In the task of quantum state exclusion, we consider a quantum system prepared in a state chosen from a known set. The aim is to perform a measurement on the system which can conclusively rule that a subset of the possible preparation procedures cannot have taken place. We ask what conditions the set of states must obey in order for this to be possible and how well we can complete the task when it is not. The task of quantum state discrimination forms a subclass of this set of problems. Within this paper, we formulate the general problem as a semidefinite program (SDP), enabling us to derive sufficient and necessary conditions for a measurement to be optimal. Furthermore, we obtain a necessary condition on the set of states for exclusion to be achievable with certainty, and we give a construction for a lower bound on the probability of error. This task of conclusively excluding states has gained importance in the context of the foundations of quantum mechanics due to a result from Pusey, Barrett, and Rudolph (PBR). Motivated by this, we use our SDP to derive a bound on how well a class of hidden variable models can perform at a particular task, proving an analog of Tsirelson's bound for the PBR experiment and the optimality of a measurement given by PBR in the process. We also introduce variations of conclusive exclusion, including unambiguous state exclusion, and state exclusion with worst-case error.

The Kibble-Zurek mechanism is central to the nonequilibrium dynamics and topological structure that occur during phase transitions, which may be manifested as the cosmological strings of the early universe or vortex lines in a superfluid. In recent years, there has been broad interest in performing quantum simulations using different well-controlled physical setups, whose full controllability allows access to regimes that may be difficult to explore. Here, we demonstrate a proof-of-principle quantum simulation of the Kibble-Zurek mechanism in the quantum Ising model as it undergoes a quenched phase transition. We used an electron charge qubit in a double quantum dot as the simulator. We engineered the qubit under Landau-Zener dynamics and successfully reproduced the Kibble-Zurek-like dependence of the topological defect density on the quench time. The high level of tunability of two-level semiconductor systems and the intriguing analogy between the two phenomena (the Kibble-Zurek mechanism and Landau-Zener transition) offer a platform on which to gain new insight into the dynamics of various phase transitions.

We study the dynamics of spatially accelerating beams impinging on refractive-index potentials. We concentrate our attention to the particular case of Airy-type optical waves that are reflected and transmitted by two generic classes of potentials. These are (a) localized potentials whose index contrast reduces to zero outside a specific region and (b) smooth-interface sigmoid-type potentials that take different constant values outside a bounded region. We find analytic expressions for the beam dynamics for particular types of potentials which are in excellent agreement with the numerical simulations. Our results show that, in general, the parabolic trajectory of the Airy wave is not maintained by the transmitted and reflected waves. An exception is made in the case of reflection from piecewise linear potentials, where the reflected wave follows a parabolic trajectory that is, in general, different from the incident.

We investigate Zitterbewegung (ZB) behavior in a graphene superlattice with generations of massless Dirac fermions having highly anisotropic group velocities, which results from a graphene subject to one-dimensional periodic potentials. It is shown that with tuning parameters of the periodic potential, the frequency of ZB oscillations can be of order ${10}^{12}$ Hz, the amplitude can increase to hundreds of angstroms, and their attenuation can become much slower. The required parameters of the graphene superlattice can be realized under current experimental conditions, thus providing a good system for probing the ZB effect experimentally.

We show that connections between a degree of incompatibility of pairs of observables and the strength of violations of Bell's inequality found in recent investigations can be extended to a general class of probabilistic physical models. It turns out that the property of universal uniform steering is sufficient for the saturation of a generalized Tsirelson bound, corresponding to maximal violations of Bell's inequality. It is also found that a limited form of steering is still available and sufficient for such saturation in some state spaces where universal uniform steering is not given. The techniques developed here are applied to the class of regular polygon state spaces, giving a strengthening of known results. However, we also find indications that the link between incompatibility and Bell violation may be more complex than originally envisaged.

The quantification of the “measurement uncertainty”aspect of Heisenberg's uncertainty principle—that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two incompatible observables—has regained a lot of interest recently. Several approaches have been proposed and debated. In this paper we consider Ozawa's definitions for inaccuracies (as root-mean-square errors) in approximate joint measurements, and study how these are constrained in different cases, whether one specifies certain properties of the approximations—namely their standard deviations and/or their bias—or not. Extending our previous work [C. Branciard, Proc. Natl. Acad. Sci. USA 110, 6742 (2013)], we derive error-trade-off relations, which we prove to be tight for pure states. We show explicitly how all previously known relations for Ozawa's inaccuracies follow from ours. While our relations are in general not tight for mixed states, we show how these can be strengthened and how tight relations can still be obtained in that case.

The boson sampler proposed by Aaronson and Arkhipov is a nonuniversal quantum computer, which can serve as evidence against the extended Church-Turing thesis. It samples the probability distribution at the output of a linear unitary optical network with indistinguishable single photons at the input. Four experimental groups have already tested their small-scale prototypes with up to four photons. A boson sampler with a few dozens of single photons is believed to be hard to simulate on a classical computer. For scalability of a realistic boson sampler with current technology it is necessary to know the effect of the photon mode mismatch on its operation. Here a nondeterministic model of the boson sampler is analyzed, which employs partially indistinguishable single photons emitted by identical sources. A sufficient condition on the average mutual fidelity $\langle \mathcal{F}\rangle$ of the single photons is found, which guarantees that the realistic boson sampler outperforms the classical computer. Moreover, the boson-sampler computer with partially indistinguishable single photons is scalable and has more power than classical computers when the single-photon mode mismatch $1-\langle \mathcal{F}\rangle$ scales as $O\left(N^{-3/2}\right)$ with the total number of photons $N$.

Encoding information in quantum systems can offer surprising advantages but at the same time there are limitations that arise from the fact that measuring an observable may disturb the state of the quantum system. In our work, we provide an in-depth analysis of a simple question: What happens when we perform two measurements sequentially on the same quantum system? This question touches upon some fundamental properties of quantum mechanics, namely the uncertainty principle and the complementarity of quantum measurements. Our results have interesting consequences, for example, they can provide a simple proof of the optimal quantum strategy in the famous Clauser-Horne-Shimony-Holt game. Moreover, we show that the way information is encoded in quantum systems can provide a different perspective in understanding other fundamental aspects of quantum information, like nonlocality and quantum cryptography. We prove some strong equivalences between these notions and provide a number of applications in all areas.

The $K$-shell level radiative, nonradiative, and total widths, $K$-shell fluorescence yields, and $K$-shell hole state lifetimes for atoms with $20\le Z\le 30$ have been calculated in a fully relativistic way using the extensive multiconfiguration Dirac-Fock calculations with the inclusion of the Breit interaction and QED corrections and also using multiconfiguration Dirac-Hartree-Slater calculations.

Scientific research fields for future source of energy such as inertial confinement fusion research and astrophysics studies, especially with satellite observatories, advance into stages of precision physics. The relevant atomic data are not only enormous but also of accuracy according to requirements, especially for both energy levels and the collision data. We propose a scenario to provide such abundant atomic data with enough accuracy based on analytical continuation properties of the scattering matrices, which is a combination of indispensable theoretical computations and benchmark experimental measurements. Using our modified $R$-matrix method we can directly calculate the scattering matrices in the whole energy regions, from which we can obtain all energy levels and the related scattering cross sections with accuracies comparable with spectroscopic precision. The $e$+Kr${}^{+}$ system is used as an illustrative example; the degrees of accuracies of scattering matrices of each partial wave are calculated within about 6%, which should be much more accurate than state-of-the-art scattering experiments.

In a high magnetic field of 3–7 T, nitric oxide (NO) molecules are excited by the double-resonance method through the intermediate $A{}^2{\Sigma }^{+}{F}_1(v^{\prime \prime }=0,N^{\prime \prime }=0)$ level to the Landau levels in the energy region above the zero-field ionization limit to the NO${}^{+}X{}^1{\Sigma }^{+}(v^{+}=0,N^{+}=0)$ ion. By detecting NO${}^{+}$ ions, the photoionization cross section through the Landau levels is determined as a function of the second laser's frequency. The cross section contains broad structures and fine structures. Fourier analysis of the cross section and classical trajectory calculations of the Rydberg electron demonstrate that the broad structure is formed by the Landau level generated by the cyclotron motion of the electron around the $N^{+}=0$ core in a plane perpendicular to the field, while the fine structure is formed by the Landau level generated by the three-dimensional cyclotron motion around the excited $N^{+}=2$ core. By simulating the energy structure of the Landau level, the electron's orbital angular momentum is confirmed to be decoupled from the core rotation in the Landau levels. From the selection rules of the excitation, it is demonstrated that the Landau levels with the $N^{+}=0$ core are excited using the $s$ character in the $A{}^2{\Sigma }^{+}$ state, while those with the $N^{+}=2$ core are excited using the $d$ character. The dominant partial wave, thus determined, explains well the starting direction of the classical trajectory.

We develop the spatiotemporal description of matter-field interaction within the strong-field approximation. We show that the space-time form of the ionized wave function has analogies with the diffraction phenomenon, allowing for the definition of two different regimes: Fresnel and Fraunhofer. We demonstrate that the standard saddle-point analysis corresponds to the paraxial approximation of the Fraunhofer case. The Fresnel number therefore appears as a useful parameter to characterize the validity of the saddle-point approach. We give a closed formula for the ionized wave function beyond the standard saddle-point analysis that takes the form of a chirped Volkov wave. We apply our results to the study of high-order-harmonic generation, demonstrating that the saddle-point approximation breaks down for extended systems, i.e., when the Fresnel number approaches or is above the unity. As a simple example, we analyze the harmonic generation of dissociating $H_2^{+}$ and demonstrate the Fresnel number as a useful parameter to determine the accuracy of the semiclassical saddle-point approach.

The recently realized spin-orbit-coupled quantum gases [Lin et al., Nature (London) 471, 83 (2011); Wang et al., Phys. Rev. Lett. 109, 095301 (2012); Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)] mark a breakthrough in the cold atom community. In these experiments, two hyperfine states are selected from a hyperfine manifold to mimic a pseudospin-1/2 spin-orbit-coupled system by the method of Raman dressing, which is applicable to both bosonic and fermionic gases. In this paper, we show that the method used in these experiments can be generalized to create any large pseudospin spin-orbit-coupled gas if more hyperfine states are coupled equally by the Raman lasers. As an example, we study, in detail, a quantum gas with three hyperfine states coupled by the Raman lasers and show, when the state-dependent energy shifts of the three states are comparable, triple-degenerate minima will appear at the bottom of the band dispersions, thus, realizing a spin-1 spin-orbit-coupled quantum gas. A novel feature of this three-minima regime is that there can be two different kinds of stripe phases with different wavelengths, which has an interesting connection to the ferromagnetic and polar phases of spin-1 spinor Bose-Einstein condensates without spin-orbit coupling.

Topological phase engineering of neutral bosons loaded in an optical lattice opens a new window for manipulating of transport phenomena in such systems. Exploiting the Bose-Hubbard model and using the magnetic Kubo formula proposed in this paper we show that the optical conductivity abruptly changes for different flux densities in the Mott phase. Especially, when the frequency of the applied field corresponds to the on-site boson interaction energy, we observe insulator or metallic behavior for a given Hofstadter spectrum. We also prove that for different synthetic magnetic-field configurations the critical conductivity at the tip of the lobe is nonuniversal and depends on the energy minima of the spectrum. In the case of $1/2$ and $1/3$ flux per plaquette, our results are in good agreement with those of the previous Monte Carlo study. Moreover, we show that for half magnetic flux through the cell the critical conductivity suddenly changes in the presence of a superlattice potential with uniaxial periodicity.

We consider dynamic, i.e., frequency-dependent, correlations in noncondensed ultracold atomic Bose gases. In particular, we consider the single-particle correlation function and its power spectrum. We compute this power spectrum for a one-component Bose gas, and we show how it depends on the interatomic interactions that lead to a finite single-particle relaxation time. As another example, we consider the power spectrum of spin-current fluctuations for a two-component Bose gas and show how it is determined by the spin-transport relaxation time.

We observed electromagnetically induced transparency-based four-wave mixing (FWM) in the pulsed regime at low light levels. The FWM conversion efficiency of $3.8\left(9\right)\%$ was observed in a four-level system of cold ${}^{87}\mathrm{Rb}$ atoms using a driving laser pulse with a peak intensity of $\approx 80$ $\mu \mathrm{W}/{\mathrm{cm}}^2$, corresponding to an energy of $\approx 60$ photons per atomic cross section. Comparison between the experimental data and the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)] showed good agreement. Additionally, a high conversion efficiency of $46\left(2\right)\%$ was demonstrated when applying this scheme using a driving laser intensity of $\approx 1.8$ $\mathrm{mW}/{\mathrm{cm}}^2$. According to our theoretical predictions, this FWM scheme can achieve a conversion efficiency of nearly $100\%$ when using a dense medium with an optical depth of 500.

We study analytically and numerically an optical analog of tachyon condensation in amplifying plasmonic arrays. Optical propagation is modeled through coupled-mode equations, which in the continuous limit can be converted into a nonlinear one-dimensional Dirac-like equation for fermionic particles with imaginary mass, i.e., fermionic tachyons. We demonstrate that the vacuum state is unstable and acquires an expectation value with broken chiral symmetry, corresponding to the homogeneous nonlinear stationary solution of the system. The quantum field theory analog of this process is the condensation of unstable fermionic tachyons into massive particles. This paves the way for using amplifying plasmonic arrays as a classical laboratory for spontaneous symmetry breaking effects in quantum field theory.

This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations of unitary quantum mechanics, extending the intuition of symmetries and conserved quantities to the dissipative case. We combine and apply various results to obtain an exhaustive characterization of the infinite-time behavior of Lindblad evolution, including both the structure of the infinite-time density matrix and its dependence on initial conditions. The effect of the environment in the infinite-time limit can therefore be tracked exactly for arbitrary state initialization and without knowledge of dynamics at intermediate time. As a consequence, sufficient criteria for determining the steady state of a Lindblad master equation are obtained. These criteria are knowledge of the initial state, a basis for the steady-state subspace, and all conserved quantities. We give examples of two-qubit dissipation and single-mode $d$-photon absorption where all quantities are determined analytically. Applications of these techniques to quantum information, computation, and feedback control are discussed.

Can a Bell test with no detection loophole be demonstrated for multiphoton entangled states of light within the current technology? We examine the possibility of a postselection-free Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality test with an unsymmetrical polarization singlet. To that end we employ a preselection procedure which is performed prior to the test. It allows using imperfect (coarse-grained) binary photodetection in the test. We show an example of a preselection scheme which improves violation of the CHSH inequality with the micro-macro polarization singlet produced by the optimal quantum cloning. The preselection is realized by a quantum filter which is believed not to be useful for this purpose.