For scattering of electromagnetic waves by a dielectric cylinder with periodically modulated permittivity we focus on the vicinity of the frequency of the wave with regard to the eigenfrequencies of bound states in the continuum. Then response of the cylinder becomes extremely sensitive to the angle of incidence and polarization of the plane wave. The cross section of the scattering of electromagnetic waves with mixed polarization undergoes crucial change from the Bragg shape to the Fano shape by rotation of the polarization that paves a way to tuning of Fano resonances by an external source.

Measurement combined with feedback that aims to restore a presumed premeasurement quantum state will yield this state after a few measurement-feedback cycles even if the actual state of the system initially had no resemblance to the presumed state. Here we introduce this mechanism of self-fulfilling prophecy and show that it can be used to prepare finite-dimensional quantum systems in target states or force them into target dynamics. Using two-level systems as an example, we demonstrate that self-fulfilling prophecy protects the system against noise and tolerates imprecision of feedback up to the level of the measurement strength. By means of unsharp measurements the system can be driven deterministically into arbitrary, smooth quantum trajectories.

A general barrier-traversal-time operator is constructed using the time-of-arrival formalism. We study the operator's dynamics and determine the role played by the time-energy commutation relation. It turns out that similar dynamics is observed whether the traversal-time operator is canonically conjugate to the system Hamiltonian or not. We also use the barrier-traversal-time operator to calculate the traversal-time distributions for different cases (free case, and above-the-barrier and under-the-barrier traversals). The peak of the traversal-time distributions coincides with the classical expected traversal times for the free case and the above-the-barrier case. We then present our interpretation of the time-energy uncertainty relation that is consistent with the different traversal-time distributions.

Quantum coherence and nonclassical correlation are key features of a quantum world. Quantifying coherence and nonclassical correlation are two key tasks in quantum information theory. First, we present a bona fide measure of quantum coherence by utilizing the Hellinger distance. This coherence measure is proven to fulfill all the criteria of a well-defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. In terms of this coherence measure, the distribution of quantum coherence in multipartite systems is studied and a corresponding polygamy relation is proposed. Its operational meanings and the relations between the generation of quantum correlations and the coherence are also investigated. Moreover, we present the Hellinger distance-based measure of nonclassical correlation, which not only inherits the nice properties of the Hellinger distance including contractivity, but also shows a powerful analytic computability for a large class of quantum states. We show that there is an explicit tradeoff relation satisfied by the quantum coherence and this nonclassical correlation.

We apply the theory of optimal control to the dynamics of two “gmon” qubits, with the goal of preparing a desired entangled ground state from an initial unentangled one. Given an initial state, a target state, and a Hamiltonian with a set of permissible controls, can we reach the target state with coherent quantum evolution, and, in that case, what is the minimum time required? The adiabatic theorem provides a far from optimal solution in the presence of a spectral gap. Optimal control yields the fastest possible way of reaching the target state and helps identify unreachable states. In the context of a simple quantum system, we provide examples of both reachable and unreachable target ground states, and show that the unreachability is due to a symmetry. We find the optimal protocol in the reachable case using three different approaches: (i) a brute-force numerical minimization, (ii) an efficient numerical minimization using the bang-bang ansatz expected from the Pontryagin minimum principle, and (iii) direct solution of the Pontryagin boundary value problem, which yields an analytical understanding of the numerically obtained optimal protocols. Interestingly, our system provides an example of singular control, where the Pontryagin theorem does not guarantee bang-bang protocols. Nevertheless, all three approaches give the same bang-bang protocol.

A closed expression is derived for the amount of resource present in a quantum state as quantified by a distance measure based on the Tsallis relative entropy introduced recently [H. Zhao and C.-s. Yu, Sci. Rep. 8, 299 (2018)], for any resource theory whose set of free states is described by the image of a unital resource-destroying map. By applying it to the resource theory of coherence it is demonstrated that the correct definition of a projective coarse-grained measurement needs to be modified in order for it to be correctly interpreted as a measurement which provides less information about a system's true state than the one obtained from a finer-grained measurement.

${}^{129}\mathrm{Xe}$ is an important candidate for the searches of electric dipole moments due to time-reversal and parity violations in diamagnetic atoms. In view of the similarities between the electric dipole moment and the polarizability from the point of view of many-body theory, we have performed rigorous calculations of the ground-state polarizability of ${}^{129}\mathrm{Xe}$ using a self-consistent relativistic coupled-cluster method and the relativistic normal coupled-cluster method. The discrepancy between the results from these two methods is 2%, but each of them differs from the accurate measurement of the polarizability of the ground state of ${}^{129}\mathrm{Xe}$ by 1%. Our results clearly suggest that the two theoretical methods we have employed in this work can be applied in the future to capture electron correlation effects in the electric dipole moment of ${}^{129}\mathrm{Xe}$ to a high degree of accuracy.

Measuring the full distribution of individual particles is of fundamental importance to characterize many-body quantum systems through correlation functions at any order. Here, we demonstrate the possibility to reconstruct the momentum-space distribution of three-dimensional interacting lattice gases atom by atom. This is achieved by detecting individual metastable ${}^4\mathrm{He}^{*}$ atoms in the far-field regime of expansion, when released from an optical lattice. We benchmark our technique with quantum Monte Carlo calculations, demonstrating the ability to resolve momentum distributions of superfluids occupying ${10}^5$ lattice sites. It permits a direct measure of the condensed fraction across phase transitions, as we illustrate on the superfluid-to-normal transition. Our single-atom-resolved approach opens a route to investigate interacting lattice gases through momentum correlations.

The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact and versatile description. However, care needs to be taken when several noise processes act simultaneously or the Hamiltonian evolution of the system is modified. Here, we show that generators can be added at the master equation level without compromising physicality only under restrictive conditions. Moreover, even when adding generators results in legitimate dynamics, this does not generally correspond to the true evolution of the system. We establish a general condition under which direct addition of dynamical generators is justified, showing that it is ensured under weak coupling and for settings where the free system Hamiltonian and all system-environment interactions commute. In all other cases, we demonstrate by counterexamples that the exact evolution derived microscopically cannot be guaranteed to coincide with the dynamics naively obtained by adding the generators.

In classic cases, Reichenbach's principle implies that discriminating between common causes and causality is unprincipled since the discriminative results essentially depend on the selection of possible conditional variables. For some typical quantum cases, K. Reid et al. [Nat. Phys. 11, 414 (2015)] presented the statistic $C$ which can effectively discriminate quantum common causes and quantum causality over two quantum random variables (i.e., qubits) and which only uses measurement information about these two variables. In this paper, we formalize general quantum common causes and general quantum causality. Based on the formal representation, we further investigate their decidability via the statistic $C$ in general quantum cases. We demonstrate that (i) $C\in \left[-1,\frac{1}{27}\right]$ if two qubits are influenced by quantum common causes; (ii) $C\in \left[-\frac{1}{27},1\right]$ if the relation between two qubits is quantum causality; (iii) a geometric picture can illuminate the geometric interpretation of the probabilistic mixture of quantum common causes and quantum causality. This geometric picture also provides a basic heuristic to develop more complete methods for discriminating the cases corresponding to $C\in \left[-\frac{1}{27},\frac{1}{27}\right]$. Our results demonstrate that quantum common causes and quantum causality can be discriminated in a considerable scope.

We study analytically the non-Markovianity of a spin ensemble, with arbitrary number of spins and spin quantum number, undergoing a pure dephasing dynamics. The system is considered as a part of a larger spin ensemble of any geometry with pairwise interactions. We derive exact formulas for the reduced dynamics of the system and for its non-Markovianity as assessed by the witness of Lorenzo et al. [Phys. Rev. A 88, 020102(R) (2013)]. The non-Markovianity is further investigated in the thermodynamic limit when the environment's size goes to infinity. In this limit and for finite-size systems, we find that the Markovian character of the system's dynamics crucially depends on the range of the interactions. We also show that when the system and its environment are initially in a product state, the appearance of non-Markovianity is independent of the entanglement generation between the system and its environment.

We consider entanglement extraction into two two-level Unruh-DeWitt detectors from a vacuum of a neutral massless quantum scalar field in a four-dimensional space-time, where the general monopole coupling to the scalar field is assumed. Based on the reduced density matrix of the two detectors derived within the perturbation theory, we show that the single copy of the entangled pair of the detectors can be utilized in quantum teleportation, even when the detectors are separated acausally, while we observe no violation of the Bell–CHSH inequality. In the case of the Minkowski vacuum, in particular, we find that entanglement usable in quantum teleportation is extracted due to the special relativistic effect when the detectors are in a relative inertial motion, while it is not when they are comoving inertially and the switching of the detectors is executed adiabatically at infinite past and future.

Implementation of logical entangling gates is an important step towards realizing a quantum computer. We use a gradient-based optimization approach to find single-qubit rotations which can be interleaved between applications of a noisy nonlocal gate to dramatically suppress arbitrary logical errors, while steering the evolution operator towards the perfectly entangling subset of $\text{SU}\left(4\right)$ gates. The modularity of the approach allows for application to any two-qubit system, regardless of the Hamiltonian or details of the experimental implementation. This approach is effective for both quasistatic and time-dependent $1/f^{\alpha }$ noise. We also show how the fidelity of the final operation depends on both the fidelity of the local rotations and the noise strength.

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way. With these ideas we find bound entangled grid states for two-particle systems of any dimension and multiparticle grid states that provide examples for the different aspects of genuine multiparticle entanglement. Our findings suggest that entanglement theory for grid states, although being a discrete set, has already a complexity similar to that for general states.

Measurement feedback is a versatile and powerful tool, although its performance is limited by several practical imperfections resulting from classical components. This paper shows that, for some typical quantum feedback control problems for state preparation (stabilization of a qubit or a qutrit, spin squeezing, and Fock state generation), the classical feedback operation can be replaced by a fully quantum one such that the state autonomously dissipates into the target or a state close to the target. The main common feature of the proposed quantum operation, which is called coherent feedback, is that it is composed of a series of dispersive and dissipative couplings inspired by the corresponding measurement feedback scheme.

We present first-principles calculations of the linear and nonlinear susceptibilities of ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and air in the midinfrared (MIR) wavelength regime from $1–4\mu \mathrm{m}$. We extract the frequency-dependent susceptibilities from the full time-dependent dipole moment that is calculated using time-dependent density functional theory. We find good agreement with curves derived from experimental results for the linear susceptibility and with measurements for the nonlinear susceptibility up to $2.4\mu \mathrm{m}$. We also find that the susceptibilities are insensitive to the laser intensity even in the strong field regime up to $5\times {10}^{13}{\mathrm{W}/\mathrm{cm}}^2$. Our results will allow accurate calculations of the long-distance propagation of intense midinfrared laser pulses in air.

Arrays of covalently bound organic molecules possess potential for light-harvesting and energy transfer applications due to the strong coherent dipole-dipole coupling between the transition dipole moments of the molecules involved. Here, we show that such molecular systems, based on perylene molecules, can be considered as arrays of qubits that are amenable for laser-driven quantum coherent control. The perylene monomers exhibit dephasing times four orders of magnitude longer than a typical gating time, thus allowing for the execution of a large number of gate operations on the subpicosecond timescale. Specifically, we demonstrate quantum logic gates and entanglement in bipartite (dimer) and tripartite (trimer) systems of perylene-based arrays. In dimers, naturally entangled states with a tailored degree of entanglement can be produced. The nonlocality of the molecular trimer entanglement is demonstrated by testing Mermin's (Bell-like) inequality violation.

We derive a theory for Bose condensation in nonequilibrium steady states of bosonic quantum gases that are coupled both to a thermal heat bath and to a pumped reservoir (or gain medium), while suffering from loss. Such a scenario describes photonic many-body systems such as exciton-polariton gases. Our analysis is based on a set of kinetic equations for a gas of noninteracting bosons. By identifying a dimensionless scaling parameter controlling the boson density, we derive a sharp criterion for which system states become selected to host a macroscopic occupation. We show that with increasing pump power, the system generically undergoes a sequence of nonequilibrium phase transitions. At each transition, a state either becomes or ceases to be Bose selected (i.e., to host a condensate): The state which first acquires a condensate when the pumping exceeds a threshold is the one with the largest ratio of pumping to loss. This intuitive behavior resembles simple lasing. In the limit of strong pumping, the coupling to the heat bath becomes dominant so that eventually the ground state is selected, corresponding to equilibrium(like) Bose condensation. For intermediate pumping strengths, several states become selected, giving rise to fragmented nonequilibrium Bose condensation. We compare these predictions to experimental results obtained for exciton polaritons in a double-pillar structure [M. Galbiati et al., Phys. Rev. Lett. 108, 126403 (2012)] and find good agreement. Our theory, moreover, predicts that the reservoir occupation is clamped at a constant value whenever the system hosts an odd number of Bose condensates.