For pure and mixed two-qubit states we present an analysis based on symmetries of vectors and matrices associated to the density operator. These symmetries are revealed by doing reflection operations on the vectors and the matrices by Cartesian planes. Then we consider states whose $4\times 4$ matrices belong to the D-$7$ manifold class and introduce a new set of parameters. This procedure allows us to establish the Peres-Horodecki separability criterion in terms of a squared distance having a Minkowski metric. Thereafter, defining a phase space in terms of those parameters, we identify two regions, a cone and elsewhere. Separable states are represented by points located within the cone or on its surface (the border), while elsewhere the points stand for the entangled states. For a system evolving in time, if its state is initially entangled, then depending on the values of its parameters and on the nature of the interactions with the environment, the trajectory in the phase space may cross the border at a finite time, going from the entangledlike to the separablelike region and vice-versa. As a particular feature, crossings in one direction stand for the phenomenon of sudden death of entanglement, while crossings in the opposite direction hint for the sudden birth of entanglement. Our method dispenses with operations on the density matrix; it is sufficient to write the expressions directly in terms of matrix entries. Some illustrative examples are worked out.

We consider a system composed of a two-level system (i.e., a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. Special emphasis is placed on the possibility of preparing nonclassical states in this system. These nonclassical states include squeezed states, Schrödinger-cat states, and entangled states. We start by comparing the predictions of a number of analytical methods that can be used to describe the system under different assumptions, thus analyzing the properties of the system in various parameter regimes. We then examine the ground state of the system and analyze its nonclassical properties. We finally discuss some questions related to the possible experimental observation of the nonclassical states and the effect of decoherence.

The current interest in producing ultracold RbCs molecules by optical excitation from weakly bound Feshbach resonances and stimulated decay to the absolute ground state requires detailed analyses of the intermediate excited states. In this study, we present two sets of experimental Fourier-transform spectroscopic data of the $A{\hspace{0.5em}}^1{\Sigma }^{+}$-$b{\hspace{0.5em}}^3\Pi$ complex. The $A$-$b$ mixed vibrational levels are the most likely candidates to be intermediates in the molecular formation. The more recent and more accurate data set is from mixed $A$-$b\to X$ transitions, while the second is derived in large part from $(4){\hspace{0.5em}}^1{\Sigma }^{+}\to A$-$b$ emission and extends to higher $A$-$b$ energy levels. From a detailed analysis of the spectroscopic data we obtain term values which allow one to construct potentials and spin-orbit functions. Vibrational numbering of the $A$ state has been raised by one quantum over a previous report [T. Bergeman et al., Phys. Rev. A 67, 050501 (2003)] while the numbering of the $b$ state is established with a considerable degree of certainty with help of data on the ${}^{85}\mathrm{Rb}$${}^{133}\mathrm{Cs}$ and ${}^{87}\mathrm{Rb}$${}^{133}\mathrm{Cs}$ isotopomers. In addition, we have performed calculations of spin-orbit functions by two distinct methods. The fitted spin-orbit coupling matrix element between the two ${\Omega }^p=0^{+}$ states, $A{\hspace{0.5em}}^1{\Sigma }^{+}$ and $b{\hspace{0.5em}}^3{\Pi }_{0+}$, happens to agree rather well with the results from both of these methods, while for the diagonal $b{\hspace{0.5em}}^3\Pi$ state spin-orbit function, the fitted function agrees fairly well with that obtained by the other method.

The binding energies of high-$L$ Rydberg levels of Pb${}^{+}$ with $n=19$ or 20 and $6⩽L⩽10$ were measured with resonant excitation Stark ionization spectroscopy (RESIS). When combined with previous measurements of members of the $\mathit{nh}$ Rydberg series in Pb${}^{+}$, and analyzed with the long-range polarization model, these determined the polarizability of the $5d^{10}6s^2$ ground state of Pb${}^{2+}$ to be ${\alpha }_d$ $=$ 13.62(8) a.u. This value is substantially larger than the estimate published recently based on the measured lifetime of the $6s6p^1{P}_1$ resonance level of Pb${}^{2+}$, 7.9(6) a.u. The difference is mostly due to the polarizability of Pb${}^{4+}$, the $5d^{10}$ core of the Pb${}^{2+}$ ion. This was established by observation of resolved fine structure in the excitation of $n=39$, high-$L$ Rydberg levels of Pb${}^{3+}$, using the same RESIS technique. Analysis of this spectra determined the polarizability of Pb${}^{4+}$ to be ${\alpha }_d$ $=$ 3.61(4) a.u. Reanalysis of optical spectra of $\mathit{nh}$ and $\mathit{ng}$ levels in Pb${}^{+}$ and Pb${}^{3+}$ in view of the polarizabilities determined in the RESIS studies indicates revised ionization energies of both ions, $E_{\mathrm{I}}$(Pb${}^{+}$) $=$ 121245.28(6) cm${}^{-1}$ and $E_{\mathrm{I}}$(Pb${}^{3+}$) $=$ 341 435.1(8) cm${}^{-1}$.

The cooling effects of a quantum $\mathit{LC}$ circuit coupled inductively with an ensemble of artificial qubits are investigated. The particles may decay independently or collectively through their interaction with the environmental vacuum electromagnetic field reservoir. For appropriate bath temperatures and the resonator’s quality factors, we demonstrate an effective cooling well below the thermal background. In particular, we found that for larger samples the cooling efficiency is better for independent qubits. However, the cooling process can be faster for collectively interacting particles.

An approximate analytical solution is presented, along with numerical calculations, for a system of two single-photon wave packets interacting via an ideal, localized Kerr medium. It is shown that, because of spontaneous emission into the initially unoccupied temporal modes, the cross-phase-modulation in the Schrödinger picture is very small as long as the spectral width of the single-photon pulses is well within the medium’s bandwidth. In this limit, the Hamiltonian used can be derived from the “giant Kerr effect” for a four-level atom, under conditions of electromagnetically induced transparency; it is shown explicitly that the linear absorption in this system increases as the pulse’s spectral width approaches the medium’s transparency bandwidth, and hence, as long as the absorption probability remains small, the maximum cross-phase-modulation is limited to essentially useless values. These results are in agreement with the general, causality-based, and unitarity-based arguments of Shapiro and Razavi [J. H. Shapiro, Phys. Rev. A 73, 062305 (2006); J. H. Shapiro and M. Razavi, New J. Phys. 9, 16 (2007)].

Non-Markovianity is a recently proposed characterization of the non-Markovian behavior in an open quantum system, based on which we first present a practical idea for directly measuring the non-Markovian character of a single qubit coupled to a zero-temperature bosonic reservoir, and then extend to investigate the dynamics of two noninteracting qubits subject to two reservoirs, respectively, with a lower bound of non-Markovianity. Our scheme, with no need for optimization procedures and quantum state tomography, is helpful for experimental implementation.

We investigate the possibility to control the $s$-wave scattering length for the interaction between cold bosonic atoms by using a microwave field. Our scheme applies to any atomic species with a ground state that is split by hyperfine interaction. We discuss more specifically the case of alkali-metal atoms and calculate the change in the scattering length for ${}^7\mathrm{Li}$, ${}^{23}\mathrm{Na}$, ${}^{41}\mathrm{K}$, ${}^{87}\mathrm{Rb}$, and ${}^{133}\mathrm{Cs}$. Our results yield optimistic prospects for experiments with the four latter species.

We demonstrate the nondispersive deflection of an optical beam in a Stern-Gerlach magnetic field. An optical pulse is initially stored as a spin-wave coherence in thermal Rb vapor. An inhomogeneous magnetic field imprints a phase gradient onto the spin wave, which upon reacceleration of the optical pulse leads to an angular deflection of the retrieved beam. We show that the obtained beam deflection is nondispersive (i.e., its magnitude is independent of the incident optical frequency). Compared to a Stern-Gerlach experiment carried out with propagating light under the conditions of electromagnetically induced transparency, the estimated suppression of the chromatic aberration reaches ten orders of magnitude.

Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyze the effective entanglement (i.e., entanglement minimized over the output data). We show that in the well-defined system of two quantum dots monitored by single-electron transistors, one may observe a sudden death of effective entanglement when real, physical entanglement is still alive. For certain measurement setups, this occurs even for initial states for which sudden death of physical entanglement is not possible at all. The principles of the analysis may be applied to other analogous scenarios, such as estimation of the parameters arising from quantum process tomography.

The two-photon decay of heavy, helium-like ions is investigated based on second-order perturbation theory and Dirac’s relativistic equation. Special attention has been paid to the angular emission of the two photons (i.e., how the angular correlation function depends on the shell structure of the ions in their initial and final states). Moreover, the effects from the (electric and magnetic) nondipole terms in the expansion of the electron-photon interaction are discussed. Detailed calculations have been carried out for the two-photon decay of the $1s2s\hspace{0.5em}{}^1{S}_0$, $1s2s\hspace{0.5em}{}^3{S}_1$, and $1s2p\hspace{0.5em}{}^3{P}_0$ states of helium-like Xe${}^{52+}$, Au${}^{77+}$, and ${\mathrm{U}}^{90+}$ ions.

We investigate quantum interference effects in high-order harmonic generation in ${\mathrm{N}}_2$ and ${{\mathrm{N}}_2}^{+}$ beyond the single-active-orbital approximation, with particular emphasis on the role of $\sigma$ and $\pi$ orbitals in the overall spectra. In the former case, we consider a simplified multielectron wave function which incorporates the $3{\sigma }_g$ and $1{\pi }_u$ orbitals, and, in the latter, we assume that the optically active electron is in a coherent superposition of the $3{\sigma }_g$ and $1{\pi }_g^{*}$ one-electron states. If the orbitals are energetically close, such as the $3{\sigma }_g$ and the $1{\pi }_u$ orbitals of ${\mathrm{N}}_2$, we show that the quantum interference patterns observed in the high-order harmonic spectra are predominantly determined by the $3{\sigma }_g$ orbital. If, on the other hand, there is a significant difference in their binding energies, such as for the $3{\sigma }_g$ and the $1{\pi }_g^{*}$ orbitals of ${{\mathrm{N}}_2}^{+}$, the most loosely bound orbital will determine the shape of the spectra. Due, however, to the different cutoffs encountered, the more deeply bound orbital will leave an imprint on the high-energy harmonics. This holds both for the situation in which the dynamics of the electron is restricted to the plane $p_x{p}_z$ and for the full three-dimensional case, if the azimuthal angle is integrated over and the degeneracy of the $\pi$ orbitals is taken into account.

A ring crystal of ions trapped in a linear multipole trap is studied as the basis for an optical frequency standard. The equilibrium conditions and cooling possibilities are discussed through an analytical model and molecular dynamics simulations. A configuration is proposed that reduces the frequency sensitivity to the fluctuations of the number of trapped ions. The systematic shifts for the electric quadrupole transition of calcium ions are evaluated for this ring configuration. This study shows that a ring of 10 or 20 ions allows a better short-term stability to be reached than for a single ion without introducing limiting long-term fluctuations.

By employing a binary mixture of Bose-Einstein condensates in a symmetric double-well potential we study the collective dynamics of a two-coupled-Hamiltonian system. There we find three interesting collective dynamic regimes. Besides measure synchronization, phase synchronization and nonlocal measure synchronization have been found. We demonstrate that by varying the interspecies interaction strength, the transitions between different regimes can be found clearly. A diagram of dynamic regimes with experimentally adjustable parameters has also been presented.

We propose a general description of adiabatic evolution of degenerate quantum systems in both linear and nonlinear cases. We derive the effective evolution equations of the considered system. For nondegenerate cases, we obtain a generalized Berry’s phase for nonlinear systems. For linear cases, the equations reduce to the Wilczek-Zee dynamics in degenerate quantum systems, where non-Abelian adiabatic connections appear. The method can be used to study the coherent atom-molecule transition in ultracold quantum gases with degeneracy and is consistent with quantized treatment.

The Lévy distribution, previously used to describe complex behavior of classical systems, is shown to characterize that of quantum many-body systems. Using two complimentary approaches, the canonical and grand-canonical formalisms, we discovered that the momentum profile of a Tonks-Girardeau gas—a one-dimensional gas of $N$ impenetrable (hard-core) bosons–harmonically confined on a lattice at finite temperatures obeys a Lévy distribution. Finally, we extend our analysis to different confinement setups and demonstrate that the tunable Lévy distribution properly reproduces momentum profiles in experimentally accessible regions. Our finding allows for calibration of complex many-body quantum states by using a unique scaling exponent.

High-quality optical cavities with wavelength-sized end mirrors are important to the growing field of micro-optomechanical systems. We present a versatile method for calculating the modes of diffraction limited optical cavities and show that it can be used to determine the effect of a wide variety of cavity geometries and imperfections. Additionally, we show these calculations agree remarkably well with FDTD simulations for wavelength-sized optical modes, even though our method is based on the paraxial approximation.

We study the propagation of few-cycle pulses in a two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of short pulses in a purely conductive material and demonstrate the diffusive behavior for the evolution of the low-frequency components of the magnetic field in the case of relatively strong conductivity. Then, numerical simulations carried out in the frame of the full nonlinear theory involving the Maxwell-Drude-Bloch model reveal the stable creation and propagation of few-cycle dissipative solitons under excitation by incident femtosecond optical pulses of relatively high energies. The broadband losses that are introduced by the medium conductivity represent the main stabilization mechanism for the dissipative few-cycle solitons.

We consider the impact of anisotropic nonlocality on the arrest of the collapse and stabilization of dipole-mode (DM) solitons in two-dimensional (2D) models of optical media with the diffusive nonlinearity. The nonlocal nonlinearity is made anisotropic through elliptic diffusivity. The medium becomes semilocal in the limit case of 1D diffusivity. Families of fundamental and DM solitons are found by means of the variational approximation and in a numerical form. We demonstrate that the collapse of 2D beams is arrested even in the semilocal system. The anisotropic nonlocality readily stabilizes the DM solitons, which are completely unstable in the isotropic medium.

The multimode dynamics of a two-level ring laser is explored numerically using a bidirectional traveling wave model retaining the spatial effects due to the presence of counter-propagating electric fields in the population inversion. Dynamical regimes where the emission in each direction occurs at different wavelengths are studied. Mode-locked unidirectional emission for large gain bandwidth and relatively small detuning is reported.