of using complex orbitals for systems described by orbital-density-dependent energy functionals.

I consider the generic situation where a finite number of identical test systems in varying (possibly unknown) initial states are subjected independently to the same unknown process. I show how one can infer from the output data alone whether the process in question induces thermalization and, if so, which constants of the motion characterize the final equilibrium states. In case thermalization does occur and there is no evidence for constants of the motion other than energy, I further show how the same output data can be used to estimate the test systems’ effective Hamiltonian. For both inference tasks I devise a statistical framework inspired by the generic techniques of factor and principal component analysis. I illustrate its use in the simple example of qubits.

In this article we obtain results for the task of converting a single $N$-qubit $W$-class state (of the form $\sqrt{x_0}|00...0\rangle +\sqrt{x_1}|10...0\rangle +\cdots +\sqrt{x_N}|00...1\rangle$) into maximum entanglement shared between two random parties. Previous studies in random distillation have not considered how the particular choice of target pairs affects the transformation, and here we develop a strategy for distilling into general configurations of target pairs. We completely solve the problem of determining the optimal distillation probability for all three-qubit configurations and most four-qubit configurations when $x_0=0$. Our proof involves deriving new entanglement monotones defined on the set of four-qubit $W$-class states. As an additional application of our results, we present new upper bounds for converting a generic $W$-class state into the standard $W$ state $|W_N\rangle =\sqrt{\frac{1}{N}}\left(\right|10...0\rangle +\cdots +|00...1\rangle )$.

We investigate the controlled production of entangled guided photons. The technique is based on a two-stage vacuum-stimulated Raman process with a single atom in a nanofiber cavity. We examine the dependences of the two-photon emission probability and the entanglement concurrence on various parameters of the system, such as the radial and axial positions of the atom, the intensities and durations of the pump pulses, the one- and two-photon detunings, the cavity finesse, and the separation time between the pump pulses. We find that, due to the confinement of the guided cavity field in the transverse plane of the fiber and in the space between the cavity mirrors, the probability of generation of a pair of entangled guided photon can be high even when the finesse of the nanofiber cavity is moderate.

Building on recent advances in ultrafast lasers and methods to slow molecules, an experiment is proposed to produce translationally cold CO${}_2$ super-rotors ($j\sim 200$) by combining an optical centrifuge with helium-buffer-gas cooling. Quantum mechanical calculations of the complex scattering length for He-CO${}_2$ collisions demonstrate that the efficiency of rotational quenching decreases rapidly with increasing rotational excitation $j$ in the ultracold regime. Extrapolating to helium cryogenic temperatures, rotational quenching is predicted to remain inefficient up to $\sim$1 K, allowing for the possible creation of a beam of translationally cold, rotationally hot molecules.

We provide analytical results obtained in the framework of the quantum theory for a single-emitter nanolaser: an incoherently pumped single two-level system interacting with a single-cavity mode of finite finesse. In the good-cavity limit we analytically calculate the linewidth of such a laser, its amplitude fluctuation spectrum, and the intracavity Mandel $Q$ parameter. Our analytical results are in very good agreement with numerical simulations of the master equation.

We use the mean-field theory to analyze the ground-state phase diagrams of spin-orbit-coupled mass-imbalanced Fermi gases throughout the BCS-BEC evolution, including both the population-balanced and -imbalanced systems. Our calculations show that the competition between the mass and population imbalance and the Rashba-type spin-orbit coupling gives rise to very rich phase diagrams, involving normal, superfluid, and phase-separated regions. In addition, we find quantum phase transitions between the topologically trivial gapped superfluid and the nontrivial gapless superfluid phases, opening the way for the experimental observation of exotic phenomena with cold atom systems.

We propose a method for optical visualization of the Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive indices than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over the direction of propagation for both ordered and disordered cases, exploring the sensitivity of the averaged picture with respect to the beam injection position. For our finite systems, the resulting patterns are reminiscent the ones set in billiards, and therefore we introduce a definition of discrete quantum billiards and discuss the possible relevance to its well-established continuous counterpart.

We investigate a witness for nonclassical multipartite states based on their disturbance under local measurements. The witness operator provides a sufficient condition for nonclassicality that coincides with a nonvanishing global quantum discord, but it does not demand an extremization procedure. Moreover, for the case of $Z_2$-symmetric systems, we rewrite the witness in terms of correlation functions so that classicality is found to necessarily require either vanishing magnetization in the invariant axis or isotropy of the two-point function in the transverse spin plane. We illustrate our results in quantum spin chains, where a characterization of factorized ground states (with spontaneously broken $Z_2$ symmetry) is achieved. As a by-product, the witness is also shown to indicate a second-order quantum phase transitions, which is illustrated for both the $XY$ and the Ashkin-Teller spin chains.

How strongly can one system be correlated with another? In the classical world, this basic question concerning correlative capacity has a very satisfying answer: The “effective size” of the marginal system, as quantified by the Shannon entropy, sets a tight upper bound to the correlations, as quantified by the mutual information. Although in the quantum world bipartite correlations, like their classical counterparts, are also well quantified by mutual information, the similarity ends here: The correlations in a bipartite quantum system can be twice as large as the marginal entropy. In the paradigm of quantum discord, the correlations are split into classical and quantum components, and it was conjectured that both the classical and quantum correlations are (like the classical mutual information) bounded above by each subsystem's entropy. In this work, by exploiting the interplay between entanglement of formation, mutual information, and quantum discord, we disprove that conjecture. We further indicate a scheme to restore harmony between quantum and classical correlative capacities. The results illustrate dramatically the asymmetric nature of quantum discord and highlight some subtle and unusual features of quantum correlations.

We develop an architecture of a hybrid quantum solid-state processing unit for universal quantum computing. The architecture allows distant and nonidentical solid-state qubits in distinct physical systems to interact and work collaboratively. All the quantum computing procedures are controlled by optical methods using classical fields and cavity QED. Our methods have a prominent advantage of the insensitivity to dissipation process benefiting from the virtual excitation of subsystems. Moreover, the quantum nondemolition measurements and state transfer for the solid-state qubits are proposed. The architecture opens promising perspectives for implementing scalable quantum computation in a broader sense that different solid-state systems can merge and be integrated into one quantum processor afterward.

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states of $n$ qubits into six classes. These include the stabilizer types of the Werner states, the Greenberger-Horne-Zeilinger state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.

We discuss the implementation of optical quantum networks where the interface between stationary and photonic qubits is realized by optomechanical transducers [K. Stannigel et al., Phys. Rev. Lett. 105, 220501 (2010)]. This approach does not rely on the optical properties of the qubit and thereby enables optical quantum communication applications for a wide range of solid-state spin- and charge-based systems. We present an effective description of such networks for many qubits and give a derivation of a state transfer protocol for long-distance quantum communication. We also describe how to mediate local on-chip interactions by means of the optomechanical transducers that can be used for entangling gates. We finally discuss experimental systems for the realization of our proposal.

We propose a scheme that is able to generate stationary continuous-variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a nanomechanical resonator. We show that when both cavities are intensely driven, one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and optomechanical entanglement.

In this work a Green-function approach for scattering quantum walks is developed. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression for arbitrary topologies and position-dependent quantum amplitudes. By introducing the step and path operators, it is shown how to extract any information about the system from the Green function. The method's relevant features are demonstrated by discussing in detail an example, a general diamond-shaped graph.