Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements leads to the generation of ensembles of random unitaries, where each random unitary is identified with a string of possible measurement results. We show that repeating an MB scheme an efficient number of times, on a simple graph state, with measurements at fixed angles and no feedforward corrections, produces a random unitary ensemble that is an $\varepsilon$-approximate $t$ design on $n$ qubits. Unlike previous constructions, the graph is regular and is also a universal resource for measurement based quantum computing, closely related to the brickwork state.

For general quantum systems, many sets of locally indistinguishable orthogonal quantum states have been constructed so far. However, it is interesting how much entanglement resources are sufficient and/or necessary to distinguish these states by local operations and classical communication (LOCC). Here we first present a method to locally distinguish a set of orthogonal product states in $5\otimes 5$ by using two copies of $2\otimes 2$ maximally entangled states. Then we generalize the distinguishing method for a class of orthogonal product states in $d\otimes d$ ($d$ is odd). Furthermore, for a class of nonlocality of orthogonal product states in $d\otimes d$ ($d\ge 5$), we prove that these states can be distinguished by LOCC with two copies of $2\otimes 2$ maximally entangled states. Finally, for some multipartite orthogonal product states, we also present a similar method to locally distinguish these states with multiple copies of $2\otimes 2$ maximally entangled states. These results also reveal the phenomenon of less nonlocality with more entanglement.

We show that the particle density $\rho \left(\mathbf{r}\right)$ and the paramagnetic current density ${\mathbf{j}}^p\left(\mathbf{r}\right)$ are not sufficient to determine the set of degenerate ground-state wave functions. This is a general feature of degenerate systems where the degenerate states have different angular momenta. We provide a general strategy for constructing Hamiltonians that share the same ground-state density pair yet differ in degree of degeneracy. We then provide a fully analytical example for a noninteracting system subject to electrostatic potentials and uniform magnetic fields. Moreover, we prove that when $(\rho ,{\mathbf{j}}^p)$ is ensemble $(v,\mathbf{A})$-representable by a mixed state formed from $r$ degenerate ground states, then any Hamiltonian $H(v^{\prime },{\mathbf{A}}^{\prime })$ that shares this ground-state density pair must have at least $r$ degenerate ground states in common with $H(v,\mathbf{A})$. Thus, any set of Hamiltonians that shares a ground-state density pair $(\rho ,{\mathbf{j}}^p)$ by necessity has to have at least one joint ground state.

Recently, the emergence of a higher-energy structure (HES) due to a spatial inhomogeneity in the laser electric field, as is typically found close to a nanotip, was reported in Phys. Rev. Lett. 119, 053204 (2017). For practical applications, such as the characterization of near fields or the creation of localized sources of monoenergetic electron beams with tunable energies, further insight into the nature of this higher-energy structure is needed. Here, we give a closed form analytical approximation to describe the movement of the electron in the inhomogeneous electric field. In particular, we derive a simple scaling law for the location of the HES peak and give a scheme to analytically tune the width of the peak, both of which will prove useful in optimizing the nanostructure size or geometry for creating the HES in experimental settings.

Understanding radiative transfer in random media like micro- or nanoporous and particulate materials, allows people to manipulate the scattering and absorption of radiation, as well as opens new possibilities in applications such as imaging through turbid media, photovoltaics, and radiative cooling. A strong-backscattering phase function, i.e., a negative scattering asymmetry parameter $g$, is of great interest, which can possibly lead to unusual radiative transport phenomena, for instance, Anderson localization of light. Here we demonstrate that by utilizing the structural correlations and second Kerker condition for a disordered medium composed of randomly distributed silicon nanoparticles, a strongly negative scattering asymmetry factor ($g\sim -0.5$) for multiple light scattering can be realized in the near infrared. Based on the multipole expansion of Foldy-Lax equations and quasicrystalline approximation (QCA), we have rigorously derived analytical expressions for the effective propagation constant and scattering phase function for a random system containing spherical particles, by taking the effect of structural correlations into account. We show that as the concentration of scattering particles rises, the backscattering is also enhanced. Moreover, in this circumstance, the transport mean free path is largely reduced and even becomes smaller than that predicted by independent scattering approximation. We further explore the dependent scattering effects, including the modification of electric and magnetic dipole excitations and far-field interference effect, both induced and influenced by the structural correlations, for volume fraction of particles up to $f_v\sim 0.25$. Our results have profound implications in harnessing micro- or nanoscale radiative transfer through random media.

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time ($\mathcal{PT}$) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other physical systems as well.

The distribution of noncollinear magnetism in an electronic system provides information about the kinetic energy as well as some kinetic energy densities. Two different everywhere-positive kinetic densities related to the Schrödinger-Pauli Hamiltonian are considered. For one-electron systems described by a single Pauli spinor, the electron density, spin density, and current density completely determines these kinetic energy densities. For many-electron systems, lower bounds on the kinetic energy densities are proved. These results generalize a lower bound due to von Weizsäcker, which is based on the electron density alone and plays an important role in density functional theory. The results have applications in extensions of density functional theory that incorporate noncollinear spin densities and current densities.

Fast ($E_0=520\mathrm{eV}$) electron-impact ionization of molecular hydrogen (${\mathrm{H}}_2$) is studied experimentally and theoretically for a resolved molecular axis angle and 10 eV ejected electron energy. Fully differential cross sections were measured using an electron-electron-ion triple coincidence experiment in which the molecular axis direction is obtained for ionic ground-state dissociation. While predictions from the standard two-wave interference model are in strong disagreement with experiment a multicenter distorted-wave method obtains much better results. This demonstrates the importance of the multicenter ionic potential for the electron emission pattern at low energy and the failure of hitherto widely used simple models which treat molecular ionization as the coherent sum of atomic ionization amplitudes.

We present a quantum many-body description of the excitation spectrum of Rydberg polarons in a Bose gas. The many-body Hamiltonian is solved with a functional determinant approach, and we extend this technique to describe Rydberg polarons of finite mass. Mean-field and classical descriptions of the spectrum are derived as approximations of the many-body theory. The various approaches are applied to experimental observations of polarons created by excitation of Rydberg atoms in a strontium Bose-Einstein condensate.

We describe the emergence of strong spatial correlations, akin to liquidlike behavior and crystallization effects, in low- (one- and two-)dimensional gases of cold Rydberg atoms. The presence of an external electric field permanently polarizes the atoms, which became highly correlated due to the long-range dipole-dipole interaction. We describe a theoretical approach particularly suited for strongly coupled systems and numerically obtain both the two-particle distribution function and the static structure factor. The experimental implementation of such highly interacting systems is discussed, including detailed calculations of the interaction strength for different Rydberg states. The results provide insights into many-body effects associated with strongly interacting Rydberg atoms, including the possibility of observing highly ordered phases.

Experiments handling Rydberg atoms near surfaces must necessarily deal with the high sensitivity of Rydberg atoms to (stray) electric fields that typically emanate from adsorbates on the surface. We demonstrate a method to modify and reduce the stray electric field by changing the adsorbate distribution. We use one of the Rydberg excitation lasers to locally affect the adsorbed dipole distribution. By adjusting the averaged exposure time we change the strength (with the minimal value less than $0.2\mathrm{V}/\mathrm{cm}$ at $78\mu \mathrm{m}$ from the chip) and even the sign of the perpendicular field component. This technique is a useful tool for experiments handling Rydberg atoms near surfaces, including atom chips.

The fragmentation of gas phase endohedral fullerene, $\mathrm{H}{\mathrm{o}}_3\mathrm{N}@{\mathrm{C}}_{80}$, was investigated using femtosecond near-infrared laser pulses with an ion velocity map imaging spectrometer. We observed that $\mathrm{H}{\mathrm{o}}^{+}$ abundance associated with carbon cage opening dominates at an intensity of $1.1\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. As the intensity increases, the $\mathrm{H}{\mathrm{o}}^{+}$ yield associated with multifragmentation of the carbon cage exceeds the prominence of $\mathrm{H}{\mathrm{o}}^{+}$ associated with the gentler carbon cage opening. Moreover, the power law dependence of $\mathrm{H}{\mathrm{o}}^{+}$ on laser intensity indicates that the transition of the most likely fragmentation mechanisms occurs around $2.0\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

We studied the ground state of alkaline-earth-metal atoms confined in one-dimensional optical lattices with an effective hybridization generated by a suitable laser field. This system is modeled by the periodic Anderson model plus a quadratic confining potential, and we adopted the density-matrix renormalization group to calculate its ground state. We found a one-to-one correspondence between the local variance, the local von Neumann entropy, and the on-site spin-spin correlation. For low global densities, we observed the formation of local singlets between delocalized and localized atoms and found Kondo spin-liquid domains that can be tuned with the confining potential, the hybridization, and the local repulsion. Band insulator, metallic, phase separation, and Kondo spin-liquid regions coexist in the ground state.

We investigated a one-dimensional system of anyons that interact with each other under a local three-body term. Using a fractional Jordan-Wigner transformation, we arrived at a modified Bose-Hubbard model, which exhibits gapped and gapless phases. We built the phase diagram of the system fixing the hopping parameter or the statistics, showing the evolution of the critical points, which were estimated with von Neumann block entropy. A superfluid to Mott insulator quantum phase transition with one particle per site can be driven by the statistics or the interaction. Specifically, we show that for larger angles there is a finite critical value of the interaction at which the Mott phase appears. Also, we found that the critical angles increase with the hopping. Diverse gapless phases were observed away from the pseudofermion limit.

We describe how color superfluidity is modified in the presence of color-flip and color-orbit fields in the context of ultracold atoms and discuss connections between this problem and that of color superconductivity in quantum chromodynamics. We study the case of $s$-wave contact interactions between different colors and we identify several superfluid phases, with five being nodal and one being fully gapped. When our system is described in a mixed-color basis, the superfluid order parameter tensor is characterized by six independent components with explicit momentum dependence induced by color-orbit coupling. The nodal superfluid phases are topological in nature and the low-temperature phase diagram of the color-flip field versus the interaction parameter exhibits a pentacritical point, where all five nodal color superfluid phases converge. These results are in sharp contrast to the case of zero color-flip and color-orbit fields, where the system has perfect U(3) symmetry and possesses a superfluid phase that is characterized by fully gapped quasiparticle excitations with a single complex order parameter with no momentum dependence and by inert unpaired fermions representing a nonsuperfluid component. In the latter case, just a crossover between a Bardeen-Cooper-Schrieffer and a Bose-Einstein-condensation superfluid occurs. Furthermore, we analyze the order parameter tensor in a total pseudospin basis, investigate its momentum dependence in the singlet, triplet, and quintet sectors, and compare the results with the simpler case of spin-1/2 fermions in the presence of spin-flip and spin-orbit fields, where only singlet and triplet channels arise. Finally, we analyze in detail spectroscopic properties of color superfluids in the presence of color-flip and color-orbit fields, such as the quasiparticle excitation spectrum, momentum distribution, and density of states to help characterize all the encountered topological quantum phases, which can be realized in fermionic isotopes of lithium, potassium, and ytterbium atoms with three internal states trapped.

We study strong, light-mediated, resonant dipole-dipole interactions in two-dimensional planar lattices of cold atoms. We provide a detailed analysis for the description of the dipolar point emitter lattice plane as a “superatom” whose response is similar to electromagnetically induced transparency but which exhibits an ultranarrow collective size-dependent subradiant resonance linewidth. The superatom model provides intuitively simple descriptions for the spectral response of the array, including the complete reflection, full transmission, narrow Fano resonances, and asymptotic expressions for the resonance linewidths of the collective eigenmodes. We propose a protocol to transfer almost the entire radiative excitation to a single correlated subradiant eigenmode in a lattice and show that the medium obtained by stacked lattice arrays can form a cooperative magnetometer. Such a magnetometer utilizes similar principles as magnetometers based on the electromagnetically induced transparency. The accuracy of the cooperative magnetometer, however, is not limited by the single-atom resonance linewidth but the much narrower collective linewidth that results from the strong dipole-dipole interactions.

In an anisotropic medium, the refractive index depends on the direction of propagation. Zero index in a fixed direction implies a stretching of the wave to uniformity along that axis, reducing the effective number of dimensions by 1. Here we investigate two-dimensional gyrotropic media where the refractive index is 0 in a complex valued direction, finding that the wave becomes an analytic function of a single complex variable $z$. For simply connected media this analyticity implies unidirectional propagation of electromagnetic waves, similar to the edge states that occur in photonic “topological insulators.” For a medium containing holes the propagation is no longer unidirectional. We illustrate the sensitivity of the field to the topology of the space using an exactly solvable example. To conclude we provide a generalization of transformation optics where a complex coordinate transformation can be used to relate ordinary anisotropic media to the recently highlighted gyrotropic ones supporting one-way edge states.

We consider the propagation of both fully coherent and partially coherent complex scalar fields, through linear shift-invariant imaging systems. The state of such imaging systems is characterized by a countable infinity of aberration coefficients, the values for which can be viewed as coordinates for an infinity of orthogonal axes that span the aberration space into which the output propagates. For fully coherent complex scalar disturbances, we study the propagation of the field through the imaging system, while for partially coherent disturbances it is the two-point correlation functions whose propagation we study. For both systems we write down generalized propagators in both real and Fourier space, differential equations for evolution through aberration space, transport equations, and Hamilton-Jacobi equations. A generalized form of the Wolf equations is a special case of our formalism.

Measurements performed on distant parts of an entangled quantum state can generate correlations incompatible with classical theories respecting the assumption of local causality. This is the phenomenon known as quantum nonlocality that, apart from its fundamental role, can also be put to practical use in applications such as cryptography and distributed computing. Clearly, developing ways of quantifying nonlocality is an important primitive in this scenario. Here, we propose to quantify the nonlocality of a given probability distribution via its trace distance to the set of classical correlations. We show that this measure is a monotone under the free operations of a resource theory and, furthermore, that it can be computed efficiently with a linear program. We put our framework to use in a variety of relevant Bell scenarios also comparing the trace distance to other standard measures in the literature.

A quantum observable and a channel are considered compatible if they form parts of the same measurement device, otherwise they are incompatible. Constrains on compatibility between observables and channels can be quantified via relations highlighting the necessary tradeoffs between noise and disturbance within quantum measurements. In this paper we shall discuss the general properties of these compatibility relations and then fully characterize the compatibility conditions for an unbiased qubit observable and a Pauli channel. The implications of the characterization are demonstrated on some concrete examples.