We describe effects of matter-wave interference of spinor states in the ${}^{87}$Rb Bose-Einstein condensate. The components of the $F=2$ manifold are populated by forced Majorana transitions and then fall freely due to gravity in an applied magnetic field. Weak inhomogeneities of the magnetic field, present in the experiment, impose relative velocities onto different $m_F$ components, which show up as interference patterns upon measurement of atomic density distributions with a Stern-Gerlach imaging method. We show that interference effects may appear in experiments even if gradients of the magnetic field components are eliminated but higher-order inhomogeneity is present and the duration of the interaction is long enough. In particular, we show that the resulting matter-wave interference patterns can mimic spontaneous pattern formation in the quantum gas.

We perform numerical tests on the quantum nonlocality of two-level quantum systems (qubits) observed by a uniformly moving observer. Under a suitable momentum setting, the quantum nonlocality of two-qubit nonmaximally entangled states could be weakened drastically by the Lorentz transformation, allowing for the existence of local-hidden-variable models, whereas three-qubit genuinely entangled states are robust. In particular, the generalized Greenberger-Horne-Zeilinger state remains nonlocal under arbitrary Wigner rotation and the generalized $W$ state could admit local-hidden-variable models within a rather narrow range of parameters.

Nuclear-spin-dependent (NSD) parity violating effects are studied for a number of diatomic molecules using relativistic Hartree-Fock and density-functional theory and accounting for core polarization effects. Heavy diatomic molecules are good candidates for the successful measurement of the nuclear anapole moment, which is the dominant NSD parity violation term in heavy elements. Improved results for the molecules studied in our previous publication [Borschevsky et al., Phys. Rev. A 85, 052509 (2012)] are presented along with the calculations for a number of other promising candidates for the nuclear anapole measurements.

We study the ground states of lattice Hamiltonians that are invariant under permutations, in the limit where the number of lattice sites $N\to \infty$. For spin systems, these are product states, a fact that follows directly from the quantum de Finetti theorem. For fermionic systems, however, the problem is very different, since mode operators acting on different sites do not commute, but anticommute. We construct a family of fermionic states, $\mathcal{F}$, from which such ground states can be easily computed. They are characterized by few parameters whose number only depends on $M$, the number of modes per lattice site. We also give an explicit construction for $M=1,2$. In the first case, $\mathcal{F}$ is contained in the set of Gaussian states, whereas in the second it is not. Inspired by that construction, we build a set of fermionic variational wave functions, and apply it to the Fermi-Hubbard model in two spatial dimensions, obtaining results that go beyond the generalized Hartree-Fock theory.

We construct a theory for long-distance quantum communication based on sharing entanglement through a linear chain of $N$ elementary swapping segments of length $L=Nl$ where $l$ is the length of each elementary swap setup. Entanglement swapping is achieved by linear optics, photon counting, and postselection, and we include effects due to multiphoton sources, transmission loss, and detector inefficiencies and dark counts. Specifically we calculate the resultant four-mode state shared by the two parties at the two ends of the chain, and we derive the two-photon coincidence rate expected for this state and thereby the visibility of this long-range-entangled state. The expression is a nested sum with each sum extending from zero to infinite photons, and we solve the case $N=2$ exactly for the ideal case (zero dark counts, unit-efficiency detectors, and no transmission loss) and numerically for $N=2$ in the nonideal case with truncation at $n_{\max }=3$ photons in each mode. For the general case, we show that the computational complexity for the numerical solution is $n_{\max }^{12N}$.

We study the ground state of two-component bosonic atoms in a one-dimensional optical lattice. By applying an external field to the atoms at one end of the lattice, the atoms are transported and becomes localized at that site. The holes are then created in the remaining sites. The particle-hole superpositions are produced in this process. We investigate the entanglement entropy between the atoms in the two different parts of a lattice. A large degree of particle-hole entanglement is generated in the ground state. The particle-hole quantum correlations can be probed by the two-site parity correlation functions. The transport properties of the low-lying excited states are also discussed.

We study the steady-state photon statistics of a quadratically coupled optomechanical cavity, which is weakly driven by a monochromatic laser field. We examine the photon blockade by evaluating the second-order correlation function of the cavity photons. By restricting the system within the zero-, one-, and two-photon subspace, we obtain an approximate analytical expression for the correlation function. We also numerically investigate the correlation function by solving the quantum master equation including both optical and mechanical dissipations. The results show that, in the deep-resolved-sideband and single-photon strong-coupling regimes, the single-photon resonant driving will induce a photon blockade, which is limited by the thermal noise of the mechanical environment.

We investigate linear and nonlinear Faraday effects in a room-temperature, coherently driven four-level active-Raman-gain (ARG) medium. By using the multiple-scale method, we derive two nonlinear coupled envelope equations governing the dynamics of left- and right-polarized components of a linearly polarized probe field. Under the weak probe field approximation, we demonstrate a factor of four increase of the Faraday rotation angle by the linear and nonlinear response of the ARG scheme without probe field loss. We further compare this ARG system with an $M$-type five-state electromagnetically induced transparency (EIT) scheme and demonstrate the superiority of the ARG scheme over the conventional EIT scheme.

We report an improved measurement of the Landé $g_J$ factor of the $5D_{5/2}$ state of singly ionized barium. Measurements were performed on single Doppler-cooled ${}^{138}$Ba${}^{+}$ ions in linear Paul traps using two similar, independent apparatuses. Transitions between Zeeman sublevels of the $6S_{1/2}$ and $5D_{5/2}$ states were driven with two independent, stabilized radio-frequency synthesizers using a dedicated electrode within each ion trap chamber. State detection within each Zeeman manifold was achieved with a frequency-stabilized fiber laser operating at 1.76 $\mu$m. By calculating the ratio of the two Zeeman splittings, and using the measured Landé $g_J$ factor of the $6S_{1/2}$ state, we find a value of 1.200 372$\left(4_{\mathrm{stat}}\right)\left(7_{\mathrm{sys}}\right)$ for $g_{D_{5/2}}$.

In 1991, Peres and Wootters wrote a seminal paper on the nonlocal processing of quantum information [Phys. Rev. Lett. 66, 1119 (1991)]. We return to their classic problem and solve it in various contexts. Specifically, for discriminating the “double trine” ensemble with minimum error, we prove that global operations are more powerful than local operations with classical communication (LOCC). Even stronger, there exists a finite gap between the optimal LOCC probability and that obtainable by separable operations (SEP). Additionally we prove that a two-way, adaptive LOCC strategy can always beat a one-way protocol. Our results demonstrate “nonlocality without entanglement” in two-qubit pure states.

Current dynamical control based on the bang-bang control mechanism involving various types of pulse sequences is essentially a perturbative theory. This paper presents a nonperturbative dynamical control approach based on the exact stochastic Schrödinger equation. We report our findings on the pulse parameter regions in which the effective dynamical control can be exercised. The onset of the effective control zones reflects the nonperturbative feature of our approach. The nonperturbative methods offer possible new implementations when several different parameter regions are available.

Based on the fundamental concept of quantum counterfactuality, we propose a protocol to achieve quantum private database queries, which is a theoretical study of how counterfactuality can be employed beyond counterfactual quantum key distribution (QKD). By adding crucial detecting apparatus to the device of QKD, the privacy of both the distrustful user and the database owner can be guaranteed. Furthermore, the proposed private-database-query protocol makes full use of the low efficiency in the counterfactual QKD, and by adjusting the relevant parameters, the protocol obtains excellent flexibility and extensibility.

An alternative separation of short-range exchange and correlation energies is used in the framework of second-order range-separated density-functional perturbation theory. This alternative separation was initially proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] and relies on a long-range-interacting wave function instead of the noninteracting Kohn-Sham one. When second-order corrections to the density are neglected, the energy expression reduces to a range-separated double-hybrid (RSDH) type of functional, RSDHf, where “f” stands for “full-range integrals” as the regular full-range interaction appears explicitly in the energy expression when expanded in perturbation theory. In contrast to the usual RSDH functionals, RSDHf describes the coupling between long- and short-range correlations as an orbital-dependent contribution. Calculations on the first four noble-gas dimers show that this coupling has a significant effect on the potential energy curves in the equilibrium region, improving the accuracy of binding energies and equilibrium bond distances when second-order perturbation theory is appropriate.

The factors that caused the Be${}_2$ potential to be quite different from other conventional van der Waals potentials are quantitatively delineated with relatively simple self-consistent-field calculations. By decomposing the potential into its three major components, we are able to show that the rather sudden change of slope in the potential energy curve around 3.2 Å is the result of the interplay between the $sp$ hybridization and the correlation energy. It also enables us to model the interaction with a classical van der Waals potential, which provides the proper long-range behavior of the system, and a short-range attraction which mimics the effects of the $sp$ hybridization.

We present the electronic Casimir-Polder effect for a system consisting of two impurities on a one-dimensional semiconductor quantum wire. Due to the charge transfer from the impurity to a one-dimensional conduction band, the impurity states are dressed by a virtual cloud of the electron field. The attractive electronic Casimir force arises due to the overlap of the virtual clouds. The Van Hove singularity causes the persistent bound state (PBS) to appear below the band edge even when the bare impurity state energy is above the band edge. Since the decay rate of the virtual cloud of the PBS in space is small, the Casimir force can be of a very long range. While the overlap of the electronic virtual cloud is consistent with the idea of the radiation reaction, it is shown that also vacuum fluctuations play a role in the electronic Casimir force as a result of the fermionic anticommutation relations. We introduce an effective mass, different from the effective band mass of the conduction band, which is associated with the distance of the energy of the PBS from the band edge where the Van Hove singularity is located and determines the decay rate of the electronic Casimir-Polder force.

We employ the time-dependent $R$-matrix (TDRM) method to calculate anisotropy parameters for positive and negative sidebands of selected harmonics generated by two-color two-photon above-threshold ionization of argon. We consider odd harmonics of an 800-nm field ranging from the 13$\text{th}$ to 19$\text{th}$ harmonic, overlapped by a fundamental 800-nm IR field. The anisotropy parameters obtained using the TDRM method are compared with those obtained using a second-order perturbation theory with a model potential approach and a soft photon approximation approach. Where available, a comparison is also made to published experimental results. All three theoretical approaches provide similar values for anisotropy parameters. The TDRM approach obtains values that are closest to published experimental values. At high photon energies, the differences between each of the theoretical methods become less significant.

A coherent superposition of two electronic states of ozone (ground and Hartley $B$) is prepared with a UV pump pulse. Using the multiconfiguration time-dependent Hartree approach, we calculate the subsequent time evolution of the two corresponding nuclear wave packets and the coherence between them. The resulting wave packet shows an oscillation between the two chemical bonds. Even more interesting, the coherence between the two electronics states reappears after the laser pulse is switched off, which could be observed experimentally with an attosecond probe pulse.

Ultracold atomic gases with short-range interactions are characterized by a number of universal species-independent relations. Many of these relations involve the two-body Tan contact. Employing the canonical ensemble, we determine the Tan contact for small harmonically trapped two-component Fermi gases at unitarity over a wide range of temperatures, including the zero and high-temperature regimes. A cluster expansion that describes the properties of the $N$-particle system in terms of those of smaller subsystems is introduced and shown to provide an accurate description of the contact in the high-temperature regime. Finite-range corrections are quantified and the role of the Fermi statistics is elucidated by comparing results for Fermi, Bose, and Boltzmann statistics.

Quantum simulations of high-energy physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge invariance and relativistic structure. In this paper we discuss these special requirements, and present a method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows us to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low-energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: U(1) (compact QED), ${\mathbb{Z}}_N$ and SU$\left(N\right)$ (Yang-Mills), which can be used to build quantum simulators in $1+1$ dimensions. We also present a loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for $d+1$ dimensional lattice gauge theories ($d>1$), but unlike in previous proposals, here gauge invariance and Gauss's law are natural symmetries, which do not have to be imposed as a constraint. We discuss in detail the quantum simulation of $2+1$ dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge-invariant elementary interactions of this model suggests it may be useful for future experimental realizations.