Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord, and quantum entanglement in multipartite systems. On this basis, we define a basis-independent measure of quantum coherence and prove that it is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two-qubit unitary gates. Intriguingly, our results demonstrate that nonlocal unitary gates do not necessarily outperform the local unitary gates. Finally, the additivity relationship of quantum coherence in tripartite systems is discussed in detail, where the strong subadditivity of von Neumann entropy plays an essential role.

Inspired by recent work [Carr and Saffman, Phys. Rev. Lett. 111, 033607 (2013)], we propose a simplified scheme to prepare the two-atom maximally entangled states via dissipative Rydberg pumping. Compared with the former scheme, the simplified one involves fewer classical laser fields and Rydberg interactions, and the asymmetric Rydberg interactions are avoided. Master equation simulations demonstrate that the fidelity and the Clauser-Horne-Shimony-Holt correlation of the maximally entangled state could reach up to 0.999 and 2.821, respectively, under certain conditions. Furthermore, we extend the physical thoughts to prepare the three-dimensional entangled state, and the numerical simulations show that, in theory, both the fidelity and the negativity of the desired entanglement could be very close to unity under certain conditions.

For dark resonance, one of the most remarkable coherent effects in light-matter interactions, it has commonly been expected that squeezing and entanglement, if existent, are formed via coherent evolutions against dissipation. Contrary to the expectations, here we show that dissipation generates entanglement between two cavity fields and between two dark-state-based spins. The latter correspond also to the atomic ground-state spin squeezing in a limited parameter domain. The dissipation effects, which are hidden deeply behind the coherence-induced nonlinearities, are extracted by probing into the dressed atom-photon interactions, and are widely applicable for the coherently prepared systems in dark resonances or beyond.

We study the tail of the spectrum for noninteracting bosons in a blue-detuned random speckle potential. Using an instanton approach, we derive the asymptotic behavior of the density of states in $d$ dimensions. The leading corrections resulting from fluctuations around the saddle-point solution are obtained by means of the Gel'fand-Yaglom method generalized to functional determinants with zero modes. We find a good agreement with the results of numerical simulations in one dimension. The effect of weak repulsive interactions in the Lifshitz tail is also discussed.

Simulations of plasmon-enhanced high-order-harmonic generation are performed for a ${\text{H}}_2{}^{+}$ molecular cation near the metallic nanostructures. We employ the numerical solution of the time-dependent Schrödinger equation in reduced coordinates. We assume that the main axis of ${\text{H}}_2{}^{+}$ is aligned perfectly with the polarization direction of the plasmon-enhanced field. We perform systematic calculations on plasmon-enhanced harmonic generation based on an infinite-mass approximation, i.e., pausing nuclear vibrations. Our simulations show that molecular high-order-harmonic generation from plasmon-enhanced laser fields is possible. We observe the dispersion of a plateau of harmonics when the laser field is plasmon enhanced. We find that the maximum kinetic energy of the returning electron follows $4U_p$. We also find that when nuclear vibrations are enabled, the efficiency of the harmonics is greatly enhanced relative to that of static nuclei. However, the maximum kinetic energy $4U_p$ is largely maintained.

The triple ionization spectrum of atomic Cd formed upon the removal of a $4p$ or a $4s$ inner-shell electron and subsequent Auger decays has been obtained at 200 eV photon energy. By using a versatile multielectron coincidence detection technique based on a magnetic bottle spectrometer in combination with multiconfiguration Dirac-Fock calculations, Auger cascades leading to tricationic final states have been analyzed and final-state configurations have been identified. The most prominent Auger cascades leading to the ground state of ${\mathrm{Cd}}^{3+}$ have been identified in good agreement with theory.

Density-functional theory is utilized to investigate the zero-temperature transition from a Fermi liquid to an inhomogeneous stripe, or Wigner crystal phase, predicted to occur in a one-component, spin-polarized, two-dimensional dipolar Fermi gas. Correlations are treated semiexactly within the local-density approximation using an empirical fit to quantum Monte Carlo data. We find that the inclusion of the nonlocal contribution to the Hartree-Fock energy is crucial for the onset of an instability to an inhomogeneous density distribution. Our density-functional theory supports a transition to both a one-dimensional stripe phase and a triangular Wigner crystal. However, we find that there is an instability first to the stripe phase, followed by a transition to the Wigner crystal at higher coupling.

With current magnetic-field shielding and high-precision detection in dipolar spinor Bose-Einstein condensates, it is possible to experimentally detect the low- or zero-field nonsecular dipolar dynamics. Here we analytically investigate the zero-field nonsecular magnetic dipolar interaction effect, with an emphasis on magnetization dynamics in a spin-1 Bose-Einstein condensate under the single spatial mode approximation within the mean-field theory. Due to the biaxial nature of the dipolar interaction, a novel resonance occurs in the condensate magnetization oscillation, in contrast to the previous assumption of a conserved magnetization in strong magnetic fields. Furthermore, we propose a dynamical-decoupling detection method for such a resonance, which cancels the stray magnetic fields in experiment but restores the magnetization dynamics. Our results shed light on the dipolar systems and may find potential applications beyond cold atoms.

We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the ground-state densities of ferromagnetic BECs are obtained from the Thomas-Fermi approximation (TFA) to this decoupled equation. Similarly, for the ground states of spin-1 antiferromagnetic and spin-2 antiferromagnetic and cyclic BECs, some of the spin-component densities are zero, which reduces the coupled GP equation to a simple reduced form. Analytic models for ground-state densities are also obtained for antiferromagnetic and cyclic BECs from the TFA to the respective reduced GP equations. The analytic densities are illustrated and compared with the full numerical solution of the GP equation with realistic experimental parameters.

We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (color) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much stronger than the other, pairing symmetry is an extended $s$ wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. On the other hand, when two of the three color-dependent repulsions are weaker than the other, pairing symmetry is a $d_{x^2-y^2}$ wave. This change in pairing symmetry is attributed to the change in the dominant quantum fluctuations from the density fluctuations of unpaired atoms and the color-density wave fluctuations to the color-selective antiferromagnet fluctuations. This phenomenon can be studied using existing experimental techniques.

This paper derives Langevin equations for an optical cavity where the dominant nonlinearity arises from free-carrier dispersion. We define a generalized Wigner function, compute a Fokker-Planck equation that approximates the master equation, and convert this to a system of stochastic differential equations. These equations are similar to the Wigner equations for an optical Kerr cavity, but have additional noise terms due to the incoherent carrier excitation and decay processes. We use these equations to simulate a phase-sensitive amplifier and latch and compare the results to a Kerr model.

We consider, in general, the collective two-photon annihilation decay of positronium atoms arising from the second quantized formalism. It is shown that two-photon annihilation of positronium atoms in a Bose-Einstein condensate (BEC) is unstable. Due to the BEC coherence, an absolute instability in such system takes place, i.e., the number of photons created as a result of positronium decay grows in every point within a BEC. The latter leads to an exponential buildup of a macroscopic population into the certain modes. Cooperative effects start for densities much smaller than the Dicke limit of spontaneous super radiation. For laserlike action, i.e., for directional radiation, we consider the BEC with elongated shape when the spontaneously emitted entangled and oppositely directed photon pairs are amplified, leading to an exponential buildup of a macroscopic population into the end-fire modes. We also consider the roles of confinement and interaction among positronium atoms in the amplification process.

We present a theory and calculations of the nuclear magnetic shielding with finite nuclear mass effects and determine the magnetic moments of deuteron and triton using the known NMR spectra of HD and HT molecules. The results ${\mu }_d=0.8574382346\left(53\right){\mu }_N$ and ${\mu }_t=2.978962471\left(10\right){\mu }_N$ are more accurate and in good agreement with the currently accepted values.

We investigate, within the weak measurement theory, the advantages of nonclassical pointer states over semiclassical ones for coherent, squeezed vacuum, and Schrödinger cat states. These states are utilized as pointer states for the system operator $\widehat{A}$ with property ${\widehat{A}}^2=\widehat{I}$, where $\widehat{I}$ represents the identity operator. We calculate the ratio between the signal-to-noise ratio of nonpostselected and postselected weak measurements. The latter is used to find the quantum Fisher information for the above pointer states. The average shifts for those pointer states with arbitrary interaction strength are investigated in detail. One key result is that we find the postselected weak measurement scheme for nonclassical pointer states to be superior to semiclassical ones. This can improve the precision of the measurement process.

We show that nonexponential fidelity decays in randomized benchmarking experiments on quantum-dot qubits are consistent with numerical simulations that incorporate low-frequency noise and correspond to a control fidelity that varies slowly with time. By expanding standard randomized benchmarking analysis to this experimental regime, we find that such nonexponential decays are better modeled by multiple exponential decay rates, leading to an instantaneous control fidelity for isotopically purified silicon metal-oxide-semiconductor quantum-dot qubits which is 98.9% when the low-frequency noise causes large detuning but can be as high as 99.9% when the qubit is driven on resonance and system calibrations are favorable. These advances in qubit characterization and validation methods underpin the considerable prospects for silicon as a qubit platform for fault-tolerant quantum computation.

In this work, we propose device-independent true random number expansion protocols based on noninequality paradoxes such as Hardy's and Cabello's nonlocality arguments, thus highlighting the noninequality paradox as an important resource for device-independent quantum-information processing, in particular for generating true randomness. As a byproduct, we find that the nonlocal bound of the Cabello argument with arbitrary dimension is the same as the one achieved in the qubits system. More interestingly, we propose a dimension witness paradox based on the Cabello argument which can be used for constructing a semi–device-independent true random number expansion protocol.

Isolated multiply charged anions exhibit a repulsive Coulomb barrier (RCB) towards electron loss. In this paper, the role of tunneling through the RCB in the delayed electron emission is addressed. Electron kinetic energy distributions of photoexcited fullerene dianions ${\mathrm{C}}_{84}{}^{2-}$ and ${\mathrm{C}}_{90}{}^{2-}$ have been measured with a velocity-map imaging spectrometer for delays of about 150 ns after the nanosecond laser excitation. On such spectra, delayed electron emission is unambiguously separated from direct detachment. These measurements display significant delayed emission below the RCB. A detailed-balance model including electron tunneling through the RCB has been developed. The very good agreement between the measurements and the model provides quantitative evidence for a thermal tunneling electron emission.

Sisyphus cooling plays an important role in many cold atom applications including the formation of Bose-Einstein condensates and collimation of atomic beams. Here we present a method for measuring the localization of atoms by monitoring the polarization of fluorescence, providing a quantitative two-dimensional image of the cooling process. We outline the concept and provide theoretical models for the optical pumping, cooling, and channeling mechanisms, and present experimental data revealing the development of strong fluorescence polarization in an atomic beam during transverse $\left(\mathrm{lin}\perp \mathrm{lin}\right)$ cooling.

We consider an experimentally realizable model of noninteracting but randomly coupled atoms in a two-dimensional optical lattice. By choosing appropriate real or complex-valued random fields and species-dependent energy offsets, this system can be used to analyze effects of disorder in four different symmetry classes: the chiral BDI and AIII and the nonchiral A and AI. These chiral classes are known to support a metallic phase at zero energy, which here, due to the inevitable finite size of the system, should also persist in a neighborhood of nonzero energies. As we discuss, this is of particular interest for experiments involving quenches. Away from the center of the spectrum, we find that excitations appear as domain walls in the cases with time-reversal symmetry or as vortices in the cases where time-reversal symmetry is absent. Therefore, a quench in a system with uniform density would lead to the formation of either vortices or domain walls depending on the symmetry class. For the nonchiral models in classes A and AI, a population imbalance between the two atomic species naturally occurs. In these cases, one of the two species is seen to favor a more uniform density. We also study the onset of localization as the disorder strength is increased for the different classes, and by deriving an effective model for the nonchiral cases we show how their eigenstates remain extended for larger values of the coupling with the disorder when compared to the nonchiral ones.

We use quantum trajectories to simulate Josephson oscillations of atomic condensates between the two sides of a double-well potential. In the simulations the atoms in both wells are monitored using off-resonant light scattering, and the ultimate outcome of our thought experiment is a sequence of photon counts probing the numbers of the atoms in each potential well. We show how to reconstruct the Josephson oscillations from the observed photon counts using Bayesian inference, and study the oscillations quantitatively by averaging the inferred time-dependent oscillation amplitude over a large number of realizations. Scaling behaviors that characterize the oscillations are uncovered and related to physics principles such as measurement back-action. It turns out that the scalings hold true for quite small atom numbers, so that in this sense four atoms in a potential well may already make a Bose-Einstein condensate.