We investigate collective aspects of Rydberg excitations in ultracold mesoscopic samples. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitations are many-body Rabi oscillations, spatial correlations between atoms, as well as fluctuations in the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schrödinger equation, using a “superatom” approach. We find that, under certain conditions, these many-body behaviors could be observed experimentally.

We propose a strategy to enhance the atom-to-molecule conversion efficiency near a Feshbach resonance. Based on the mean-field approximation, we derive the fixed point solutions of the classical Hamiltonian. Rabi oscillation between the atomic and molecular states around fixed point solutions and its oscillation period are discussed. By designing a sequence of magnetic field pulses in analogy with Ramsey experiments, we show that a much higher atom-to-molecule conversion efficiency can be accessed by tuning the pulse durations appropriately.

We analyze how noise correlations probed by time-of-flight experiments reveal antiferromagnetic (AF) correlations of fermionic atoms in two-dimensional and three-dimensional optical lattices. Combining analytical and quantum Monte Carlo calculations using experimentally realistic parameters, we show that AF correlations can be detected for temperatures above and below the critical temperature for AF ordering. It is demonstrated that spin-resolved noise correlations yield important information about the spin ordering. Finally, we show how to extract the spin correlation length and the related critical exponent of the AF transition from the noise.

Classical and quantum theories of time-symmetric smoothing, which can be used to optimally estimate wave forms in classical and quantum systems, are derived using a discrete-time approach, and the similarities between the two theories are emphasized. Application of the quantum theory to homodyne phase-locked loop design for phase estimation with narrowband squeezed optical beams is studied. The relation between the proposed theory and weak value theory of Aharonov et al. is also explored.

We investigate realistic experimental conditions under which the collective Dicke model can be implemented in the ion-cavity QED context. We show how ideal subradiance and superradiance can be observed and we propose an experiment to generate entanglement exploiting the existence of the subradiant state. We explore the conditions to achieve optimal entanglement generation and we show that they are reachable with current experimental technology.

We address quantum estimation of displacement and squeezing parameters by the class of probes made of Gaussian states undergoing Kerr interaction. If we fix the overall energy available to the probe, without posing any constraint on the available Gaussian squeezing, then Gaussian squeezing represents the optimal resource for parameter estimation. On the other hand, in the more realistic case where the amount of Gaussian squeezing is fixed, or even absent, then Kerr interaction turns out to be useful to improve estimation, especially for probe states with large amplitude. Our results indicate that precision achievable with current technology Gaussian squeezing may be attained and surpassed for realistic values of the Kerr coupling.

Resonance fluorescence equations are derived and solved for strong-coupling semiconductor quantum-dot systems using a fully quantized multimode theory and a cluster-expansion approach. A reduced model is developed to explain the origin of autocorrelation and cross-correlation resonances in the two-photon emission spectrum of the fluorescent light. These resonances are traced back to the two-photon strong-coupling states of Jaynes-Cummings ladder. The accuracy of the reduced model is verified via numerical solution of the resonance fluorescence equations. The analysis reveals the direct relation between the squeezed-light emission and the strong-coupling states in optically excited semiconductor systems.

Nonlinearity and sharp transmission spectra of random one-dimensional nonlinear layered structures are combined together to produce photon pairs with extremely narrow spectral bandwidths. Indistinguishable photons in a pair are nearly unentangled. Also two-photon states with coincident frequencies can be conveniently generated in these structures if photon pairs generated into a certain range of emission angles are superposed. If two photons are emitted into two different resonant peaks, the ratio of their spectral bandwidths may differ considerably from one and two photons remain nearly unentangled.

It is discovered theoretically that significant confinement resonances in an $nl$ photoionization of a multielectron atom $A$ encaged in carbon fullerenes $A@{\text{C}}_{60}$ may reappear and be strong at photon energies far exceeding the $nl$ ionization threshold, as a general phenomenon. The reasons for this phenomenon are unraveled. The $\text{Ne}2p$ photoionization of the endohedral anion $\text{Ne}@\text{C}_{60}{}^{5-}$ in the photon energy region of about a thousand eV above the $2p$ threshold is chosen as a case study.

The optimum gauge function is determined for an $\text{H}_2{}^{+}$ ion in an ultra strong magnetic field by using the Kennedy-Kobe theory [P. K. Kennedy and D. H. Kobe, Phys. Rev. A 30, 51 (1984)] combined with the finite element method. The divergence-free current density obtained by this method vanishes at the positions of protons. From this observation, we put the question as to whether there exists the nuclear cusp condition of current density or not, which is analogous to Kato’s cusp condition of electron density. We will show a few cases where the current density vanishes exactly at the maximum of electron density.

In terms of a photon wave function corresponding to the $\left(1,0\right)+\left(0,1\right)$ representation of the Lorentz group, the radiation and Coulomb fields within a source-free region can be described unitedly by a Lorentz-covariant Dirac-like equation. In our formalism, the relation between the positive- and negative-energy solutions of the Dirac-like equation corresponds to the duality between the electric and magnetic fields, rather than to the usual particle-antiparticle symmetry. The Zitterbewegung (ZB) of photons is studied via the momentum vector of the electromagnetic field, which shows that only in the presence of virtual longitudinal and scalar photons, the ZB motion of photons can occur, and its vector property is described by the polarization vectors of the electromagnetic field.

A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission coefficients. This property reveals an interesting resonance effect with possible applications in waveguide physics. We study the spectral singularities of a complex barrier potential and explore their application in designing a waveguide that functions as a resonator. We show that for the easily accessible sizes of the waveguide and its gain region, we can realize the spectral singularity-related resonance phenomenon at almost every wavelength within the visible spectrum or outside it.

We report measurements and simulations of laser-induced fluorescence in ultracold neutral plasmas. We focus on the earliest times, when the plasma equilibrium is evolving and before the plasma expands. In the simulation, the ions interact via the Yukawa potential in a small cell with wrapped boundary conditions. We solve the optical Bloch equation for each ion in the simulation as a function of time. Both the simulation and experiment show the initial increase in ion fluorescence, disorder-induced heating, and coherent oscillation of the rms ion velocity. Detailed modeling of the fluorescence signal makes it possible to use fluorescence spectroscopy to probe ion dynamics in ultracold and strongly coupled plasmas.

We study the ionization of a highly excited Rydberg atom subjected to a periodic sequence of external electric-field pulses. Such systems are important laboratory and theoretical models of classical and quantum chaos. Furthermore, a good theoretical understanding of this chaos is important for controlling electronic states in atoms, as has been demonstrated in a series of recent experiments on the creation and control of electronic wave packets. Here, we present a theoretical analysis of the chaotic ionization of a hydrogen atom subjected to alternating positive and negative impulses. This analysis is based on the observation that the ionization of the atom is due to a turnstile in phase space which promotes the electronic state from negative to positive energy. The geometry of the lobes associated with the turnstile provides a clear picture of how the ionization process proceeds. Using this geometric intuition, we propose two experimental protocols to directly reveal the importance of the turnstile lobes in the laboratory.

We introduce a two-dimensional model of a laser cavity based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity and a lattice potential accounting for the transverse grating. A remarkable fact is that localized vortices, built as sets of four peaks pinned to the periodic potential, may be stable without the unphysical diffusion term, which was necessary for the stabilization in previously studied models. The vortices are chiefly considered in the onsite (rhombic) form, but the stabilization of offsite vortices (square-shaped ones) and quadrupoles is demonstrated too. Stability regions for the rhombic vortices and fundamental solitons are identified in the model’s parameter space, and scenarios of the evolution of unstable vortices are described. An essential result is a minimum strength of the lattice potential which is necessary to stabilize the vortices. The stability border is also identified in the case of the self-focusing quintic term in the underlying model, which suggests a possibility of the supercritical collapse. Beyond this border, the stationary vortex turns into a vortical breather, which is subsequently replaced by a dipolar breather and eventually by a single-peak breather.

We characterize attosecond pulses in a train using both the well established “reconstruction of attosecond beating by interference of two-photon transitions” (RABITT) technique and the recently demonstrated in situ method, which is based on a weak perturbation of the harmonic generation process by the second harmonic of the laser field. The latter technique determines the characteristics of the single atom emission, while RABITT allows one to measure attosecond pulses “on target.” By comparing the results of the two methods, the influence of propagation and filtering on the attosecond pulses can be extracted.

This paper extends the existing theory of two-carrier photorefractivity resonance, which is generally applied to iron doped indium phosphide (InP:Fe), to the case of low nonharmonic illumination. The space charge field profile is computed, and the variations of its amplitude, width and position are determined as functions of the background intensity. The effect of photorefractive resonance on these quantities is evidenced, contributing to the understanding of published experimental results in InP:Fe.

For an arbitrary field with finite photon number inside a leaky cavity, we show that the null-result measurement can be conditionally reversed, using either multiple atoms or a multilevel atom. Even with photons detected, a certain class of fields can still be probabilistically recovered. The state protection probability in such a system can be significantly high.

A general quantum theory of self-induced transparency (SIT) solitons is developed with nonlinear quantum effects of atoms taken into account. The quantization starts from the coarse-grain-averaged light-atom interaction Hamiltonian by which the quantum effects of ensemble atoms are modeled. The calculation of quantum properties is performed by the backpropagation method, which takes into account the contribution of the field continuum parts and the atomic fluctuations. The detectable squeezing ratio with a general homodyne local oscillator can be simulated for practical experimental realizations. Schemes for generating quantum correlation through SIT soliton interaction are also proposed and analyzed.

We investigate the entanglement of assistance which quantifies capabilities of producing pure bipartite entangled states from a pure tripartite state. The lower bound and upper bound of entanglement of assistance are obtained. In the light of the upper bound, monogamy constraints are proved for arbitrary $n$-qubit states.