The spin-$1/2$ chain with $\mathit{XY}$ anisotropic coupling in the plane and the $\mathit{XX}$ isotropic dimerized chain are shown to be equivalent in the bulk. For finite systems, we prove that the equivalence is exact in given parity sectors, after taking care of the precise boundary conditions. The proof is given constructively by finding unitary transformations that map the models onto each other. Moreover, we considerably generalized our mapping and showed that even in the case of fully site-dependent couplings the $\mathit{XY}$ chain can be mapped onto an $\mathit{XX}$ model. This result has potential application in the study of disordered systems.

Contributions to the energy levels in light muonic atoms and, in particular, to the Lamb shift fall into a few well-distinguished classes. The related diagrams are calculated using different approaches. In particular, there is a specific type of nonrelativistic (NR) contribution. Here, we consider such corrections to the Lamb shift of order ${\alpha }^5{m}_{\mu }$. These contributions are due to free vacuum-polarization loops as well as to various effects of light-by-light scattering. The closed loop in the related diagrams is an electronic one, which allows an NR consideration of the muon. Both types of contributions have been known for some time, however, the results obtained to date are only partial results. We complete a calculation of the ${\alpha }^5{m}_{\mu }$ contributions for muonic hydrogen. The results are also adjusted for muonic deuterium atom and helium ion.

We study the dynamics of entanglement transfer in a system composed of two initially correlated three-level atoms, each located in a cavity interacting with its own reservoir. Instead of tracing out reservoir modes to describe the dynamics using the master equation approach, we consider explicitly the dynamics of the reservoirs. In this situation, we show that the entanglement is completely transferred from atoms to reservoirs. Although the cavities mediate this entanglement transfer, we show that under certain conditions, no entanglement is found in cavities throughout the dynamics. Considering the entanglement dynamics of interacting and noninteracting bipartite subsystems, we found time windows where the entanglement can only flow through interacting subsystems, depending on the system parameters.

Recently, a measure for the non-Markovian behavior of quantum processes in open systems has been developed, which is based on the quantification of the flow of information between the open system and its environment [Phys. Rev. Lett. 103, 210401 (2009)]. The information flow is connected to the rate of change of the trace distance between quantum states, which can be interpreted in terms of the distinguishability of these states. Here, we elaborate the mathematical details of this theory, present applications to specific physical models, and discuss further theoretical and experimental implications as well as relations to alternative approaches proposed recently.

We derive a single inequality as the sufficient and necessary condition for two unsharp observables of a two-level system to be jointly measurable in a single apparatus and construct explicitly the joint observables of two jointly measurable observables. By introducing a generalized distinguishability as a measure of the unsharpness of an unsharp measurement, we derive a complementarity inequality, which generalizes Englert’s duality inequality, from the condition of joint measurement of two orthogonal unsharp observables.

Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable, requiring an optimization over an infinite number of uses of the channel. Researchers have rarely found quantum channels with a tractable classical or quantum capacity, but when such a finding occurs, it demonstrates a complete understanding of that channel’s capabilities for transmitting classical or quantum information. Here we show that the three-dimensional capacity region for entanglement-assisted transmission of classical and quantum information is tractable for the Hadamard class of channels. Examples of Hadamard channels include generalized dephasing channels, cloning channels, and the Unruh channel. The generalized dephasing channels and the cloning channels are natural processes that occur in quantum systems through the loss of quantum coherence or stimulated emission, respectively. The Unruh channel is a noisy process that occurs in relativistic quantum information theory as a result of the Unruh effect and bears a strong relationship to the cloning channels. We give exact formulas for the entanglement-assisted classical and quantum communication capacity regions of these channels. The coding strategy for each of these examples is superior to a naïve time-sharing strategy, and we introduce a measure to determine this improvement.

We present all-electron relativistic studies of the polarizability properties of the Xe dimer. The studies rely on finite-field calculations of the dimer energies obtained by ab initio methods including electron correlations. An extended set of basis functions is designed in order to ensure a high accuracy of the calculations. Particular attention is paid to the analysis of the nonadditivity and anisotropy of the polarizability of the dimer. It is found that the polarizability of the dimer relative to that of the atoms can be accurately described analytically, at least for internuclear distances around and larger than the equilibrium distance of the dimer.

We investigate the phase diagram of two-component fermions in the BCS-BEC (Bose-Einstein condensate) crossover. Using functional renormalization-group equations we calculate the effect of quantum fluctuations on the fermionic self-energy parametrized by a wave-function renormalization, an effective Fermi radius, and the gap. This allows us to follow the modifications of the Fermi surface and the dispersion relation for fermionic excitations throughout the whole crossover region. We also determine the critical temperature of the second-order phase transition to superfluidity. Our results are in agreement with BCS theory including Gorkov’s correction for a small negative scattering length $a$ and with an interacting Bose gas for a small positive $a$. At the unitarity point the result for the gap at zero temperature agrees well with quantum Monte Carlo simulations, while the critical temperature differs.

We study an ultracold Bose gas in an optical dipole trap consisting of one single focused laser beam. An analytical expression for the corresponding density of states beyond the usual harmonic approximation is obtained. We are thus able to discuss the existence of a critical temperature for Bose-Einstein condensation and find that the phase transition must be enabled by a cutoff near the threshold. Moreover, we study the dynamics of evaporative cooling and observe significant deviations from the findings for the well-established harmonic approximation. Furthermore, we investigate Bose-Einstein condensates in such a trap in Thomas-Fermi approximation and determine analytical expressions for chemical potential, internal energy, and Thomas-Fermi radii beyond the usual harmonic approximation.

We study the quantum phase transitions of a model that describes the interconversion of interacting bosonic atoms and molecules. Using a classical analysis, we identify a threshold coupling line separating a molecular phase and a mixed phase. Through studies of the energy gap, von Neumann entanglement entropy, and fidelity, we give evidence that this line is associated with a boundary line in the ground-state phase diagram of the quantum system.

We report two theoretical results for transverse spin waves, which arise in a system with a persistent spin current. Using Fermi liquid theory, we introduce a spin current in the ground state of a polarized or unpolarized Fermi liquid, and we derive the resultant spin waves using the Landau kinetic equation. The resulting spin waves have a $q^1$ and $q^{1/2}$ dispersion to leading order for the polarized and unpolarized systems, respectively.

We have solved numerically the ground states of a Bose-Einstein condensate in the presence of dipolar interparticle forces using a semiclassical approach. Our motivation is to model, in particular, the spontaneous spin textures emerging in quantum gases with large dipole moments, such as ${}^{52}\mathrm{Cr}$ or $\mathrm{Dy}$ condensates, or ultracold gases consisting of polar molecules. For a pancake-shaped harmonic (optical) potential, we present the ground-state phase diagram spanned by the strength of the nonlinear coupling and dipolar interactions. In an elongated harmonic potential, we observe a helical spin texture. The textures calculated according to the semiclassical model in the absence of external polarizing fields are predominantly analogous to previously reported results for a ferromagnetic $F=1$ spinor Bose-Einstein condensate, suggesting that the spin textures arising from the dipolar forces are largely independent of the value of the quantum number $F$ or the origin of the dipolar interactions.

By using the extended boundary condition method, the Debye series is developed for light scattered by a coated nonspherical particle in order to interpret the angular dependence of the scattered intensity in terms of various physical processes. Numerical calculations are performed to study the influence of the coating thickness and the ellipticity of a coated spheroid on the angular position of the $\alpha$ and $\beta$ primary rainbows, which are produced by partial waves experiencing one internal reflection. The hyperbolic umbilic focal section is demonstrated and is analyzed for both the $\alpha$ and the $\beta$ rainbows.

We show that the noise threshold for optical quantum computing obtained by Varnava et al. [Phys. Rev. Lett. 100, 060502 (2008)] can be significantly improved by replacing the single-photon source with the Einstein-Podolsky-Rosen (EPR) type of photon source. In this implementation, for an EPR source that emits either nothing (a vacuum state) or a perfect EPR state with probability ${\eta }_s$, the detector efficiency ${\eta }_d$ is required to be larger than $50\%$ and the source efficiency ${\eta }_s$ can be an arbitrarily small positive number. We also present the error threshold for a more general noise model including additional photon absorption and show that the threshold still compares favorably with the previous results. We discuss several physical setups for realization of the required EPR photon source, including a photon emitter in a single-atom cavity.

We analyze the nonequilibrium dynamics of a gas of interacting photons in an array of coupled dissipative nonlinear cavities when driven by a pulsed external coherent field. Using a mean-field approach, we show that the response of the system is strongly sensitive to the underlying (equilibrium) quantum phase transition from a Mott insulator to a superfluid state at commensurate filling. We find that the coherence of the cavity emission after a quantum quench can be used to determine the phase diagram of an optical many-body system even in the presence of dissipation.

The screened QED corrections of first order in $\alpha$ and $1/Z$ to the $g$ factor and the hyperfine splitting of lithiumlike ions are evaluated within ab initio quantum-electrodynamical approach. The complete gauge-invariant set of the two-electron self-energy diagrams in the presence of the magnetic field and a dominant part of the two-electron vacuum-polarization diagrams are calculated. The most accurate values of the $g$ factor of Li-like lead and uranium are presented. The theoretical prediction for the specific difference of the hyperfine splittings of H- and Li-like bismuth is improved.

We present in a unified manner the existing methods for scalable partial quantum process tomography. We focus on two main approaches: the one presented in Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)] and the ones described, respectively, in Emerson et al. [Science 317, 1893 (2007)] and López et al. [Phys. Rev. A 79, 042328 (2009)], which can be combined together. The methods share an essential feature: They are based on the idea that the tomography of a quantum map can be efficiently performed by studying certain properties of a twirling of such a map. From this perspective, in this paper we present extensions, improvements, and comparative analyses of the scalable methods for partial quantum process tomography. We also clarify the significance of the extracted information, and we introduce interesting and useful properties of the $\chi$-matrix representation of quantum maps that can be used to establish a clearer path toward achieving full tomography of quantum processes in a scalable way.

We study the von Neumann block entropy in the Kondo necklace model for different anisotropies $\eta$ in the $\mathit{XY}$ interaction between conduction spins using the density matrix renormalization group method. It was found that the block entropy presents a maximum for each $\eta$ considered, and, comparing it with the results of the quantum criticality of the model based on the behavior of the energy gap, we observe that the maximum block entropy occurs at the quantum critical point between an antiferromagnetic and a Kondo singlet state, so this measure of entanglement is useful for giving information about where a quantum phase transition occurs in this model. We observe that the block entropy also presents a maximum at the quantum critical points that are obtained when an anisotropy $\Delta$ is included in the Kondo exchange between localized and conduction spins; when $\Delta$ diminishes for a fixed value of $\eta$, the critical point increases, favoring the antiferromagnetic phase.

There have been numerous studies of entanglement in spin systems. These have usually focused on examining the entanglement between individual spins or determining whether the state of the system is completely separable. Here, we present conditions that allow us to determine whether blocks of spins are entangled. We show that sometimes these conditions can detect entanglement better than conditions involving individual spins. We apply these conditions to study entanglement in spin-wave states, both when there are only a few magnons present and also at finite temperature.