Using the example of dysprosium atoms in an optical lattice, we show how dipolar interactions between magnetic dipoles can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-$\frac{1}{2}$ or spin-1 degree of freedom in each atom. Thinking of spin-$\frac{1}{2}$ particles as hard-core bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the $\nu =\frac{1}{2}$ Laughlin state. Thinking of spin-1 particles as two-component hard-core bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed.

Optical forces acting on dielectric particles inside waveguides are studied. The investigation is carried out within the framework of the two-dimensional model: a cylinder inside a parallel-plate waveguide with perfect metal walls. It is shown that although the appearance of resonant states can lead to a significant increase of backscattering and, therefore, the propelling force, the transverse force can either keep the particle in the location of the efficient propulsion or push it away. The propulsion and trapping regimes are related to the change of the resonant wavelength with particle location. Besides the geometrical and material parameters, the polarization of the incident mode is shown to significantly affect the particle dynamics. The relation of the resonant-state formation and Wood's anomalies in periodic gratings is also discussed.

We present an experimental study of optical frequency comb generation based on cascaded quadratic nonlinearities inside a continuous-wave-pumped optical parametric oscillator. We demonstrate comb states which produce narrow-linewidth intermode beat note signals, and we verify the mode-spacing uniformity of the comb at the Hertz level. We also show that the spectral quality of the comb can be improved by modulating the parametric gain at a frequency that corresponds to the comb mode spacing. We have reached a high average output power of over 4 W in the near-infrared region, at $\sim 2\mu \mathrm{m}$.

In a three-body system of identical bosons interacting through a large $S$-wave scattering length $a$, there are several sets of features related to the Efimov effect that are characterized by discrete scale invariance. Effective field theory was recently used to derive universal relations between these Efimov features that include the first-order correction due to a nonzero effective range $r_s$. We reveal a simple pattern in these range corrections that had not been previously identified. The pattern is explained by the renormalization group for the effective field theory, which implies that the Efimov three-body parameter runs logarithmically with the momentum scale at a rate proportional to $r_s/a$. The running Efimov parameter also explains the empirical observation that range corrections can be largely taken into account by shifting the Efimov parameter by an adjustable parameter divided by $a$. The accuracy of universal relations that include first-order range corrections is verified by comparing them with various theoretical calculations using models with nonzero range.

The temperature dependence of the asymmetry between Stokes and anti-Stokes Raman scattering can be exploited for self-calibrating, optically based thermometry. In the context of cavity optomechanics, we observe the cavity-enhanced scattering of light interacting with the standing-wave drumhead modes of a ${\mathrm{Si}}_3{\mathrm{N}}_4$ membrane mechanical resonator. The ratio of the amplitude of Stokes to anti-Stokes scattered light is used to measure temperatures of optically cooled mechanical modes, down to the level of a few vibrational quanta. We demonstrate that the Raman-ratio technique allows the measurement of the physical temperature of our device over a range extending from cryogenic temperatures to within an order of magnitude of room temperature.

We derive explicit bounds for the average entropy characterizing measurements of a pure quantum state of size $N$ in $L$ orthogonal bases. Lower bounds lead to novel entropic uncertainty relations, while upper bounds allow us to formulate universal certainty relations. For $L=2$ the maximal average entropy saturates at $logN$ because there exists a mutually coherent state, but certainty relations are shown to be nontrivial for $L\ge 3$ measurements. In the case of a prime power dimension, $N=p^k$, and the number of measurements $L=N+1$, the upper bound for the average entropy becomes minimal for a collection of mutually unbiased bases. An analogous approach is used to study entanglement with respect to $L$ different splittings of a composite system linked by bipartite quantum gates. We show that, for any two-qubit unitary gate $U\in \text{U}\left(4\right)$ there exist states being mutually separable or mutually entangled with respect to both splittings (related by $U$) of the composite system. The latter statement follows from the fact that the real projective space $\mathbb{R}{P}^3\subset \mathbb{C}{P}^3$ is nondisplaceable by a unitary transformation. For $L=3$ splittings the maximal sum of $L$ entanglement entropies is conjectured to achieve its minimum for a collection of three mutually entangled bases, formed by two mutually entangling gates.

The Lieb-Liniger model describes bosons with contact interactions in one-dimensional space. In the limit of weak repulsive particle interactions, there are two types of low-lying excitation spectrum. The first is reproduced by the Bogoliubov dispersion relation, and the other is believed to correspond to dark soliton excitations. While there are various evidences that the type II spectrum is related to dark solitons, it has not been shown that measurements of positions of particles reveal dark soliton density profiles. Here, we employ the Bethe ansatz approach and show that dark solitons emerge in the measurement process if the system is prepared in an eigenstate corresponding to the type II spectrum. We analyze single and double dark solitons as well as weak and strong interaction regimes.

The simulation of quantum systems has been a key aim of quantum technologies for decades, and generalization to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open system dynamics in terms of an environment of minimal size and a time-dependent Hamiltonian. This enables the implementation of a continuous-time simulation with a finite environment, whereas state-of-the-art methods require an infinite environment or only match the simulation at discrete times. We find the necessary and sufficient conditions for this Hamiltonian to be well behaved, and when these are not met, we show that there exists an approximate Hamiltonian that is well behaved and look into its applications.

Using a classical ensemble method, a scaling law of nonsequential double ionization (NSDI) of atoms was concluded by comparing the correlated momentum distributions (CMDs) of two electrons from NSDI. The scaling law states that the CMD from an atom driven by a laser field of frequency $\omega$ and intensity $I$ is the same as that from another atom irradiated by the laser field of frequency $k\omega$ and intensity $k^{3}I$. The scaling ratio $k$ equals the ratio of the second ionization potentials (IPs) of two atoms. This study suggests that the target atoms with smaller second IPs would be a better choice for enhancing the NSDI rate.

We study the generation of terahertz radiation from atoms and molecules driven by an ultrashort fundamental laser and its second-harmonic field by solving the time-dependent Schrödinger equation (TDSE). The comparisons between one-, two-, and three-dimensional TDSE numerical simulations show that the initial ionized wave packet and its subsequent acceleration in the laser field and rescattering with long-range Coulomb potential play key roles. We also present the dependence of the optimum phase delay and yield of terahertz radiation on the laser intensity, wavelength, duration, and ratio of two-color laser components. Terahertz wave generation from model hydrogen molecules is further investigated by comparing with high harmonic emission. It is found that the terahertz yield follows the alignment dependence of the ionization rate, while the optimal two-color phase delays vary by a small amount when the alignment angle changes from 0 to 90 degrees, which reflects the alignment dependence of attosecond electron dynamics. Finally, we show that terahertz emission might be used to clarify the origin of interference in high harmonic generation from aligned molecules by coincidentally measuring the alignment-dependent THz yields.

The key feature of optomechanics is that its basic interactions are inherently nonlinear. This feature allows coherent and nonclassical effects such as squeezing on the mechanical mode induced by chaotic incoherent light. Since this effect is too challenging to observe directly in the membrane-in-the-middle arrangement of quantum optomechanics, we analyze an analogical high-order nonlinear effect and propose to simulate it all-optically. Specifically, we exploit hybrid quantum optics based on single photon states and homodyne detection to conditionally construct a simulator for noise-driven nonclassical effects. We show that this simulation can confirm the presence of squeezing caused by nonlinear coupling pumped by a noisy light. Our proposal opens the possibilities to emulate nonclassical effects challenging on the natural experimental platforms.

The dynamics involved in three-body breakup of carbon dioxide upon the impact of 1-MeV ${\mathrm{Ar}}^{8+}$ ions is investigated. Among the six possible fragmentation channels of ${\mathrm{CO}}_2{}^{q+}$ $(q=4,5)$, where all fragments are charged, two charge-asymmetric fragmentation channels show evidence of a sequential breakup process. It has been observed that the molecular structures tend towards deformed geometry as the initial charge on the precursor molecular ion increases. The total energy deposition to the system is found to play a key role in deciding between different breakup pathways.

We formulate a quantum-mechanical model for infrared-streaked photoelectron (PE) emission by ultrashort extreme ultraviolet (XUV) pulses from an adsorbate-covered metal surface, exposing the influence of microscopic PE dispersion in substrate and adsorbate on the interpretation of streaked photoemission spectra and photoemission time delays. We validate this numerical model first by reproducing measured relative photoemission delays (a) between valence-band and $2p$-core-level (CL) PEs emitted from clean Mg(0001) surfaces and (b) between conduction-band (CB) and $4f$-CL PEs from clean W(110) surfaces at two XUV-pulse central photon energies. Next, applying this model to ultrathin Mg adsorbate layers on W(110) substrates, we reproduce (i) the measured nonmonotonic dependence of relative photoemission delays between CB and $\mathrm{Mg}(2p$) PEs and (ii) the monotonic dependence of relative delays between $\mathrm{W}(4f$) and $\mathrm{Mg}(2p$) PEs in a recent experiment [S. Neppl et al., Nature (London) 517, 342 (2015)].

We present a unified axiomatic approach to contextuality and nonlocality based on the fact that both are resource theories. In those theories, the main objects are consistent boxes, which can be transformed by certain operations to achieve certain tasks. The amount of resource is quantified by appropriate measures of the resource. Following a recent paper [J. I. de Vicente, J. Phys. A: Math. Theor. 47, 424017 (2014)], and recent development of abstract approach to resource theories, such as entanglement theory, we propose axioms and welcome properties for operations and measures of resources. As one of the axioms of the measure we propose the asymptotic continuity: the measure should not differ on boxes that are close to each other by more than the distance with a factor depending logarithmically on the dimension of the boxes. We prove that relative entropy of contextuality is asymptotically continuous. Considering another concept from entanglement theory (the convex roof of a measure), we prove that for some nonlocal and contextual polytopes, the relative entropy of a resource is upper bounded up to a constant factor by the cost of the resource. Finally, we prove that providing a measure $X$ of resource does not increase under allowed class of operations such as, e.g., wirings, the maximal distillable resource which can be obtained by these operations is bounded from above by the value of $X$ up to a constant factor. We show explicitly which axioms are used in the proofs of presented results, so that analogous results may remain true in other resource theories with analogous axioms. We also make use of the known distillation protocol of bipartite nonlocality to show how contextual resources can be distilled.

Open quantum walks (OQWs) are exclusively driven by dissipation and are formulated as completely positive trace-preserving (CPTP) maps on underlying graphs. The microscopic derivation of discrete and continuous-in-time OQWs is presented. It is assumed that connected nodes are weakly interacting via a common bath. The resulting reduced master equation of the quantum walker on the lattice is in the generalized master equation form. The time discretization of the generalized master equation leads to the OQW formalism. The explicit form of the transition operators establishes a connection between dynamical properties of the OQWs and thermodynamical characteristics of the environment. The derivation is demonstrated for the examples of the OQW on a circle of nodes and on a finite chain of nodes. For both examples, a transition between diffusive and ballistic quantum trajectories is observed and found to be related to the temperature of the bath.

It is well known that Hermitian operators have real eigenvalues while non-Hermitian ones may have complex eigenvalues. Recently, numerical and analytical results indicated that the spectra of many non-Hermitians Hamiltonians $H$ are indeed real if they are invariant under the combined action of self-adjoint parity $P$ and time reversal $T.$ The concept of a pseudo-Hermitian operator showed that the remarkable spectral properties of the $PT$-symmetric Hamiltonians follow from their pseudo-Hermiticity. It is possible to explain these observations by the concept of pseudo-Hermitian operators and to formulate completeness and orthonormality relations. Most of the effort has been devoted to study time-independent non-Hermitian systems. In this paper, we study the exactly solvable time-dependent periodic pseudo-Hermitian Hamiltonians. The method introduced, to make the reality of eigenvalues and phases, is based on a Floquet decomposition of the evolution operator $U^H\left(t\right)=Z^H\left(t\right)exp\left(i{M}^{H}t\right)$ associated with the periodic pseudo-hermitian Hamiltonian $H\left(t\right)=H(t+T)$. One of the results found in this paper concerns a calculation of Berry's phase for periodic, but not necessarily adiabatic, pseudo-Hermitian Hamiltonians. A two-level pseudo-Hermitian system is discussed as an illustrative example.