We present a scheme to implement a Fermi-Hubbard-like model in ultracold atoms in optical lattices and analyze the topological features of its ground state. In particular, we show that the ground state for appropriate parameters has a large overlap with a lattice version of the bosonic Laughlin state at filling factor one-half. The scheme utilizes laser assisted and normal tunneling in a checkerboard optical lattice. The requirements on temperature, interactions, and hopping strengths are similar to those needed to observe the Néel antiferromagnetic ordering in the standard Fermi-Hubbard model in the Mott insulating regime.

A system with a topological insulator slab sandwiched by two one-dimensional photonic crystals as a defect is investigated. A giant topological magnetoelectric effect is proposed which is characterized by two resonant peaks with half-unit transmissions and rich polarization behaviors in the photonic band gap. We also predict a giant optical Hall effect in our system, in which the transverse shift of the transmitted light could be 1000 times larger than the wavelength. These effects are purely from the $\Theta$-domain walls at the topological insulator interfaces and could be observed easily.

For several types of correlations (mixed-state entanglement in systems of distinguishable particles, particle entanglement in systems of indistinguishable bosons and fermions, and non-Gaussian correlations in fermionic systems) we estimate the fraction of noncorrelated states among the density matrices with the same spectra. We prove that for the purity exceeding some critical value (depending on the considered problem) fraction of noncorrelated states tends to zero exponentially fast with the dimension of the relevant Hilbert space. As a consequence, a state randomly chosen from the set of density matrices possessing the same spectra is asymptotically a correlated one. To prove this we developed a systematic framework for detection of correlations via nonlinear witnesses.

We report the implementation of the relativistic equation-of-motion coupled-cluster method to calculate the double-ionization spectra (DI-EOMCC) of the closed-shell atomic systems. This method is employed to calculate the principal valence double-ionization potential values of He and alkaline-earth-metal (Be, Mg, Ca, Sr, and Ba) atoms. Our results are compared with the results available from the NIST database and other $\mathit{ab}\mathit{initio}$ calculations. We have achieved an accuracy of $\sim 0.1\%$, which is an improvement over the first-principles $T$-matrix calculations [Y. Noguchi et al., J. Chem. Phys. 123, 144112 (2005)]. We also present results using the second-order many-body perturbation theory and the random-phase approximation in the equation-of-motion framework, and these results are compared with the DI-EOMCC results.

We investigate the inhomogeneous unitary Fermi gas and use the long-wavelength properties to predict the energies of small clusters of unitary fermions trapped in harmonic potentials. The large pairing gap and scale invariance place severe restrictions on the form of the density functional. We determine the relevant universal constants needed to constrain the functional from calculations of the bulk in oscillating external potentials. Comparing with exact quantum Monte Carlo calculations, we find that the same functional correctly predicts the lack of shell closures for small clusters of fermions trapped in harmonic wells as well as their absolute energies. A rapid convergence to the bulk limit in three dimensions, where the surface-to-volume ratio is quite large, is demonstrated. The resulting functional can be tested experimentally, and is a key ingredient in predicting possible polarized superfluid phases and the properties of the unitary Fermi gas in optical lattices.

A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in the non-Hermitian $\mathcal{PT}-\mathrm{symmetric}$ Ising model, which is driven by a staggered complex transverse field. Exact solution shows that the Laplacian of the ground-state energy density, with respect to real and imaginary components of the transverse field, diverges on the boundary in the complex plane. The phase diagram indicates that the imaginary transverse field has the effect of shrinking the paramagnetic phase. In addition, we also investigate the connection between the geometric phase and the QPT.

Precise experimental implementation of unitary operators is one of the most important tasks for quantum information processing. Numerical optimization techniques are widely used to find optimized control fields to realize a desired unitary operator. However, finding high-fidelity control pulses to realize an arbitrary unitary operator in larger spin systems is still a difficult task. In this work, we demonstrate that a combination of the grape algorithm, which is a numerical pulse optimization technique, and a unitary operator decomposition algorithm [Ajoy et al., Phys. Rev. A 85, 030303 (2012)] can realize unitary operators with high experimental fidelity. This is illustrated by simulating the mirror-inversion propagator of an XY spin chain in a five-spin dipolar coupled nuclear spin system. Further, this simulation has been used to demonstrate the transfer of entangled states from one end of the spin chain to the other end.

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

We consider the process consisting of preparation, transmission through a quantum channel, and subsequent measurement of quantum states. The communication complexity of the channel is the minimal amount of classical communication required for classically simulating it. Recently, we reduced the computation of this quantity to a convex minimization problem with linear constraints. Every solution of the constraints provides an upper bound on the communication complexity. In this paper, we derive the dual maximization problem of the original one. The feasible points of the dual constraints, which are inequalities, give lower bounds on the communication complexity, as illustrated with an example. The optimal values of the two problems turn out to be equal (zero duality gap). By this property, we provide necessary and sufficient conditions for optimality in terms of a set of equalities and inequalities. We use these conditions and two reasonable but unproven hypotheses to derive the lower bound $n\times 2^{n-1}$ for a noiseless quantum channel with capacity equal to $n$ qubits. This lower bound can have interesting consequences in the context of the recent debate on the reality of the quantum state.

We study the competing effects of simultaneous Markovian and non-Markovian decoherence mechanisms acting on a single spin. We show the existence of a threshold in the relative strength of such mechanisms above which the spin dynamics becomes fully Markovian, as revealed by the use of several non-Markovianity measures. We identify a measure-dependent nested structure of such thresholds, hinting at a causality relationship among the various non-Markovianity witnesses used in our analysis. Our considerations are then used to argue the unavoidably non-Markovian evolution of a single-electron quantum dot exposed to both intrinsic and Markovian technical noise, the latter of arbitrary strength.

We experimentally demonstrate, with an all-optical setup, a nonlocal deterministic quantum nondemolition interaction gate applicable to quantum states at nodes separated by a physical distance and connected by classical communication channels. The gate implementation, based on entangled states shared in advance, local operations, and classical communication, runs completely in parallel fashion at both of the local nodes, requiring minimum resources. The nondemolition character of the gate up to the local unitary squeezing is verified by the analysis using several coherent states. A genuine quantum nature of the gate is confirmed by the capability of deterministically producing an entangled state at the output from two separable input states. The all-optical nonlocal gate operation can be potentially incorporated into distributed quantum computing with atomic or solid-state systems as a cross-processor unitary operation.

As a first step towards meeting the recent demand for new computational tools capable of reproducing molecular-ionization continua in a wide energy range, we introduce a hybrid Gaussian–$B$-spline basis (GABS) that combines short-range Gaussian functions, compatible with standard quantum-chemistry computational codes, with $B$ splines, a basis appropriate to represent electronic continua. We illustrate the performance of the GABS hybrid basis for the hydrogen atom by solving both the time-independent and the time-dependent Schrödinger equation for a few representative cases. The results are in excellent agreement with those obtained with a purely $B$-spline basis, with analytical results, when available, and with recent above-threshold ionization spectra from the literature. In the latter case, we report fully differential photoelectron distributions which offer further insight into the process of above-threshold ionization at different wavelengths.

By solving the quantum field theoretical Dirac and Klein-Gordon equations numerically we analyze the different roles of discrete and continuum states for the pair-creation process from the vacuum. If this process is solely induced by discrete states that have become degenerate with the negative energy continuum, the complex scaling method can predict the time scales associated with the bosonic as well as fermionic growth of the particle yield. We show that for bosons the long-time exponential growth behavior is not affected by additional continuum-continuum degeneracies, while for fermions they characterize the asymptotic (linear) growth. We illustrate the impact of these degeneracies on the temporally resolved energy and spatial distributions of the created particles.

Here we provide a scheme of transforming the one-axis twisting Hamiltonian into a two-axis twisting Hamiltonian based on the higher-order Trotter-Suzuki approximation. Compared with the paper by Liu et al. [Phys. Rev. Lett. 107, 013601 (2011)], our method can reduce the number of controlling cycles from 1000 to 50. Moreover, it is also spin number independent and takes a shorter optimal evolution time as compared with the method of Shen et al. [Phys. Rev. A 87, 051801 (2013)]. The corresponding error analysis is also provided.

We investigate the reduced dimensionality of highly anisotropic Bose-Einstein condensates (BECs) in connection with the entanglement between the spatial degrees of freedom. We argue that the reduced dimensionality of the BEC is physically meaningful in a regime where spatial correlations are negligible. We handle the problem analytically within the mean-field approximation for general quasi-one-dimensional and quasi-two-dimensional geometries and obtain the optimal reduced-dimension, pure-state description of the condensate mean field. We give explicit solutions for the case of harmonic potentials, which we compare against exact numerical integration of the three-dimensional Gross-Pitaevskii equation.

The resolution of conventional optical lenses is limited by the wavelength. Materials with a negative refractive index have been shown to enable the generation of an enhanced resolution image where both propagating and nonpropagating waves are employed. We analyze such a Veselago lens by exploiting some exact one-dimensional integral expressions for the quasistatic electric potential of a point charge in that system. These were recently obtained by expanding that potential in the quasistatic eigenfunctions of a three-flat-slabs composite structure. Numerical evaluations of those integrals, using realistic values for physical parameters like the electric permittivities of the constituent slabs and their thickness, reveal some surprising effects: For example, the maximum concentration of the electric field occurs not at the geometric optics foci but at the interfaces between the negative permittivity slab and the positive permittivity slabs. The analysis provides simple computational guides for designing such structures to achieve enhanced resolution of an optical image.

Optimal measurement scheme with an efficient data processing is important in quantum-enhanced interferometry. Here we prove that for a general binary-outcome measurement, the simplest data processing based on inverting the average signal can saturate the Cramér-Rao bound. This idea is illustrated by binary-outcome homodyne detection, even-odd photon counting (i.e., parity detection), and zero-nonzero photon counting that have achieved super-resolved interferometric fringe and shot-noise limited sensitivity in coherent-light Mach-Zehnder interferometer. The roles of phase diffusion are investigated in these binary-outcome measurements. We find that the diffusion degrades the fringe resolution and the achievable phase sensitivity. Our analytical results confirm that the zero-nonzero counting can produce a slightly better sensitivity than that of the parity detection, as demonstrated in a recent experiment.

Higher-order nonclassical properties of fields propagating through a codirectional asymmetric nonlinear optical coupler which is prepared by combining a linear waveguide and a nonlinear (quadratic) waveguide operated by second harmonic generation are studied. A completely quantum mechanical description is used here to describe the system. Closed form analytic solutions of Heisenberg's equations of motion for various modes are used to show the existence of higher-order antibunching, higher-order squeezing, and higher-order two-mode and multimode entanglement in the asymmetric nonlinear optical coupler. It is also shown that nonclassical properties of light can transfer from a nonlinear waveguide to a linear waveguide.

We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework of direct-sum decomposition of state space. They include not only separable states with vanishing or nonvanishing quantum discord but also entangled states. A general expression of the families as well as the Kraus operators for the completely positive maps are explicitly given. It significantly extends the previous results.