Any lossless transformation on $n_s$ spatial and $n_p$ internal modes of light can be described by an $n_s{n}_p\times n_s{n}_p$ unitary matrix, but there is no known procedure to effect an arbitrary $n_s{n}_p\times n_s{n}_p$ unitary matrix on light in $n_s$ spatial and $n_p$ internal modes. We devise an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. Our realization uses beam splitters and operations on internal modes to effect arbitrary linear transformations. The number of beam splitters required to realize a unitary transformation is reduced as compared to existing realization by a factor $n_p^2/2$ at the cost of increasing the number of internal optical elements by a factor of 2. Our algorithm thus enables the optical implementation of higher dimensional unitary transformations.

We show that the frequency spectrum of two-dimensional photonic crystals is strongly influenced by Fano resonances which can be excited already in the linear array of dielectric cylinders. To support this claim, we calculate the transmission of an electromagnetic wave through a linear array of dielectric cylinders and show that the frequencies of observed Fano resonances coincide with the position of narrow frequency bands found in the spectra of corresponding two-dimensional photonic crystals. The split of the frequency band and the overlap of two bands, observed in the band structure of photonic structures, are also associated with Fano resonances.

In recent years, many efforts have been devoted to the construction of a proper measure of quantum non-Markovianity. However, those proposed measures are shown to be at variance in different situations. In this work, we utilize the theory of $k$-positive maps to generalize a hierarchy of $k$ divisibility and develop a powerful tool, called $k$-divisibility phase diagram, to show the landscape of non-Markovianity. This allows one to study different measures in a unified framework and provides a deeper insight into the nature of quantum non-Markovianity. By exploring the phase diagram with several paradigms, we can explain the origin of the discrepancy between three frequently used measures and find the condition under which these measures coincide with each other.

We analyze the influence of relativistic effects on the minimum evolution time between two orthogonal states of a quantum system. Defining the initial state as a homogeneous superposition between two Hamiltonian eigenstates of an electron in a uniform magnetic field, we obtain a relation between the minimum evolution time and the displacement of the mean radial position of the electron wave packet. The quantum speed limit time is calculated for an electron dynamics described by Dirac and Schrödinger-Pauli equations considering different parameters, such as the strength of magnetic field and the linear momentum of the electron in the axial direction. We highlight that when the electron undergoes a region with extremely strong magnetic field the relativistic and nonrelativistic dynamics differ substantially, so that the description given by the Schrödinger-Pauli equation enables the electron to travel faster than $c$, which is prohibited by Einstein's theory of relativity. This approach allows a connection between the abstract Hilbert space and the space-time coordinates, besides the identification of the most appropriate quantum dynamics used to describe the electron motion.

Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To overcome constraints imposed by restricted connectivity between qubits, a larger set of interactions can be approximated using minor embedding techniques whereby several physical qubits are used to represent a single logical qubit. However, minor embedding introduces new types of errors due to its approximate nature. We introduce and study quantum annealing correction schemes designed to improve the performance of quantum annealers in conjunction with minor embedding, thus leading to a hybrid scheme defined over an encoded graph. We argue that this scheme can be efficiently decoded using an energy minimization technique provided the density of errors does not exceed the per-site percolation threshold of the encoded graph. We test the hybrid scheme using a D-Wave Two processor on problems for which the encoded graph is a two-level grid and the Ising model is known to be NP-hard. The problems we consider are frustrated Ising model problem instances with “planted” (a priori known) solutions. Applied in conjunction with optimized energy penalties and decoding techniques, we find that this approach enables the quantum annealer to solve minor embedded instances with significantly higher success probability than it would without error correction. Our work demonstrates that quantum annealing correction can and should be used to improve the robustness of quantum annealing not only for natively embeddable problems but also when minor embedding is used to extend the connectivity of physical devices.

We implement a quantum-key-distribution protocol which works in analogy to the BB84 protocol with two discrete states each in frequency and time. Its security relies on the frequency-time uncertainty. We show how the protocol is realized with commercial telecom components and discuss technical constraints of existing equipment. In order to evaluate the performance and the security of the protocol against specific attacks we explore quantitatively a large set of parameters. Based on these studies we suggest how further enhancement of security can be obtained with existing technology.

An alternate method of two-photon spectroscopy is presented where cesium atoms interact with a phase-modulated laser beam. Doppler-free two-photon spectroscopy of the cesium atom $6S\to 8S$ hyperfine transition was used to experimentally demonstrate quantum interfered two-photon spectra. We calculated the photon-atom interaction by second-order perturbation theory and assumed that the one-photon frequency is detuned far from any intermediate state. Then we calculated the relative transition rates of all spectral lines resolved by the laser carrier and sidebands. A physical picture of multipathway quantum interference in the frequency domain is given that explains the unusual line strength, based on the trick that a phase-modulated laser beam can be decomposed into a series of coherent and collinear laser modes (carrier and sidebands). For all pairs of modes in which the sum frequency of each pair was on resonance with the cesium atom $6S\to 8S$ transition, the superposition of all pathways induced by the different mode pairs resulted in a destructive interference, which then leads to a lack of absorption. We have shown in this paper that our calculation agrees very well with our experimental results in terms of the relative interfered line strengths, which were functions of modulation depth. We further discuss some related issues concerning laser stabilization and we demonstrate an approach for simultaneously comparing two cesium cells.

The critical nuclear charge $Z_c$ required for a heliumlike atom to have at least one bound state was recently determined with a high accuracy from variational calculations. Analysis of the wave functions further suggested that the bound state changes smoothly into a shape resonance as $Z$ crosses the critical value. Using variational calculations combined with the complex coordinate rotation method, we evidence the existence of resonances for $Z<Z_c$ up to the very close vicinity of $Z=Z_c$, thus strengthening this hypothesis. The variation of the resonance width with $Z$ is found to be in good agreement with a model derived from analysis of the $1/Z$ perturbation series.

Percolation theory is applied to the phase-transition dynamics of domain pattern formation in segregating binary Bose-Einstein condensates in quasi-two-dimensional systems. Our finite-size-scaling analysis shows that the percolation threshold of the initial domain pattern emerging from the dynamic instability is close to 0.5 for strongly repulsive condensates. The percolation probability is universally described with a scaling function when the probability is rescaled by the characteristic domain size in the dynamic scaling regime of the phase-ordering kinetics, independent of the intercomponent interaction. It is revealed that an infinite domain wall sandwiched between percolating domains in the two condensates has a noninteger fractal dimension and keeps the scaling behavior during the dynamic scaling regime. This result seems to be in contrast to the argument that the dynamic scale invariance is violated in the presence of an infinite topological defect in numerical cosmology.

We study a non-Hermitian version of the Rabi model, where a two-level system is periodically driven with an imaginary-valued drive strength, leading to alternating gain and loss. In the Floquet picture, the model exhibits $\mathcal{PT}$ symmetry, which can be broken when the drive is sufficiently strong. We derive the boundaries of the $\mathcal{PT}$ phase diagram for the different resonances by doing perturbation theory beyond the rotating-wave approximation. For the main resonance, we show that the non-Hermitian analog of the Bloch-Siegert shift corresponds to maximal $\mathcal{PT}$ breaking. For the higher-order resonances, we capture the boundaries to lowest order. We also solve the regime of high frequency by mapping to the Wannier-Stark ladder. Our model can be experimentally realized in waveguides with spatially modulated loss or in atoms with time-modulated spontaneous decay.

An atom attached to a micrometer-scale wire that is vibrating at a frequency $\sim 100\mathrm{MHz}$ and with displacement amplitude $\sim 1\mathrm{nm}$ experiences an acceleration magnitude $\sim {10}^9{\mathrm{m}\mathrm{s}}^{-2}$, approaching the surface gravity of a neutron star. As one application of such extreme noninertial forces in a mesoscopic setting, we consider a model two-path atom interferometer with one path consisting of the $100\mathrm{MHz}$ vibrating wire atom guide. The vibrating wire guide serves as a noninertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We furthermore consider the effect on the two-path atom wave interference when the vibrating wire is modeled as a quantum object, hence functioning as a quantum noninertial reference frame. We outline a possible realization of the vibrating wire, atom interferometer using a superfluid helium quantum interference setup.

We propose the square of convex-roof extended negativity (SCREN) as a powerful candidate to characterize strong monogamy of multiparty quantum entanglement. We first provide a strong monogamy inequality of multiparty entanglement using SCREN and show that the tangle-based multiqubit strong-monogamy inequality can be rephrased by SCREN. We further show that the SCREN strong-monogamy inequality is still true for the counterexamples that violate tangle-based the strong-monogamy inequality in higher-dimensional quantum systems other than qubits. We also analytically show that SCREN strong-monogamy inequality is true for a large class of multiqudit states, a superposition of multiqudit generalized $W$-class states and vacuums. Thus SCREN is a good alternative to characterize the strong monogamy of entanglement even in multiqudit systems.

Many-body quantum eigenstates of generic Hamiltonians at finite-energy density typically satisfy the “volume law” of entanglement entropy: the von Neumann entanglement entropy and the Renyi entropies for a subregion scale in proportion to its volume. Here we provide a connection between the volume law and the sign structure of eigenstates. In particular, we ask the following question: Can a positive wave function support a volume law entanglement? Remarkably, we find that a typical random positive wave function exhibits a constant law for Renyi entanglement entropies $S_n$ for $n>1$, despite arbitrary large-amplitude fluctuations. We also provide evidence that the modulus of the finite-energy density eigenstates of generic local Hamiltonians shows similar behavior.

What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of simulation and permit a reasoning beyond the limitations of the usual explicit Lie closure. Conserved quantities induced by symmetries pave the way to a resource theory for simulability. On a general level, one can now decide equality for any pair of compact Lie algebras just given by their generators without determining the algebras explicitly. Several physical examples are illustrated, including entanglement invariants, the relation to unitary gate membership problems, as well as the central-spin model.

We perform a detailed analysis of how the interplay between the residual binding potential and a strong laser field influences above-threshold ionization (ATI), employing a semianalytical, Coulomb-corrected strong-field approximation (SFA) in which the Coulomb potential is incorporated in the electron propagation in the continuum. We find that the Coulomb interaction lifts the degeneracy of some SFA trajectories and we identify a set of orbits that, for high enough photoelectron energies, may be associated with rescattering. Furthermore, by performing a direct comparison with the standard SFA, we show that several features in the ATI spectra can be traced back to the influence of the Coulomb potential on different electron trajectories. These features include a decrease in the contrast, a shift towards lower energies in the interference substructure, and an overall increase in the photoelectron yield. All features encountered exhibit very good agreement with the ab initio solution of the time-dependent Schrödinger equation.

Electron dynamics excited by an optical near field (ONF) in a two-dimensional quantum dot model was investigated by solving a time-dependent Schrödinger equation. It was found that the ONF excitation of the electron caused two characteristic phenomena: a two-photon absorption and an induction of a magnetic dipole moment with a strong third-harmonic component. By analyzing the interaction dynamics of the ONF and the electron, we explained that the physical mechanism underlying these phenomena was the second-harmonic electric-field component concomitant with the near-field excitation originating from the nonuniformity of the ONF. Despite a $y$-polarized ONF source, the second-harmonic component of an $x$-polarized electric field was inherently generated. The effect of the second-harmonic electric-field component is not due to usual second-order nonlinear response but appears only when we explicitly consider the electron dynamics interacting with the ONF beyond the conventional optical response assuming the dipole approximation.

We consider a two-dimensional homogeneous ensemble of cold bosonic atoms loaded inside two optical cavities and pumped by a far-detuned external laser field. We examine the conditions for these atoms to self-organize into triangular and honeycomb lattices as a result of superradiance. By collectively scattering the pump photons, the atoms feed the initially empty cavity modes. As a result, the superposition of the pump and cavity fields creates a space-periodic light-shift external potential and atoms self-organize into the potential wells of this optical lattice. Depending on the phase of the cavity fields with respect to the pump laser, these minima can either form a triangular or a hexagonal lattice. By numerically solving the dynamical equations of the coupled atom-cavity system, we have shown that the two stable atomic structures at long times are the triangular lattice and the honeycomb lattice with equally populated sites. We have also studied how to drive atoms from one lattice structure to another by dynamically changing the phase of the cavity fields with respect to the pump laser.

The influence of cyclic electron delocalization associated with aromaticity on the high-order-harmonic generation (HHG) process is investigated in organic molecules. We show that the aromatic molecules benzene $\left({\mathrm{C}}_6{\mathrm{H}}_6\right)$ and furan $\left({\mathrm{C}}_4{\mathrm{H}}_4\mathrm{O}\right)$ produce high-order harmonics more efficiently than nonaromatic systems having the same ring structure. We also demonstrate that the relative strength of plateau harmonics is sensitive to the aromaticity in five-membered-ring molecules using furan, pyrrole $\left({\mathrm{C}}_4{\mathrm{H}}_4\mathrm{NH}\right)$, and thiophene $\left({\mathrm{C}}_4{\mathrm{H}}_4\mathrm{S}\right)$. Numerical time-dependent Schrödinger equation simulations of total orientation-averaged strong-field ionization yields show that the HHG from aromatic molecules comes predominantly from the two highest $\pi$ molecular orbitals, which contribute to the aromatic character of the systems.