We describe propagation of light in a gas with periodic density modulation, demonstrating photonic-crystal-like refraction with negative refraction angles. We address the role of poorly defined boundaries and damping and derive an optical analog of the quantum adiabatic theorem. For Cs atoms in an optical lattice, we show that relying on semiadiabatic propagation one can excite and spatially split positively and negatively refracting modes at experimentally available gas densities.

The knowledge of the x-ray index of refraction of materials is important for the interpretation or simulation of many x-ray physics phenomena. But its precise and accurate experimental determination is challenging, particularly in the hard x-ray energy range above 100 keV. In this article we present and discuss experimental measurements of the real and imaginary part of the index of refraction for different materials based on x-ray grating interferometry at energies above 130 keV.

We study the possibility of asymmetric transmission induced by a non-Hermitian scattering center embedded in a one-dimensional waveguide, motivated by the aim of realizing quantum diodes in a non-Hermitian system. It is shown that a $\mathcal{PT}$-symmetric non-Hermitian scattering center always has symmetric transmission although the dynamics within the isolated center can be unidirectional, especially at its exceptional point. We propose a concrete scheme based on a flux-controlled non-Hermitian scattering center, which comprises a non-Hermitian triangular ring threaded by an Aharonov-Bohm flux. The analytical solution shows that such a complex scattering center acts as a diode at the resonant energy level of the spectral singularity, exhibiting perfect unidirectionality of the transmission. The connections between the phenomena of the asymmetric transmission and reflectionless absorption are also discussed.

The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits. We also analyze the quantum circuits implementing the various entanglement classes.

Motivated by recent experimental implementations of artificial gauge fields for gases of cold atoms, we study the scattering properties of particles that are subjected to time-periodic Hamiltonians. Making use of Floquet theory, we focus on translationally invariant situations in which the single-particle dynamics can be described in terms of spatially extended Floquet-Bloch waves. We develop a general formalism for the scattering of these Floquet-Bloch waves. An important role is played by the conservation of Floquet quasienergy, which is defined only up to the addition of integer multiples of $\hslash \omega$ for a Hamiltonian with period $T=2\pi /\omega$. We discuss the consequences of this for the interpretation of “elastic” and “inelastic” scattering in cases of physical interest. We illustrate our general results with applications to the scattering of a single particle in a Floquet-Bloch state from a static potential and the scattering of two bosonic particles in Floquet-Bloch states through their interparticle interaction. We analyze examples of these scattering processes that are closely related to the schemes used to generate artificial gauge fields in cold-atom experiments, through optical dressing of internal states, or through time-periodic modulations of tight-binding lattices. We show that the effects of scattering cannot, in general, be understood by an effective time-independent Hamiltonian, even in the limit $\omega \to \infty$ of rapid modulation. We discuss the relative sizes of the elastic scattering (required to stabilize many-body phases) and of the inelastic scattering (leading to deleterious heating effects). In particular, we describe how inelastic processes that can cause significant heating in the current experimental setup can be switched off by additional confinement of transverse motion.

The search for robust experimental proof of supersolidity has encountered many complicating factors, such as temperature-dependent changes in the mechanical properties of solid ${}^4\mathrm{He}$ which mimic the signature of superfluid flow. As a result, the physical existence and true nature of this unique state of matter are still under debate. Here we consider ${}^4\mathrm{He}$ stabilized by a one-dimensional periodic potential whose lattice spacing is similar to the length scale of the ${}^4\mathrm{He}{\text{−}}^4\mathrm{He}$ interaction. We use the Bogoliubov transformation to calculate the excitation spectrum, finding that when interactions between nearest or next-nearest neighbors are strongly attractive, there is a finite positive gap in energy between the delocalized ground state and the lowest energy excitations, which is significantly larger than the both the lambda temperature and the melting temperature. Not only does this make the system stable against phase separation of particles and vacancies, but it also means that it should be possible to observe a supersolid at a high-enough temperature that superfluidity in bulk liquid ${}^4\mathrm{He}$ or changes in the mechanical properties of bulk solid ${}^4\mathrm{He}$ do not obscure it. The properties of experimentally achievable materials which could support this type of supersolid are also discussed.

We investigate quadratic solitons consisting of fundamental waves and oscillatory second harmonics, which can be stable when subject to boundary confinement. A family of quadratic solitons whose fundamental waves can be monopole, dipole, or even multipole are found numerically. The existence of solitons, depending on the sample size and degree of nonlocality, are given for strongly, generally, and weakly nonlocal cases, respectively.

We present extreme-ultraviolet (EUV) fluorescence spectra of Ar clusters irradiated by intense EUV free-electron-laser (FEL) pulses focused to intensities of up to $3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ at a wavelength of 51 nm. The spectra reveal fluorescence at wavelengths shorter than that of the incident radiation, which can be assigned to EUV fluorescence lines from excited multiply charged ions $\mathrm{A}{\mathrm{r}}^{z+*}$ with $z$ as high as 6. This demonstrates that charge states as high as 7+ are produced by the FEL irradiation. The dependence of the spectra on cluster size shows that the highly charged ions are generated at the cluster surface, indicating inhomogeneous charging. The FEL power dependencies of the spectral features suggest that the inhomogeneous distribution of charge within the clusters reduces ionization thresholds at the cluster surface.

We have demonstrated that supersonic beams of oxygen molecules $\left({\text{O}}_2\right)$ in the ground rotational state were slowed to a near standstill by a linear Zeeman decelerator and successfully confined spatially in an anti-Helmholtz magnetic trap. The translational temperature of the decelerated ${\text{O}}_2$ molecules was about 800 mK. The demonstrated trapping capability of paramagnetic species opens up various possibilities for the investigation of cold collisions and reactions of various radicals in the sub-kelvin regime by spatially confining them in a magnetic trap.

Quantum contextuality is a nonintuitive property of quantum mechanics that distinguishes it from any classical theory. A complementary quantum property is quantum nonlocality, which is an essential resource for many quantum information tasks. Here we experimentally study the contextual and nonlocal properties of polarization biphotons. First, we investigate the ability of the biphotons to exhibit contextuality by testing the violation of the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality. In order to do so, we used the original protocol suggested in the KCBS paper and adjusted it to the real scenario, where some of the biphotons are distinguishable. Second, we transmitted the biphotons through different unital channels with a controlled amount of noise. We measured the decohered output states and demonstrated that the ability to exhibit quantum contextuality using the KCBS inequality is more fragile to noise than the ability to exhibit nonlocality.

In the study of systems that cannot be described classically, the Wigner inequality, has received only a small amount of attention. In this paper we extend the Wigner inequality—originally derived in 1969—and show how it may be used to contradict local realism with only coincidence detections in the absence of two-outcome measurements—that is, for any system where only one possible result of a pair of potential outcomes can be registered. It thus encapsulates a much broader class of measurement schemes than could previously violate a local-realistic inequality. This is possible due to an assumption of “extended fairness” on the measurement outcomes, which we posit is highly plausible. We then apply this inequality to a recently constructed setup with access to entangled pairs of photons with very high angular momenta, in which no previously derived local-realistic inequality could successfully be used without making very broad assumptions. We thus demonstrate the versatility of this inequality under very lossy conditions.

We compare the accuracy, precision, and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modeling and maximum likelihood estimation is superior to common techniques based on Fourier analysis. Even for simple two-parameter estimation problems, the Bayesian approach yields higher accuracy and precision for the parameter estimates obtained. It requires less data, is more flexible in dealing with different model systems, can deal better with uncertainty in initial conditions and measurements, and enables adaptive refinement of the estimates. The comparison results show that this holds for measurements of large ensembles of spins and atoms limited by Gaussian noise as well as projection noise limited data from repeated single-shot measurements of a single quantum device.

We consider fundamental features which emerge in the mechanics of quasiparticles with nonmonotonic (as a function of $p^2$) dispersion law. Quasiparticles of this kind abound in modern physics, with examples ranging from holes in quantum wells to edge magnetic states in quantum wires to photons in atomic vapors to polaritons in photonic crystals and in trapped-atom lattices. The motion of such a particle in repulsive potentials gives rise to a number of counterintuitive phenomena, which carry a promise of unusual optical manifestations. A classical particle can be trapped by repulsive potentials, and the likelihood of this trapping may increase with the value of the angular momentum. Further, in contrast to the usual quantum-mechanical notion, the particle always has a quasibound state in a two-dimensional, central-force repulsive potential, while it may have no bound states in a one-dimensional analog of this potential. The binding energy of these states and their inherent decay rate are determined by a complex interplay of the parameters of the potential, the particle dispersion law, and the value of the angular momentum. We construct the energy spectrum of quasibound states in a repulsive Coulomb potential, estimate their lifetime, and predict their optical manifestations as inverted hydrogen spectral-line series.

We identify gauge freedoms in quantum error correction (QEC) codes and introduce strategies for optimal control algorithms to find the gauges which allow the easiest experimental realization. Hereby, the optimal gauge depends on the underlying physical system and the available means to manipulate it. The final goal is to obtain optimal decompositions of QEC codes into elementary operations which can be realized with high experimental fidelities. In the first part of this paper, this subject is studied in a general fashion, while in the second part, a system of trapped ions is treated as a concrete example. A detailed optimization algorithm is explained and various decompositions are presented for the three qubit code, the five qubit code, and the seven qubit Steane code.

Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the Rényi entropies is expected to enhance their scope in applications. We prescribe Rényi generalizations for any quantum information measure which consists of a linear combination of von Neumann entropies with coefficients chosen from the set $\left\{-1,0,1\right\}$. As examples, we describe Rényi generalizations of the conditional quantum mutual information, some quantum multipartite information measures, and the topological entanglement entropy. Among these, we discuss the various properties of the Rényi conditional quantum mutual information and sketch some potential applications. We conjecture that the proposed Rényi conditional quantum mutual informations are monotone increasing in the Rényi parameter, and we have proof of this conjecture for some special cases.

Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon-number distribution of a linear-optical interferometric network, which is fed with single-photon Fock-state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear-optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fock states by a displacement operation, namely the displaced Fock states and the photon-added coherent states. It is easy to show that the sampling problem associated with displaced single-photon Fock states and a displaced photon-number detection scheme is in the same complexity class as boson sampling for all values of displacement. On the other hand, we show that the sampling problem associated with single-photon-added coherent states and the same displaced photon-number detection scheme demonstrates a computational-complexity transition. It transitions from being just as hard as boson sampling when the input coherent amplitudes are sufficiently small to a classically simulatable problem in the limit of large coherent amplitudes.

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit, more accurate approximations that still allow for efficient simulation can be obtained by including Clifford operators and Pauli operators conditional on measurement. We examine the feasibility of employing these expanded error approximations to obtain better threshold estimates. We calculate the level-1 pseudothreshold for the Steane [[7,1,3]] code for amplitude damping and dephasing along a non-Clifford axis. The expanded channels estimate the actual channel action more accurately than the Pauli channels before error correction. However, after error correction, the Pauli twirling approximation yields very accurate estimates of the performance of quantum error-correcting protocols in the presence of the actual noise channel.

High-dimensional quantum key distribution (HD-QKD) allows two parties to generate multiple secure bits of information per detected photon. In this work, we show that decoy-state protocols can be practically implemented for HD-QKD using only one or two decoy states. HD-QKD with two decoy states, under realistic experimental constraints, can generate multiple secure bits per coincidence at distances over 200 km and at rates similar to those achieved by a protocol with infinite decoy states. Furthermore, HD-QKD with only one decoy state is practical at short distances, where it is almost as secure as a protocol with two decoy states. HD-QKD with only one or two decoy states can therefore be implemented to optimize the rate of secure quantum communications.

We propose and study a model of forced evaporation of atomic clouds in crossed-beam optical dipole traps that explicitly includes the growth of a population in the “wings” of the trap and its subsequent impact on dimple temperature and density. It has long been surmised that a large wing population is an impediment to the efficient production of Bose-Einstein condensates in crossed-beam traps. Understanding the effect of the wings is particularly important for $\lambda =1.06\mu \mathrm{m}$ traps, for which a large ratio of Rayleigh range to beam waist results in wings that are large in volume and extend far from the dimple. Key ingredients to our model's realism are (1) our explicit treatment of the nonthermal, time-dependent energy distribution of wing atoms in the full anharmonic potential and (2) our accurate estimations of transition rates among dimple, wing, and free-atom populations, obtained with Monte Carlo simulations of atomic trajectories. We apply our model to trap configurations in which neither, one, or both of the wing potentials are made unbound by applying a “tipping” gradient. We find that forced evaporation in a trap with two bound wing potentials produces a large wing population which can collisionally heat the dimple so strongly as to preclude reaching quantum degeneracy. Evaporation in a trap with one unbound wing, such as that made by crossing one vertical beam and one horizontal beam, also leads to a persistent wing population which dramatically degrades the evaporation process. However, a trap with both wings tilted so as to be just unbound enjoys a nearly complete recovery of efficient evaporation. By introducing to our physical model an ad hoc, tunable escape channel for wing atoms, we study the effect of partially filled wings, finding that a wing population caused by single-beam potentials can drastically slow down evaporative cooling and increase the sensitivity to the choice of $\eta$.

Motivated by recent efforts in creating flat bands in ultracold atomic systems, we investigate how to probe a flat band in an optically trapped spin-orbital-coupled Bose-Einstein condensate using Bragg spectroscopy. We find that the excitation spectrum and the dynamic structure factor of the condensate are dramatically altered when the band structure exhibits various levels of flatness. In particular, when the band exhibits perfect flatness around the band minima corresponding to a near-infinite effective mass, a quadratic dispersion emerges in the low-energy excitation spectrum; in sharp contrast, for the opposite case when an ordinary band is present, the familiar linear dispersion arises. Such linear-to-quadratic crossover in the low-energy spectrum presents a striking manifestation of the transition of an ordinary band into a flat band, thereby allowing a direct probe of the flat band by using Bragg spectroscopy.