We study the dynamics of coherent waves in nonlinear honeycomb lattices and show that nonlinearity breaks down the Dirac dynamics. As an example, we demonstrate that even a weak nonlinearity has major qualitative effects on one of the hallmarks of honeycomb lattices: conical diffraction. Under linear conditions, a circular input wave packet associated with the Dirac point evolves into a ring, but even a weak nonlinearity alters the evolution such that the emerging beam possesses triangular symmetry, and populates Bloch modes outside of the Dirac cone. Our results are presented in the context of optics, but we propose a scheme to observe equivalent phenomena in Bose-Einstein condensates.

After reviewing parity-measurement-based interferometry with twin Fock states, which allows for supersensitivity (Heisenberg limited) and super-resolution, we consider interferometry with two different superpositions of twin Fock states, namely, two-mode squeezed vacuum states and pair coherent states. This study is motivated by the experimental challenge of producing twin Fock states on opposite sides of a beam splitter. We find that input two-mode squeezed states, while allowing for Heisenberg-limited sensitivity, do not yield super-resolutions, whereas both are possible with input pair coherent states.

We deduce the coherent backscattering signal from two distant laser-driven atoms using single-atom equations. The background and interference components of the double scattering spectrum obtained by this alternative approach agree exactly with the results of the standard master equation treatment. In contrast to the master equation, however, the new approach is suitable for the generalization to a large number of atomic scatterers.

We report a single-photon frequency down-conversion experiment. Using the difference frequency generation process in a periodically poled lithium niobate waveguide, we successfully observed the phase-preserved frequency down-conversion of a coherent pulse train with an average photon number per pulse of $<$$1$, from the $0.7$ $\mu$m visible wavelength band to the $1.3$ $\mu$m telecom band. We expect this technology to become an important tool for flexible photonic quantum networking, including the realization of quantum repeater systems over optical fiber using atom-photon entanglement sources for the visible wavelength bands.

In this work, we theoretically study the absorption and dispersion coefficients of a probe field in four-level N-scheme atomic systems driven by two additional fields. We separate the steady-state solution of the appropriate density matrix element into the sum of three resonances. The effect of each resonance on the overall absorption and dispersion experienced by the probe is studied as a function of the strengths of the two other fields. In the limit of low saturation, we reveal the physics of these resonances and associate them with atomic excitation pathways, which we explicitly explain in the bare-states picture.

We investigate the spatiotemporal structure of the biphoton correlation in type-II parametric down-conversion (PDC). As in type-I PDC [Phys. Rev. Lett. 102, 223601 (2009)], we find that the correlation is nonfactorizable in space and time. Differently from type I, the type-II correlation in the spontaneous regime displays an asymmetric V-shaped structure in any cross section including time and one transverse dimension. This asymmetry along the temporal coordinate originates from the signal-idler group velocity mismatch and tends to disappear as the parametric gain is raised. We observe a progressive transition toward a symmetric X-shaped geometry similar to that found in type I when stimulated PDC becomes dominant. We also give quantitative evaluations of the localization in space and in time of the correlation, analyze its behavior for different crystal tuning angles, and underline qualitative differences with respect to type-I PDC.

A coarse-grained version of quantum density-functional theory featuring a limited spatial resolution is shown to model formal density-functional theory (DFT). This means that all densities are ensemble-$V$-representable (that is, by mixed states), the intrinsic energy functional $F$ is a continuous function of the density, and the representing external potential is the functional derivative of the intrinsic energy, in the sense of directional derivatives within the domain of $F$. The representing potential $v[\rho ]$ also has a quasicontinuity property, specifically, $v[\rho ]\rho$ is continuous as a function of $\rho$. Convergence of the intrinsic energy, coarse-grained densities, and representing potentials in the limit of coarse-graining scale going to zero are studied vis-à-vis Lieb’s $L^1\cap L^3$ theory. The intrinsic energy converges monotonically to its fine-grained (continuum) value, and coarse-grainings of a density $\rho$ converge strongly to $\rho$. If a sequence of coarse-grained densities converges strongly to $\rho$ and their representing potentials converge weak-${}^{*}$, the limit is the representing potential for $\rho$. Conversely, $L^{3/2}+L^{\infty }$ representability implies the existence of such a coarse-grained sequence.

We investigate the generation of entanglement between the axial degrees of freedom of electrons confined in separated locations in planar Penning traps. We show that there are two different sources of entanglement: one is related with the mechanism of switching on and off the electrical coupling between the two electrons, and the other is due to the two-quanta-transition term of the coupling interaction. We show that the degree of entanglement can be controlled by adjusting the strength of the coupling between the traps and the time of interaction. We show that the coupled electrons behave as a temporal active interferometer.

We introduce the quantum mechanical formalism for treating surface plasmon polariton scattering at an interface. Our developed theory—which differs fundamentally from the analogous photonic scenario—is used to investigate the possibility of plasmonic beam splitters at the quantum level. Remarkably, we find that a wide range of splitting ratios can be reached. As an application, we characterize a 50:50 plasmonic beam splitter and investigate first-order quantum interference of surface plasmon polaritons. The results of this theoretical study show that surface plasmon beam splitters are able to reliably and efficiently operate in the quantum domain.

Quantum algorithms for searching for one or more marked items on a $d$-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For $d=2$ and $d=3$, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

We consider the mixed three-qubit bound entangled state defined as the normalized projector on the subspace that is complementary to an unextendible product basis [C. H. Bennett et al., Phys. Rev. Lett. 82, 5385 (1999)]. Using the fact that no product state lies in the support of that state, we compute its entanglement by providing a basis of its subspace formed by “minimally entangled” states. The approach is in principle applicable to any entanglement measure; here we provide explicit values for both the geometric measure of entanglement and a generalized concurrence.

We present a scheme to investigate energy transfer by real-time propagation of the Kohn-Sham equations. The scheme’s purpose is to check and go beyond the dipole coupling approximation underlying a Förster-type energy transfer, and to obtain information about the coupling on the grounds of the density-functional theory. We observe deviations from the dipole coupling approximation for small molecules.

Transition state theory forms the basis of computing reaction rates in chemical and other systems. Recently, it has been shown how transition state theory can rigorously be realized in phase space by using an explicit algorithm. The quantization has been demonstrated to lead to an efficient procedure to compute cumulative reaction probabilities and the associated Gamov-Siegert resonances. In this paper, these results are used to express the cumulative reaction probability as an absolutely convergent sum over periodic orbits contained in the transition state.

Near-threshold resonances have been studied for Be-like ions with a focus on overlapping resonances among Rydberg series converging to different thresholds. The behavior of the overlapping as a function of $Z$ and the approach to the limit of infinite $Z$ are investigated. The $4$$s$$4$$p$ resonance is shown and discussed in detail as an example.

We observe signatures of disorder-induced order in one-dimensional $\mathit{XY}$ spin chains with an external site-dependent uniaxial random field within the $\mathit{XY}$ plane. We numerically investigate signatures of a quantum phase transition at $T=0$, in particular, an upsurge of the magnetization in the direction orthogonal to the external magnetic field and the scaling of the block entropy with the amplitude of this field. Also, we discuss possible realizations of this effect in ultracold atomic experiments.

Spectral shifts in stochastic beam-like fields on interaction with layers of positive- and negative-phase materials are examined on the basis of the ABCD-matrix approach and generalized Huygens-Fresnel principle. It is found that boundaries between such materials may cause spectral switches. Effect of absorption of negative-phase materials on the beam spectrum is discussed. Our results may find applications in connection with spectrum-selection optical interconnects, spectrally encoded information transfer, image formation in systems involving negative-phase materials, and geometrically tunable metamaterials.

We propose a theoretical protocol for a quantum phase gate between two transmon qubits capacitively coupled to a superconducting transmission line resonator driven by a strong microwave field. Compared with previous protocols involving a dispersive regime, our protocol works at a small detuning, $\Delta ~g$, and the nontrivial two-qubit gates can be realized in a short time, $~$$1/g$, where $g$ is the qubit-resonator coupling strength. Our analysis shows that the protocol is robust against the main decoherence sources and unavoidable parameter variations. Moreover, our protocol can be implemented using the current experimental design of circuit QED.

In a distributed quantum computer, scalability is accomplished by networking together many elementary nodes. Typically the network is optical and internode entanglement involves photon detection. In complex networks the entanglement fidelity may be degraded by the twin problems of photon loss and dark counts. Here we describe an entanglement protocol which can achieve high fidelity even when these issues are arbitrarily severe; indeed the method succeeds with finite probability even if the photon detectors are entirely removed from the network. An experimental demonstration should be possible with existing technologies.

We present nonstandard optical Ramsey schemes that use pulses individually tailored in duration, phase, and frequency to cancel spurious frequency shifts related to the excitation itself. In particular, the field shifts and their uncertainties can be radically suppressed (by two to four orders of magnitude) in comparison with the usual Ramsey method (using two equal pulses) as well as with single-pulse Rabi spectroscopy. Atom interferometers and optical clocks based on two-photon transitions, heavily forbidden transitions, or magnetically induced spectroscopy could significantly benefit from this method. In the latter case, these frequency shifts can be suppressed considerably below a fractional level of $10$${}^{-17}$. Moreover, our approach opens the door for high-precision optical clocks based on direct frequency comb spectroscopy.

The exact non-Markovian dynamics of a microcavity strongly coupled to a general reservoir at arbitrary temperature are studied. With the exact master equation for the reduced density operator of the cavity system, we analytically solve the time evolution of the cavity state and the associated physical observables. We show that the non-Markovian dynamics are completely determined by the propagating (retarded) and correlation Green functions. Comparing the non-Markovian behavior at finite temperature with those at the zero-temperature limit or Born-Markov limit, we find that the non-Markovian memory effect can dramatically change the coherent and thermal dynamics of the cavity. We also numerically study the dissipation dynamics of the cavity through the mean mode amplitude decay and the average photon number decay in the microwave regime. It is shown that the strong coupling between the cavity and the reservoir results in a long-time dissipationless evolution to the cavity field amplitude, and its noise dynamics undergo a critical transition from the weak to the strong coupling due to the non-Markovian memory effect.