In a three-level $\Lambda$ atomic system coupled by a symmetrical bichromatic laser field, a weak probe laser field shows multiple absorption peaks in the case of cold atoms. As for hot atomic vapors, we experimentally observe double symmetrical electromagnetically induced transparency windows instead of multiple absorption peaks. This abnormal spectrum is due to the Doppler averaging. The electromagnetically induced transparency windows observed here are useful for obtaining slow photons at different frequencies.

We propose a scheme to achieve controllable self-pulsing operation in a semiconductor photonic-crystal nanolaser. The scheme is based on coupling two asymmetric nanocavities and pumping only one of them. As a result, either periodic or chaotic subnanosecond $Q$-switched pulses can emerge. A coupled-mode approach is used to model the system and study the bifurcation diagram. An experimental realization is proposed on the basis of two evanescently coupled photonic-crystal nanocavities.

We propose a scheme to dynamically realize a quantum memory based on the toric code. The code is generated from qubit systems with typical two-body interactions (Ising, $XY$, Heisenberg) using periodic, NMR-like, pulse sequences. It allows one to encode the logical qubits without measurements and to protect them dynamically against the time evolution of the physical qubits. A weakly coupled cavity mode mediates a long-range attractive interaction between the stabilizer operators of the toric code, thereby suppressing the creation of thermal anyons. This significantly increases the lifetime of the memory compared to the code with noninteracting stabilizers. We investigate how the fidelity, with which the toric code is realized, depends on the period length $T$ of the pulse sequence and the magnitude of possible pulse errors. We derive an optimal period $T_{\text{opt}}$ that maximizes the fidelity.

The Floquet theorem allows one to reformulate periodic time-dependent problems such as the interaction of a many-body system with a laser field in terms of time-independent, field-dressed states, also known as Floquet states. If this was possible for density-functional theory as well, one could reduce in such cases time-dependent density-functional theory to a time-independent Floquet density-functional theory. We analyze under which conditions the Floquet theorem is applicable in a density-functional framework. By employing numerical ab initio solutions of the interacting time-dependent Schrödinger equation with time-periodic external potentials we show that the exact effective potential in the corresponding Kohn-Sham equation is not unconditionally periodic. Whenever several Floquet states in the interacting system are involved in a physical process the corresponding Hartree-exchange-correlation potential is not periodic with the external frequency only. Using an analytically solvable example we demonstrate that, in general, the periodicity of the time-dependent Kohn-Sham Hamiltonian cannot be restored by choosing a different initial state. Only if the external periodic potential is sufficiently weak such that the initial state of the interacting system evolves adiabatically to a single, field-dressed state, the resulting Kohn-Sham system admits the application of the Floquet theorem.

We present direct measurements of the hyperfine splitting of Rydberg states in ${}^{87}$Rb using electromagnetically induced transparency (EIT) spectroscopy in a room-temperature vapor cell. With this method, and in spite of Doppler broadening, linewidths of 3.7 MHz FWHM, i.e., significantly below the intermediate-state natural linewidth, are reached. This allows resolving hyperfine splittings for Rydberg $s$ states with $n=20,...,24$. With this method we are able to determine Rydberg state hyperfine splittings with an accuracy of approximately 100 kHz. Ultimately, our method allows accuracies of order 5 kHz to be reached. Furthermore, we present a direct measurement of hyperfine-resolved Rydberg-state Stark shifts. These results will be of great value for future experiments relying on excellent knowledge of Rydberg-state energies and polarizabilities.

Absolute cross sections for charge exchange, ionization, stripping, and excitation in K${}^{+}$-He collisions were measured in the ion energy range 0.7–10 keV. The experimental data and the schematic correlation diagrams are used to analyze and determine the mechanisms for these processes. The increase of the excitation probability of inelastic channels with the angle of scattering is revealed. An exceptionally highly excited state of He is observed and a peculiarity for the excitation function of the resonance line is explained. The intensity ratio for the excitation of the K II $\lambda =60.1$ nm and $\lambda =61.2$ nm lines is 5:1, which indicates the high probability for excitation of the singlet resonance level ${}^1{P}_1$ compared to the triplet level ${}^3{P}_1$. The similarity of the population of the $4p$ state of the potassium ion and atom as well as the anomalously small values of the excitation cross sections are explained.

We predict that classes of coherent matter waves can self-accelerate without the presence of an external potential. Such Bose-Einstein condensates can follow arbitrary power-law trajectories and can also take the form of diffraction-free Airy waves. We also show that suitably engineered radially symmetric matter waves can abruptly autofocus in space and time. We suggest different schemes for the preparation of the condensate using laser beams to imprint an amplitude or a phase pattern onto the matter wave. Direct and Fourier space generation of such waves is discussed using continuous and binary masks as well as magnetic mirrors and lenses. We study the effect of interactions and find that independently of the type and strength of the nonlinearity, the dynamics are associated with the generation of accelerating matter waves. In the case of strong attractive interactions, the acceleration is increased while the radiation reorganizes itself in the form of soliton(s).

We investigate light scattering by coated spheres composed of a dispersive plasmonic core and a dielectric shell. By writing the absorption cross section in terms of the internal electromagnetic fields, we demonstrate it is an observable sensitive to interferences that ultimately lead to the Fano effect. In particular, we show that unconventional Fano resonances, recently discovered for homogeneous spheres with large dielectric permittivities, can also occur for metallic spheres coated with single dielectric layers. These resonances arise from the interference between two electromagnetic modes with the same multipole moment inside the shell and not from interactions between the various plasmon modes of different layers of the particle. In contrast to the case of homogeneous spheres, unconventional Fano resonances in coated spheres exist even in the Rayleigh limit. These resonances can induce an off-resonance field enhancement, which is approximately 1 order of magnitude larger than the one achieved with conventional Fano resonances. We find that unconventional and conventional Fano resonances can occur at the same input frequency provided the dispersive core has a negative refraction index. This leads to an optimal field enhancement inside the particle, a result that could be useful for potential applications in plasmonics.

Beam propagation beyond the paraxial approximation is studied in an optically written waveguide structure. The waveguide structure, which leads to diffractionless light propagation, is imprinted on a medium consisting of a five-level atomic vapor driven by an incoherent pump and two coherent spatially dependent control and plane-wave fields. We first study beam propagation in a single optically written waveguide and find that the paraxial approximation does not provide an accurate description of the probe propagation. We then employ coherent control fields such that two parallel and one tilted Gaussian beams produce a branched waveguide structure. The tilted beam allows selective steering of the probe beam into different branches of the waveguide structure. The transmission of the probe beam for a particular branch can be improved by changing the width of the titled Gaussian control beam as well as the intensity of the spatially dependent incoherent pump field.

A simple conserved quantity for electromagnetic fields in vacuum was discovered by Lipkin in 1964. In recent years, this “zilch” has been used as a measure of the chirality of light. The conservation of optical zilch is here derived from a simple symmetry of the standard electromagnetic action. The symmetry transformation allows the identification of circularly polarized plane waves as zilch eigenstates. The same symmetry is present for electromagnetism in a homogeneous, dispersive medium, allowing the derivation of the zilch density and flux in such a medium. Optical helicity density and flux are also derived for a homogeneous, dispersive medium. For monochromatic beams in vacuum, optical zilch is proportional to optical helicity. This monochromatic zilch-helicity relation acquires a factor of the square of the phase index in a dispersive medium.

We present a rigorous formulation of the effects of spectral broadening on emission of partially coherent source ensembles embedded in multilayered formations with arbitrarily shaped interfaces, provided geometrical optics is valid. The resulting ray-optical theory, applicable to a variety of optical systems from terahertz lenses to photovoltaic cells, quantifies the fundamental interplay between bandwidth and layer dimensions, and sheds light on common practices in optical analysis of statistical fields, e.g., disregarding multiple reflections or neglecting interference cross terms.

We study a strongly interacting array of Bose-Einstein condensates trapped in a one-dimensional (1D) optical lattice. The system is described by a nonstandard 1D Bose-Hubbard model in which both the tunneling matrix element and the on-site atomic interaction depend on the lattice site due to the interaction broadening of the local wave function and the system inhomogeneity. We quantitatively compare theoretical analyses based on the Gutzwiller approximation with experimental observations obtained using ytterbium atoms. We show that atomic states are highly number squeezed owing to strong interatomic interactions as the lattice potential becomes deeper. Furthermore, the calculated inhomogeneous collisional broadening of spectroscopic line shapes agrees well with high-resolution spectra measured by using the ultranarrow magnetic quadrupole ${}^1{S}_0{-}^3{P}_2$ transition.

Geometric phase plays an important role in evolution of pure or mixed quantum states. However, when a system undergoes decoherence the development of geometric phase may be inhibited. Here we show that when a quantum system interacts with two competing environments there can be enhancement of geometric phase. This effect is akin to a Parrondo-like effect on the geometric phase which results from quantum frustration of decoherence. Our result suggests that the mechanism of two competing decoherence can be useful in fault-tolerant holonomic quantum computation.

Uncertainty relations are often considered to be a measure of incompatibility of noncommuting observables. However, such a consideration is not valid in general, motivating the need for an alternate measure that applies to any set of noncommuting observables. We present an operational approach to quantifying incompatibility without invoking uncertainty relations. Our measure aims to capture the incompatibility of noncommuting observables as manifest in the nonorthogonality of their eigenstates. We prove that this measure has all the desired properties: It is zero when the observables commute, strictly greater than zero when they do not, and is maximum when they are mutually unbiased. We also obtain tight upper bounds on this measure for any $N$ noncommuting observables and compute it exactly when the observables are mutually unbiased.

We use a quasi-Hamiltonian formalism to describe the dissipative dynamics of a circuit-QED qubit that is affected by several fluctuating two-level systems with a $1/f$-noise power spectrum. The qubit-resonator interactions are described by the Jaynes-Cummings model. We argue that the presence of pure dephasing noise in such a qubit-resonator system will also induce an energy relaxation mechanism via a fluctuating dipole-coupling term. This random modulation of the coupling is seen to lead to rich physical behavior. For non-Markovian noise, the coupling can either worsen or alleviate decoherence, depending on the initial conditions. The magnetization noise leads to behavior resembling the collapse and revival of Rabi oscillations if the photons are in a coherent state. For a broad distribution of noise couplings, the frequency of these oscillations depends on the mean noise strength. We describe this behavior semianalytically and find it to be independent of the number of fluctuators. This phenomenon could be used as an in situ probe of the noise characteristics.

We investigate entanglement generation in one-dimensional quantum spin systems with the sinusoidal deformation. In the system, the energy scale of each local term in the Hamiltonian is modified according to a position-dependent function ${\sin }^{\alpha }\left[\frac{\pi }{N}(x-\frac{1}{2})\right]$, where $x$ is the position of the local term and $N$ is the length of the system. We show that at zero temperature the system with $\alpha \ge 2$ is able to generate a sizable entanglement between two spins at open edges, even when the two spins are infinitely far apart. This long-distance entanglement is rather robust against thermal fluctuations and survives up to a temperature that decays with the system size slowly, in an algebraic form.

An atomic comb structure consisting of both spatial and spectral components is proposed for the implementation of quantum memory using inhomogeneously broadened atomic ensembles, such as rare-earth ions trapped in solids. The spatiospectral comb can be prepared in two-level atoms provided a third energy level is available for atomic population storage. The output photon is retrieved from the memory as a spatially diffracted photon echo. The angle between the input and output directions is controlled by the spatial component of the atomic comb. The memory efficiency is analyzed using coupled wave theory, which results in memory efficiency varying with the retrieval angle: 54.1$\%$ in collinear, 81.6$\%$ in perpendicular, and 100$\%$ in counterpropagating configurations. An experimental method for creating a multidimensional atomic comb is suggested.

We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-$1/2$ fermions to encode the classical information, we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be sufficiently wide while the momentum wave packets of other particles are kept relatively narrow. In this way, one can take advantage of the fact that boosts entangle the spin and momentum degrees of freedom of spin-$1/2$ fermions to increase the accessible information in the former. We close the paper with a discussion of how this relativistic quantum channel cannot in general be described by completely positive quantum maps.

The dynamic polarizabilities of the $4s$, $3d$, and $4p$ states of Ca${}^{+}$, are calculated using a relativistic structure model. The wavelengths at which the Stark shifts between different pairs of transitions are zero are computed. Experimental determination of the magic wavelengths can be used to estimate the ratio of the $f_{3d_J\to 4p_{J^{\prime }}}$ and $f_{4s_{1/2}\to 4p_{J^{\prime }}}$ oscillator strengths. This could prove valuable in developing better atomic structure models and, in particular, lead to improved values of the polarizabilities needed in the evaluation of the blackbody radiation shift of the Ca${}^{+}$ ion.