Motivated by the first experimental evidence of ferromagnetic behavior in a three-dimensional ultracold atomic gas, we explore the possibility of itinerant ferromagnetism in a trapped two-dimensional atomic gas. Firstly, we develop a formalism that demonstrates how quantum fluctuations drive the ferromagnetic reconstruction first order, and consider the consequences of an imposed population imbalance. Secondly, we adapt this formalism to elucidate the key experimental signatures of ferromagnetism in a realistic trapped geometry.

The law of momentum conservation and its applications for partially coherent electromagnetic fields has been recently studied with the emphasis on the electric polarization. In this work, we provide more complete expressions of the formalism by including magnetization. Even though polarization gives a dominant effect in momentum flow in electromagnetic wave systems in general, magnetization can also be important in optical metamaterials. Therefore, this more general formalism will be useful for some physical situations where magnetization can be nonnegligible.

The Müller-Bethe-Schwinger-Casimir formulas for the frequency shift in electromagnetic resonators are generalized to the case of big variations of electric permittivity inside small regions. These formulas are important, in particular, for the studies of the dynamical Casimir effect.

We explore the possibility of using quantum walks on graphs to find structural anomalies, such as extra edges or loops, on a graph. We focus our attention on star graphs, whose edges are like spokes coming out of a central hub. If there are $N$ spokes, we show that a quantum walk can find an extra edge connecting two of the spokes or a spoke with a loop on it in $O(\sqrt{N})$ steps. We initially find that if all except one of the spokes have loops, the walk will not find the spoke without a loop, but this can be fixed if we choose the phase with which the particle is reflected from the vertex without the loop. Consequently, quantum walks can, under some circumstances, be used to find structural anomalies in graphs.

Parameters $\beta 1$ and $\beta 2$ describing the angular distribution of circularly polarized fluorescence photons emitted by randomly oriented diatomic molecules excited by circularly polarized radiation are derived. We prove theoretically that measuring these parameters allows a partial-wave analysis of the emitted photoelectrons in the case of closed-shell diatomic molecules. The determination of the relative partial cross sections for emission of the $\varepsilon \sigma$, $\varepsilon \pi$, and $\varepsilon \delta$ photoelectrons is of fundamental importance for a sensitive test of corresponding calculations.

We formulate quantum mechanics for non-Hermitian Hamiltonians that are invariant under $\mathcal{P}\mathcal{T}$, where $\mathcal{P}$ is the parity and $\mathcal{T}$ denotes time reversal, for the case that time-reversal symmetry is odd (${\mathcal{T}}^2=-1$), generalizing prior work for the even case (${\mathcal{T}}^2=1$). We discover an analog of Kramer’s theorem for $\mathcal{P}\mathcal{T}$ quantum mechanics, present a prototypical example of a $\mathcal{P}\mathcal{T}$ quantum system with odd time reversal, and discuss potential applications of the formalism.

We investigate theoretically an open dynamics for two modes of electromagnetic field inside a microwave cavity. The dynamics is Markovian and determined by two types of reservoirs: the “natural” reservoirs due to dissipation and temperature of the cavity, and an engineered one, provided by a stream of atoms passing trough the cavity, as devised by Pielawa et al. [Phys. Rev. Lett. 98, 240401 (2007)]. We found that, depending on the reservoir parameters, the system can have distinct “phases” for the asymptotic entanglement dynamics: it can disentangle at finite time or it can have persistent entanglement for large times, with the transition between them characterized by the possibility of asymptotical disentanglement. Incidentally, we also discuss the effects of dissipation on the scheme proposed in the above reference for generation of entangled states.

We return to the question of how the choice of stabilizer generators affects the preservation of information on structures whose degenerate ground state encodes a classical redundancy code. Controlled-not gates are used to transform the stabilizer Hamiltonian into a Hamiltonian consisting of uncoupled single spins and/or pairs of spins. This transformation allows us to obtain an analytical partition function and derive closed-form equations for the relative magnetization and susceptibility. These equations are in agreement with the numerical results presented in Viteri et al. [Phys. Rev. A 80, 042313 (2009)] for finite size systems. Analytical solutions show that there is no finite critical temperature, $T_c=0$, for all of the memory structures in the thermodynamic limit. This is in contrast to the previously predicted finite critical temperatures based on extrapolation. The mismatch is a result of the infinite system being a poor approximation even for astronomically large finite-size systems, where spontaneous magnetization still arises below an apparent finite critical temperature. We extend our analysis to the canonical stabilizer Hamiltonian. Interestingly, Hamiltonians with two-body interactions have a higher apparent critical temperature than the many-body Hamiltonian.

Photoionization by attosecond extreme ultraviolet (xuv) pulses into the laser-dressed continuum of the ionized atom is commonly described in strong-field approximation, neglecting the Coulomb interaction between the emitted photoelectron (PE) and the residual ion. By solving the time-dependent Schrödinger equation, we identify a temporal shift $\delta \tau$ in streaked PE spectra, which becomes significant at low PE energies. Within an eikonal approximation, we trace this shift to the combined action of Coulomb and laser forces on the released PE, suggesting the experimental and theoretical scrutiny of their coupling in streaked PE spectra. Further, we examined the effect of initial state polarization by the laser pulse on the xuv streaked spectrum.

We present a theoretical study of the quantum corrections to the revival time due to finite tunneling in the collapse and revival of matter-wave interference after a quantum quench. We study hard-core bosons in a superlattice potential and the Bose-Hubbard model by means of exact numerical approaches and mean-field theory. We consider systems without and with a trapping potential present. We show that the quantum corrections to the revival time can be used to accurately determine the value of the hopping parameter in experiments with ultracold bosons in optical lattices.

We present a quantum treatment of polarization of optical beams and discuss some properties of beams of any state of polarization. The analysis is based on quantum-mechanical interpretation of a canonical experiment that is used to elucidate polarization properties of stochastic fields in classical optics. Our work shows how to apply some ideas and techniques, commonly used in the classical theory, for fields that cannot be treated classically.

In this paper, we present experimental evidence of a third-order nonlinear optical process, self-induced spin-to-orbital conversion (SISTOC) of the photon angular momentum. This effect is the physical mechanism at the origin of the depolarization of very intense laser beams propagating in isotropic materials. The SISTOC process, like self-focusing, is triggered by laser heating leading to a radial temperature gradient in the medium. In this work we tested the occurrence of SISTOC in a terbium-gallium-garnet rod for an impinging laser power of about 100 W. To study the SISTOC process we used different techniques: polarization analysis, interferometry, and tomography of the photon orbital angular momentum. Our results confirm, in particular, that the apparent depolarization of the beam is due to the occurrence of maximal entanglement between the spin and orbital angular momentum of the photons undergoing the SISTOC process. This explanation of the true nature of the depolarization mechanism could be of some help in finding novel methods to reduce or to compensate for this usually unwanted depolarization effect in all cases where very high laser power and good beam quality are required.

Spectator resonant Auger-electron spectra have been measured in the Si $1s$ photoexcitation region of SiF${}_4$ using an electron spectroscopic technique combined with undulator radiation. A transition with the highest intensity in the total ion yield spectrum, which comes from excitation of a $1s$ electron into the $6t_2$ valence orbital, generates resonant Auger decays in which the excited electron remains predominantly in the valence orbital or is partly shaken up into a high-lying Rydberg orbital. The higher-lying peak generated through excitation into Rydberg orbitals induces resonant Auger decays in which the excited Rydberg electron is partly shaken up to a higher-lying Rydberg orbital or shaken down to a lower-lying valence molecular orbital. These findings exhibit a clear disentanglement effect among excited orbitals which are smeared out in the $1s$ electron excitation spectrum.

The theory of supercontinuum generation in microstructured fibers is based on notions of soliton fission and subsequent dispersive wave radiation. In bulk media, in contrast, the paradigm of effective three-wave mixing (ETWM) proves useful for understanding the supercontinuum spectral properties and revealing the dynamics within the high-intensity core of the collapsing filament. Previously, it has been shown that the bulk theory applies accurately even to so-called glass-membrane fibers in which the guided light is free to diffract in one dimension. In the same spirit, this work extends that result and brings the fiber and bulk supercontinuum approaches closer together. Specifically, we demonstrate that the ETWM paradigm can be modified for fibers, where it provides an accurate analytic description of the supercontinuum component due to dispersive waves.

Using the threshold condition relating the rate of pumping with the transverse decay rate and the real part of the eigenvalue of the dominant eigenmode of the dipole-dipole interaction kernel, I obtain the minimum radius which a cloud of $N$ two-level atoms in infinite-cylindrical geometrical configuration coherently excited must obey to permit open-ended cw lasing.

A passive scheme with a beam splitter and a photon-number-resolving (PNR) detector is proposed to verify the photon statistics of an untrusted source in a plug-and-play quantum-key-distribution system by applying a three-intensity decoy-state protocol. The practical issues due to statistical fluctuation and detection noise are analyzed. The simulation results show that the scheme can work efficiently when the total number of optical pulses sent from Alice to Bob is above ${10}^8$, and the dark count rate of the PNR detector is below 0.5 counts/pulse, which is realizable with current techniques. Furthermore, we propose a practical realization of the PNR detector with a variable optical attenuator combined with a threshold detector.

A canonical approach to Cherenkov radiation in the presence of a magnetodielectric medium is presented in classical, nonrelativistic, and relativistic quantum regimes. The equations of motion for the canonical variables are solved explicitly for both positive and negative times. Maxwell and related constitute equations are obtained. In the large-time limit, the vector potential operator is found and expressed in terms of the medium operators. The energy loss of a charged particle, emitted in the form of radiation, in finite temperature is calculated. A Dirac equation concerning the relativistic motion of the particle in presence of the magnetodielectric medium is derived and the relativistic Cherenkov radiation at zero and finite temperature is investigated. Finally, it is shown that the Cherenkov radiation in nonrelativistic and relativistic quantum regimes, unlike its classical counterpart, introduces automatically a cutoff for higher frequencies beyond which the power of radiation emission is zero.

Using a triatomic molecular model, we show that the interference pattern in the high-order above-threshold ionization (HATI) spectrum depends dramatically on the charge distribution of the molecular ion. Therefore the charge distribution can be considered a crucial factor for imaging a molecular geometric structure. Based on this study, a general destructive interference formula for each above-threshold ionization channel is obtained for a polyatomic molecule concerning the positions and charge values of each nuclei. Comparisons are made for the HATI spectra of ${\mathrm{CO}}_2$, ${\mathrm{O}}_2$, ${\mathrm{NO}}_2$, and ${\mathrm{N}}_2$. These results may shed light on imaging complex molecular structure by the HATI spectrum.

Magneto-optical traps (MOTs) of Er and Dy have recently been shown to exhibit populationwide sub-Doppler cooling due to their near degeneracy of excited- and ground-state Landé $g$ factors. We discuss here an additional, unusual intra-MOT sub-Doppler cooling mechanism that appears when the total Dy MOT cooling laser intensity and magnetic quadrupole gradient increase beyond critical values. Specifically, anisotropically sub-Doppler-cooled cores appear, and their orientation with respect to the quadrupole axis flips at a critical ratio of the MOT laser intensity along the quadrupole axis versus that in the plane of symmetry. This phenomenon can be traced to a loss of the velocity-selective resonance at zero velocity in the cooling force along directions in which the atomic polarization is oriented by the quadrupole field. We present data characterizing this anisotropic laser cooling phenomenon and discuss a qualitative model for its origin based on the extraordinarily large Dy magnetic moment and Dy’s near degenerate $g$ factors.

We study the quantum control of multilevel atoms with rotationally degenerate levels using short laser pulses. Various control schemes are considered, ones using $\pi$ pulses, frequency-chirped pulses, two consecutive pulses, or two pulses that overlap each other partially. We study the possibilities of controlling the quantum state of an ensemble of atoms distributed randomly over one or more rotationally degenerate levels initially. For the sake of concreteness we use the hyperfine level scheme of the ${}^{85}\mathrm{Rb}$ $D$ line, but the results can easily be generalized for any of the alkali-metal atoms used in cooling and trapping experiments. We find that even though a number of difficulties arise, such as unequal coupling constants between rotational sublevels or dephasing between different hyperfine levels during the interaction, control schemes using simple or multiphoton adiabatic passage can be used to control the internal states of the atoms effectively as well as the center-of-mass motion. Furthermore, it is shown that in some cases it is possible to exploit the inequality of the coupling constants to entangle the rotational substates with specific distinct translational quantum states and hence separate these substates in momentum space.