Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely correlated states or matrix-product operators, designed to capture mixed states of one-dimensional quantum systems. It is a well-known open problem to find an efficient algorithm that decides whether a given matrix-product operator actually represents a physical state that in particular has no negative eigenvalues. We address and answer this question by showing that the problem is provably undecidable in the thermodynamic limit and that the bounded version of the problem is NP-hard (nondeterministic-polynomial-time hard) in the system size. Furthermore, we discuss numerous connections between tensor network methods and (seemingly) different concepts treated before in the literature, such as hidden Markov models and tensor trains.

For a self-gravitating particle of mass $\mu$ in orbit around a Kerr black hole of mass $M\gg \mu$, we compute the $\mathcal{O}(\mu /M)$ shift in the frequency of the innermost stable circular equatorial orbit due to the conservative piece of the gravitational self-force acting on the particle. Our treatment is based on a Hamiltonian formulation of the dynamics in terms of geodesic motion in a certain locally defined effective smooth spacetime. We recover the same result using the so-called first law of binary black-hole mechanics. We give numerical results for the innermost stable circular equatorial orbit frequency shift as a function of the black hole’s spin amplitude, and compare with predictions based on the post-Newtonian approximation and the effective one-body model. Our results provide an accurate strong-field benchmark for spin effects in the general-relativistic two-body problem.

We present constraints on models containing non-standard-model values for the spin $J$ and parity $P$ of the Higgs boson $H$ in up to $9.7{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected with the D0 detector at the Fermilab Tevatron Collider. These are the first studies of Higgs boson $J^P$ with fermions in the final state. In the $ZH\to \ell \ell b\overline{b}$, $WH\to \ell \nu b\overline{b}$, and $ZH\to \nu \nu b\overline{b}$ final states, we compare the standard model (SM) Higgs boson prediction, $J^P=0^{+}$, with two alternative hypotheses, $J^P=0^{-}$ and $J^P=2^{+}$. We use a likelihood ratio to quantify the degree to which our data are incompatible with non-SM $J^P$ predictions for a range of possible production rates. Assuming that the production rate in the signal models considered is equal to the SM prediction, we reject the $J^P=0^{-}$ and $J^P=2^{+}$ hypotheses at the 97.6% CL and at the 99.0% CL, respectively. The expected exclusion sensitivity for a $J^P=0^{-}$ ($J^P=2^{+}$) state is at the 99.86% (99.94%) CL. Under the hypothesis that our data are the result of a combination of the SM-like Higgs boson and either a $J^P=0^{-}$ or a $J^P=2^{+}$ signal, we exclude a $J^P=0^{-}$ fraction above 0.80 and a $J^P=2^{+}$ fraction above 0.67 at the 95% CL. The expected exclusion covers $J^P=0^{-}$ ($J^P=2^{+}$) fractions above 0.54 (0.47).

Maximizing the information transmission rate through quantum channels is essential for practical implementation of quantum communication. Time-division multiplexing is an approach for which the ultimate rate requires the ability to manipulate and detect single photons on ultrafast time scales while preserving their quantum correlations. Here we demonstrate the demultiplexing of a train of pulsed single photons using time-to-frequency conversion while preserving their polarization entanglement with a partner photon. Our technique converts a pulse train with 2.69 ps spacing to a frequency comb with 307 GHz spacing which may be resolved using diffraction techniques. Our work enables ultrafast multiplexing of quantum information with commercially available single-photon detectors.

We determine the optical response of a thin and dense layer of interacting quantum emitters. We show that, in such a dense system, the Lorentz redshift and the associated interaction broadening can be used to control the transmission and reflection spectra. In the presence of overlapping resonances, a dipole-induced electromagnetic transparency (DIET) regime, similar to electromagnetically induced transparency (EIT), may be achieved. DIET relies on destructive interference between the electromagnetic waves emitted by quantum emitters. Carefully tuning material parameters allows us to achieve narrow transmission windows in, otherwise, completely opaque media. We analyze in detail this coherent and collective effect using a generalized Lorentz model and show how it can be controlled. Several potential applications of the phenomenon, such as slow light, are proposed.

The concept of volume holography is applied to the design of an optical superlattice for the nonlinear harmonic generation. The generated harmonic wave can be considered as a holographic image caused by the incident fundamental wave. Compared with the conventional quasi-phase-matching method, this new method has significant advantages when applied to complicated nonlinear processes such as the nonlinear generation of special beams. As an example, we experimentally realized a second-harmonic Airy beam, and the results are found to agree well with numerical simulations.

We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at a finite electron density nonperturbatively, i.e., by including vertex corrections to high orders. Using the Holstein model on a square lattice as a prototypical example, we demonstrate that our method is capable of providing accurate results in the thermodynamic limit in all regimes from a renormalized Fermi liquid to a single polaron, across the nonadiabatic region where Fermi and Debye energies are of the same order of magnitude. By accounting for vertex corrections, the accuracy of the theoretical description is increased by orders of magnitude relative to the lowest-order self-consistent Born approximation employed in most studies. We also find that for the electron-phonon coupling typical for real materials, the quasiparticle effective mass increases and the quasiparticle residue decreases with increasing the electron density at constant electron-phonon coupling strength.

Quantum Hall edge channels at integer filling factor provide a unique test bench to understand the decoherence and relaxation of single-electron excitations in a ballistic quantum conductor. In this Letter, we obtain a full visualization of the decoherence scenario of energy (Landau)- and time (Levitov)-resolved single-electron excitations at filling factor $\nu =2$. We show that the Landau excitation exhibits a fast relaxation followed by spin-charge separation whereas the Levitov excitation only experiences spin-charge separation. We finally suggest to use Hong-Ou-Mandel-type experiments to probe specific signatures of these different scenarios.

In high energy physics, unknown particles are identified by determining their mass from the Cherenkov radiation cone that is emitted as they pass through the detector apparatus. However, at higher particle momentum, the angle of the Cherenkov cone saturates to a value independent of the mass of the generating particle, making it difficult to effectively distinguish between different particles. Here, we show how the geometric formalism of transformation optics can be applied to describe the Cherenkov cone in an arbitrary anisotropic medium. On the basis of these results, we propose a specific anisotropic metamaterial to control Cherenkov radiation, leading to enhanced sensitivity for particle identification at higher momentum.

We have studied neutron diffuse scattering in a ${\mathrm{Sr}}_{0.61}{\mathrm{Ba}}_{0.39}{\mathrm{Nb}}_2{\mathrm{O}}_6$ single crystal by neutron backscattering at sub-$\mu \mathrm{eV}$ energy resolution. We can identify two response components with transverse polarization: an elastic (resolution limited) central peak, which monotonically increases with decreasing temperature, and a quasielastic central peak, having a maximum intensity around the ferroelectric phase transition close to 350 K. In contrast to previous neutron experiments on this and other relaxor materials, we were able to observe a temperature dependence of the characteristic frequency of these fluctuations, obeying the same Vogel-Fulcher law as the dynamic part of the dielectric permittivity of this material. In this way our findings provide a first direct link between the Vogel-Fulcher-type frequency dependence of dielectric permittivity and dynamic nanoscale lattice modulations with a transverse correlation length of about 5–10 unit cells.

Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper’s quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the $d$-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.

Beyond mean-field methods are very successful tools for the description of large-amplitude collective motion for even-even atomic nuclei. The state-of-the-art framework of these methods consists in a generator coordinate method based on angular-momentum and particle-number projected triaxially deformed Hartree-Fock-Bogoliubov (HFB) states. The extension of this scheme to odd-mass nuclei is a long-standing challenge. We present for the first time such an extension, where the generator coordinate space is built from self-consistently blocked one-quasiparticle HFB states. One of the key points for this success is that the same Skyrme interaction is used for the mean-field and the pairing channels, thus avoiding problems related to the violation of the Pauli principle. An application to ${}^{25}\mathrm{Mg}$ illustrates the power of our method, as agreement with experiment is obtained for the spectrum, electromagnetic moments, and transition strengths, for both positive and negative parity states and without the necessity for effective charges or effective moments. Although the effective interaction still requires improvement, our study opens the way to systematically describe odd-$A$ nuclei throughout the nuclear chart.

We suggest and analyze a laser with a mirror realized by Fano interference between a waveguide and a nanocavity. For small-amplitude modulation of the nanocavity resonance, the laser can be modulated at frequencies exceeding 1 THz, not being limited by carrier dynamics as for conventional lasers. For larger modulation, a transition from pure frequency modulation to the generation of ultrashort pulses is observed. The laser dynamics is analyzed by generalizing the field equation for conventional lasers to account for a dynamical mirror, described by coupled mode theory.

We study the ground state phases of a rotating two-component, or binary, Bose-Einstein condensate, wherein one component possesses a large permanent magnetic dipole moment. A variety of nontrivial phases emerge in this system, including a half-quantum vortex (HQV) chain phase and a HQV molecule phase, where HQVs bind at short distances. We attribute these phases to the development of a minimum in the HQV interaction potential, which emerges without coherent coupling or attractive interactions between the components. Thus, we show that the presence of dipolar interactions in this system provides a unique mechanism for the formation of HQV molecules and results in a rich ground state phase diagram.

The atomic structure of the $\mathrm{Si}(111)\text{−}(5\times 2)\text{−}\mathrm{Au}$ surface, a periodic gold chain on the silicon surface, has been a long-debated issue in surface science. The recent three candidates, the so-called Erwin-Barke-Himpsel (EBH) model [S. C. Erwin, I. Barke, and F. J. Himpsel, Phys. Rev. B 80, 155409 (2009)], the Abukawa-Nishigaya (AN) model [T. Abukawa and Y. Nishigaya, Phys. Rev. Lett. 110, 036102 (2013)], and the Kwon-Kang (KK) model [S. G. Kwon and M. H. Kang, Phys. Rev. Lett. 113, 086101 (2014)] that has one additional Au atom than the EBH model are tested by surface x-ray diffraction data. A two-dimensional Patterson map constructed from the in-plane diffraction intensities rejects the AN model and prefers the KK model over the EBH model. On the basis of the arrangement of Au obtained from the Patterson map, all the reconstructed Si atoms, such as the so-called honeycomb chain structure, are directly imaged out by utilizing a holographic method. The KK model reproduces out-of-plane diffraction data as well.