The quantum relative Rényi entropy of two noncommuting density matrices was recently defined from which its conditional entropy is deduced. This framework is here extended to the corresponding Tsallis relative entropy and to its conditional form. This expression of Tsallis conditional entropy is shown to witness entanglement beyond the method based on global and local spectra of composite quantum states. When the reduced density matrix happens to be a maximally mixed state, this conditional entropy coincides with the expression in terms of Tsallis entropies derived earlier by Abe and Rajagopal [Physica A 289, 157 (2001)]. The separability range in a noisy one-parameter family of $W$ and Greenberger-Horne-Zeilinger states with three and four qubits is explored here and it is shown that the results inferred from negative Tsallis conditional entropy matches that obtained through Peres's partial transpose criterion for one-parameter family of $W$ states, in one of its partitions. The criterion is shown to be nonspectral through its usefulness in identifying entanglement in isospectral density matrices.

We provide the entanglement criterion of computable cross norm and realignment for any two-mode continuous-variable state with permutational symmetry. The entanglement criterion for a non-Gaussian state is obtained from its Gaussian kernel by employing the technique of functional analysis. The entanglement conditions turn out to be necessary and sufficient for the non-Gaussian states prepared by one-photon subtracting from or adding to symmetric Gaussian states. The entanglement criterion of non-Gaussian states evolved in thermal noise and amplitude damping environment also is obtained.

A method for calculating the oscillator strengths for rovibrational transitions of a diatomic system within an approach that is not based on the Born-Oppenheimer (BO) approximation is presented. The non-BO wave functions representing the bound states of the system are expanded in terms of explicitly correlated Gaussian functions. The method is applied to calculate oscillator strengths for the ${\text{HD}}^{+}$ ion for transitions between rotationless vibrational states and vibrational states which are rotationally singly excited. The effect of the asymmetry of the ${\text{HD}}^{+}$ charge distribution on the oscillator strengths and on the lifetimes of the states is elucidated.

The electron-detachment cross section was measured for the molecular negative ions ${\mathrm{CN}}^{-}$ and ${\mathrm{O}}_2^{-}$ incident on N${}_2$, in the 0.08–1.2 a.u. velocity region. Our setup uses the gas stripper of a tandem accelerator as a gas chamber. All cross sections present a maximum near 0.4 a.u., a velocity corresponding to the well-known shape-resonance that appears in the electron-N${}_2$ collisions. A semiclassical model is employed to analyze the data. The role of this shape resonance is discussed in this article.

The weak-field asymptotic theory of tunneling ionization in an external static uniform electric field [Tolstikhin et al., Phys. Rev. A 84, 053423 (2011)] is extended to many-electron atomic and molecular systems treated in the frozen-nuclei approximation. The leading-order term in the asymptotic expansion of the ionization rate $\Gamma$ in the value of the field $F$ for $F\to 0$ is obtained. The resulting formulas express $\Gamma$ in terms of properties of the unperturbed system. The most essential difference from the one-electron case, through which the many-electron character of the present theory reveals itself, is that the structure factor for a given ionization channel, defining the dependence of the ionization rate into this channel on the orientation of the system with respect to the field, is determined by the corresponding Dyson orbital. The theory is illustrated by calculations for several few-electron systems. The asymptotic results are compared with accurate fully correlated calculations of tunneling ionization rates available in the literature.

We investigate strong-field ionization dynamics of atoms in circularly polarized laser fields by a three-dimensional electron ensemble method which is validated by comparison with ab initio results of solving the time-dependent Schrödinger equation. We show that the Coulomb potential and the electron recollision play very crucial roles for single ionization of atoms with a lower ionization potential in circularly polarized laser fields. We find that the critical laser field strength for recollision scales as $F_0\sim 2ln10{\omega }^2/\sqrt{2I_p}$($I_p$, ionization potential; $\omega ,$ laser frequency), below which the rescattering is very crucial. As a consequence of recollision, a large amount of tunneled electrons will be ejected into the elliptical orbits of Rydberg states or strongly rescattered off the nucleus and eventually achieve large energy from laser fields. The characteristic feature is that both the relative frustrated tunneling rate and the hard rescattering rate decrease with increasing the laser intensity and the wavelength. This study sheds a light on those processes that are closely related with electron rescattering in circularly polarized laser fields, e.g., high-order harmonic generation and nonsequential double ionization.

We show that massive low-energy particles traversing a branching zone or a crossing of quantum waveguides may experience a nonstandard trapping force that can not be derived from a potential. For interacting cold Bose atoms, we report on the formation of a localized Hartree ground state for three prototype waveguide geometries with broken translational symmetry: a cranked L-shaped waveguide $\mathcal{L}$, a T-shaped waveguide $\mathcal{T}$, and the crossing $\mathcal{C}$ of two quantum waveguides. The phenomenon is kinetic energy driven and can not be described within the Thomas-Fermi approximation. Depending on the ratio ${\kappa }^{\left(\Gamma \right)}$ of joining lateral tube diameters of the respective waveguides $\Gamma \in \{\mathcal{C},\mathcal{L},\mathcal{T}\}$, delocalization commences when the particle number $N$ approaches a critical value $N_c^{\left(\Gamma \right)}$. For the case of a binary mixture of two different Bose atom species $A$ and $B$, we observe nonstandard trapping of both atom species for subcritical particle numbers. A sudden demixing quantum transition takes place as the total particle number $N=N_A+N_B$ is increased at fixed mixing ratio $N_A/N_B$. Depending on the mass ratio $m_A/m_B$, the heavier atom species delocalizes first for a wide range of interaction parameters. The numerical calculations are based on a splitting scheme involving an analytic approximation to the short-time asymptotics of the imaginary-time quantum propagator of a single particle obeying Dirichlet boundary conditions at the walls inside the respective waveguides.

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ from the Hubbard model in exhibiting additional density-dependent interaction terms that affect the hopping processes. In addition to the spin-SU(2) symmetry, they also possess a charge-SU(2) symmetry, which opens the possibility of investigating the $\eta$-pairing mechanism for superconductivity introduced by Yang for the Hubbard model. We discuss the known solution of the model in one dimension (where $\eta$ states have been found in the degenerate manifold of the ground state) and show that, away from the integrable point, quantum Monte Carlo simulations at half filling predict the emergence of a phase with coexisting incommensurate spin and charge order.

We show how to exploit the rich hyperfine structure of fermionic alkali-metal atoms to produce a quasi-one-dimensional (quasi-1D) topological superfluid while avoiding excessive heating from off-resonant scattering. We model interacting fermions where four hyperfine states are coupled by a variety of optical and microwave fields. We calculate the local density of states in a trap, finding regimes with zero-energy topological edge modes. Heating rates in this system are significantly suppressed compared to simple Raman-induced spin-orbit coupling approaches. We also estimate the two- and three-body decay rates and find a reasonable lifetime at small but experimentally relevant densities.

We report a method that is able to provide refined structural information on molecular packing in biomolecular assemblies using polarization-resolved four-wave mixing and coherent anti-Stokes Raman-scattering microscopy. These third-order nonlinear processes allow quantifying high orders of symmetry which are exploited here to reveal a high level of detail in the angular disorder behavior at the molecular scale in lipid membranes.

We investigate the resonant cooling phenomena of a driven two-level radiator embedded in a photonic-crystal structure. We find that cooling occurs even at laser-atom-frequency resonance. This happens due to atomic dressed-state coupling with different strengths, resulting in population redistribution and cooling. Furthermore, for off-resonant driving the two-level particle can be in either the ground or excited bare state. This may help in the engineering of different amplified optical devices as well as highly coherent light sources.

Adaptive feedback normally provides the greatest accuracy for optical phase measurements. New advances in nitrogen-vacancy-center technology have enabled magnetometry via individual spin measurements, which are similar to optical phase measurements but with low visibility. The adaptive measurements that previously worked well with high-visibility optical interferometry break down and give poor results for nitrogen-vacancy-center measurements. We use advanced search techniques based on swarm optimization to design better adaptive measurements that can provide improved measurement accuracy with low-visibility interferometry, with applications in nitrogen-vacancy-center magnetometry.

We consider ultracold atoms subjected to a cavity-assisted two-photon Raman transition. The Raman coupling gives rise to effective spin-orbit interaction which couples the atom's center-of-mass motion to its pseudospin degrees of freedom. Meanwhile, the cavity photon field is dynamically affected by the atom. This feedback between the atom and photons leads to a dramatic modification of the atomic dispersion relation, and further leads to dynamical instability of the system. We propose to detect the change in the cavity photon number as a direct way to demonstrate dynamical instability.

We report polarimetric measurements of geometric phases that are generated by evolving polarized photons along nongeodesic trajectories on the Poincaré sphere. The core of our polarimetric array consists of seven wave plates that are traversed by a single-photon beam. With this array, any SU(2) transformation can be realized. By exploiting the gauge invariance of geometric phases under U(1) local transformations, we nullify the dynamical contribution to the total phase, thereby making the latter coincide with the geometric phase. We demonstrate our arrangement to be insensitive to various sources of noise entering it. This makes the single-beam, polarimetric array a promising, versatile tool for testing robustness of geometric phases against noise.

By combining the postulates of macrorealism with Bell locality, we derive a qualitatively different hybrid inequality that avoids two loopholes that commonly appear in Leggett-Garg and Bell inequalities. First, locally invasive measurements can be used, which avoids the “clumsiness” Leggett-Garg inequality loophole. Second, a single experimental ensemble with fixed analyzer settings is sampled, which avoids the “disjoint sampling” Bell inequality loophole. The derived hybrid inequality has the same form as the Clauser-Horne-Shimony-Holt Bell inequality; however, its quantum violation intriguingly requires weak measurements. A realistic explanation of an observed violation requires either the failure of Bell locality or a preparation conspiracy of finely tuned and nonlocally correlated noise. Modern superconducting and optical systems are poised to implement this test.

We use the approach of “transitionless quantum driving” proposed by Berry to construct shortcuts to the population transfer and the creation of maximal entanglement between two $\Lambda$-type atoms based on the cavity quantum electronic dynamics system. An effective Hamiltonian is designed by resorting to an auxiliary excited level, a classical driving field, and an extra cavity field mode to supplement or substitute the original reference Hamiltonian, and steer the system evolution along its instantaneous eigenstates in an arbitrarily short time, speeding up the rate of population transfer and creation of maximal entanglement between the two atoms inside a cavity. Numerical simulation demonstrates that our shortcuts are robust against the decoherences caused by atomic spontaneous emission and cavity photon leakage.

We explore the possibility of entangling an excitonic two-level system in a semiconductor quantum dot with a cavity defined on a photonic crystal by sweeping the cavity frequency across its resonance with the exciton transition. The dynamic cavity detuning is established by a radio frequency surface acoustic wave (SAW). It induces Landau-Zener transitions between the excitonic and the photonic degrees of freedom and thereby creates a superposition state. We optimize this scheme by using tailored Fourier-synthesized SAW pulses with up to five harmonics. The theoretical study is performed with a master equation approach for present state-of-the-art setups. Assuming experimentally demonstrated system parameters, we show that the composed pulses increase both the maximum entanglement and its persistence. The latter is only limited by the dominant dephasing mechanism, i.e., the photon loss from the cavity.

Because of potential relevance to topological quantum information processing, we introduce and study the self-dual family of representations of the braid group. Self-dual representations are physically well motivated and provide a natural generalization of the Majorana and Gaussian representations, which appear as particular instances. To show that self-dual representations admit a particle interpretation, we introduce and describe in second quantization a family of particle species with $p=2,3,\cdots$ exclusion and $\theta =2\pi /p$ exchange statistics. We call these anyons Fock parafermions, because they are the particles naturally associated to the parafermionic zero-energy modes, potentially realizable in mesoscopic arrays of fractional topological insulators. Josephson junctions modeled with Fock parafermions may display a $2\pi p$ periodic relation between the Josephson current and the phase difference across the junction. Self-dual representations can be realized in terms of local quadratic combinations of either parafermions or Fock parafermions, an important requisite for physical implementation of quantum logic gates. The second-quantization description of Fock parafermions entails the concept of Fock algebra, i.e., a Fock space endowed with a statistical multiplication that captures and logically correlates these anyons' exclusion and exchange statistics. As a consequence normal ordering continues to be a well-defined operation.

We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the $6s^{21}{S}_0$, $6s6p{}^3{P}_0^o$, and $6s6p{}^3{P}_1^o$ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the $C_6$ coefficients for the Yb-Yb ${}^1{S}_0+{}^3{P}_{0,1}^o$ and ${}^3{P}_0^o+{}^3{P}_0^o$ dimers and $C_8$ coefficients for the ${}^1{S}_0+{}^1{S}_0$ and ${}^1{S}_0+{}^3{P}_1^o$ dimers.