Following the idea of the density-functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap by using a local chemical potential, calculated with the Lieb-Liniger exact solution, as the exchange energy. At zero temperature, we use the theory to describe collective modes of a finite-particle system in all interaction regimes from the ideal gas limit to the mean-field Thomas-Fermi regime and to the strongly interacting Tonks-Girardeau regime. At finite temperature, we investigate the temperature dependence of collective modes in the weak-coupling regime by means of a Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the effects of finite particle number and nonzero temperature on collective-mode frequencies, we compare our results with a recent experimental measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous theoretical predictions. We show that the experimental data are still not fully explained within current theoretical framework.

Finite systems of bosons and/or fermions described by the Hubbard model can be realized using ultracold atoms confined in optical lattices. The ground states of these systems often exhibit a coexistence of compressible superfluid and incompressible Mott insulating domains. We analyze such systems by studying the out-of-equilibrium dynamics following a weak sudden quench of the trapping potential. In particular, we show how the temporal variance of the site occupations reveals the location of spatial boundaries between compressible and incompressible regions. The feasibility of this approach is demonstrated for several models using numerical simulations. We first consider integrable systems, hard-core bosons (spinless fermions) confined by a harmonic potential, where space-separated Mott and superfluid phases coexist. Then, we analyze a nonintegrable system, a $J\text{−}V\text{−}{V}^{\prime }$ model, with coexisting charge density wave and superfluid phases. We find that the temporal variance of the site occupations is a more effective measure than other standard indicators of phase boundaries such as a local compressibility. Finally, to make contact with experiments, we propose a consistent estimator for such temporal variance. Our numerical experiments show that the phase boundary is correctly spotted using as little as 30 measurements. Based on these results, we argue that analyzing temporal fluctuations is a valuable experimental tool for exploring phase boundaries in trapped atom systems.

Recent demonstrations of cavity quantum electrodynamics (QED) with a single quantum emitter coupled to an optical microcavity have shown the great potential of this system for engineering the light-matter interaction and developing a wide range of robust quantum devices. Here, we study the creation and all-optical control of optical frequency combs (OFCs) in photon emission from a single-quantum-emitter-microcavity QED system driven with a biharmonic pump light in the presence of a classical control light. We find that, when the strengths and phases of the applied control light are appropriately tuned, enhanced OFC generation can occur by using the parameters of currently existing QED systems. The interference between the biharmonic pump light, which is used to drive the cavity mode, and the light scattered by the two-level emitter into the cavity mode due to the second control light are responsible for the enhancement or suppression of OFCs. We further analyze in detail the influences of the other system parameters including the emitter-cavity coupling strength, the incident pump power, and all kinds of relative frequency detunings on all-optical generation of OFCs. In addition to numerical simulations demonstrating this controlled OFC effect, a complete physical explanation of the underlying mechanism is presented. The presented mechanism can be employed for tailoring and controlling OFCs in a cavity QED architecture.

Magnetic resonance in an ensemble of laser-cooled trapped Rb atoms is excited using a microcantilever with a magnetic tip. The cantilever is mounted on a multilayer chip designed to capture, cool, and magnetically transport cold atoms. The coupling is observed by measuring the loss from a magnetic trap as the oscillating cantilever induces Zeeman-state transitions in the atoms. Interfacing cold atoms with mechanical devices could enable probing and manipulating atomic spins with nanometer spatial resolution and single-spin sensitivity, leading to new capabilities in quantum computation, quantum simulation, and precision sensing.

Single quantum dots (QDs) are frequently used as single-photon sources, taking advantage of the final exciton decay in a cascade that produces energetically detuned photons. We propose and analyze a new concept of single-photon source, namely, a few-QD microcavity system driven close to, but below the lasing threshold under strong excitation. Surprisingly, even for two or three QDs inside a cavity, antibunching is observed. To quantify the results, we find that a classification of single-photon emission in terms of antibunching in the autocorrelation function $g^{\left(2\right)}\left(0\right)$ is insufficient and more details of the photon statistics are required. Our investigations are based on a quantum-optical theory that we solve to obtain the density operator for the quantum-mechanical active medium and radiation field.

The Casimir force between two parallel plates separated by anisotropic media is investigated. We theoretically calculate the Casimir force between two parallel plates when the interspace between the plates is filled with anisotropic media. Our result shows that the anisotropy of the material between the plates can significantly affect the Casimir force, especially the direction of the force. If ignoring the anisotropy of the in-between material makes the force repulsive (attractive), by contrast taking the anisotropy into account may produce an extra attractive (repulsive) force. The physical explanation for this phenomenon is also discussed.

Based on the scattering theory, simultaneously enhanced energy transport and suppressed momentum exchange are demonstrated by patterning doped-silicon surfaces in the near field. The radiative heat flux between doped-silicon gratings exceeds that between planar surfaces and can be one or even two orders of magnitude higher than what is predicted by the geometry-based Derjaguin proximity approximation (PA). The underlying mechanism is interpreted as due to the excitation of broadband hyperbolic modes that facilitate photon tunneling, especially when the period is small. This is confirmed by a comparison of the results from the scattering theory with those from the effective-medium theory. The Casimir force, which may cause stiction and even failure of mesoscopic devices, is reduced with the grating structures as predicted by both the scattering theory and PA. However, depending on the separation distance, the PA may over- or underpredict the Casimir force.

The Lamb shift in the light hydrogenlike atoms is evaluated for the state-dependent part of the $S$ states $(n^3\mathrm{\Delta }{E}_n-\mathrm{\Delta }{E}_1)/n^3$ and $P_{1/2}$ states by means of a recently proposed relativistic generalization of multipole expansion. We obtain the results for $Z=1–5$ and $n=2–10$, where $Z$ is the charge of the nucleus and $n$ is the principal quantum number of the state under consideration. The results are in an excellent agreement with the results obtained by means of $Z\alpha$ expansion truncated after the $\alpha {\left(Z\alpha \right)}^6$ term. The state-dependent part of the $S$ states for $n=2–4$ is evaluated also for the case of moderately strong Coulomb fields, $Z=10–50$. It is argued that the present results for the state-dependent part of the $S$ states for low $Z$ are the most accurate results given so far in the literature. In the case of hydrogen the uncertainty is significantly less than 1 Hz. Finally, the extrapolation of the results to infinite $n$ is performed.

We have obtained accurate ab initio ${}^4\mathrm{\Sigma }^{+}$ quartet potentials for the diatomic metastable triplet helium+alkali-metal (Li, Na, K, Rb) systems, using all-electron restricted open-shell coupled cluster singles and doubles with noniterative triples corrections CCSD(T) calculations and accurate calculations of the long-range $C_6$ coefficients. These potentials provide accurate ab initio quartet scattering lengths, which for these many-electron systems is possible, because of the small reduced masses and shallow potentials that result in a small amount of bound states. Our results are relevant for ultracold metastable triplet helium+alkali-metal mixture experiments.

The electron angular distribution after atomic photoionization by the fundamental frequency and its second harmonic is analyzed for a case when the frequency of the fundamental scans the region of an intermediate atomic state. The angular distribution and its left-right asymmetry, due to the two-pathway interference between nonresonant one-photon and resonant two-photon ionization, sharply change as a function of the photon energy. The phenomenon is exemplified by both solving the time-dependent Schrödinger equation on a numerical space-time grid and by applying perturbation theory for ionization of the hydrogen atom in the region of the $1s\text{−}2p$ transition for femtosecond pulses as well as an infinitely long exposure to the radiation. Parametrizations for the asymmetry and the anisotropy coefficients, obtained within perturbation theory, reveal general characteristics of observable quantities as functions of the parameters of the radiation beam.

We report about possible formation of highly correlated electron pairs in the heterocyclic aromatic hydrocarbons pyridine, pyrimidine, and 1,3,5-triazine. Previously, these electron pairs have been observed in the acenes and in coronene, but not in pyrrole and furan. Our measurements presented here shed some light on the conditions for electron-pair formation and emission. Aromatic hydrocarbons are discussed as candidates for high-temperature superconductors and our findings may help to better understand the mechanisms in organic superconductors.

We have studied computationally the collision dynamics of spin-2 Bose-Einstein condensates initially confined in a triple-well trap. Depending on the phase structure of the initial-state spinor wave function, the collision of the three condensate fragments produces one of many possible vortex-antivortex lattices, after which the system transitions to quantum turbulence. We find that the emerging vortex lattice structures can be described in terms of multiwave interference. We show that the three-fragment collisions can be used to systematically produce staggered vortex-antivortex honeycomb lattices of fractional-charge vortices, whose collision dynamics are known to be non-Abelian. Such condensate collider experiments could potentially be used as a controllable pathway to generating non-Abelian superfluid turbulence with networks of vortex rungs.

We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter $r$ and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter $r$.

Strong deformation of ultrashort laser pulse shapes is unavoidable when delivering high intensities at remote distances due to nonlinear effects taking place while propagating. Relying on the reversibility of laser filamentation, we propose to explicitly design laser pulse shapes so that propagation serves as a nonlinear field synthesizer at a remote target location. Such an approach allows, for instance, coherent control of molecules at a remote distance, in the context of standoff detection of pathogens or explosives.

We give a necessary condition that a separable measurement can be implemented by local quantum operations and classical communication (LOCC) in any finite number of rounds of communication, generalizing and strengthening a result obtained previously. That earlier result involved a bound that is tight when the number of measurement operators defining the measurement is relatively small. The present results generalize that bound to one that is tight for any finite number of measurement operators, and we also provide an extension which holds when that number is infinite. We apply these results to the famous example on a $3\times 3$ system known as “domino states,” which were the first demonstration of nonlocality without entanglement. Our extended necessary condition provides another way of showing that these states cannot be perfectly distinguished by (finite-round) LOCC. It directly shows that this conclusion also holds for their related rotated domino states. We also introduce a class of problems involving the unambiguous discrimination of quantum states, each of which is an example where the states can be optimally discriminated by a separable measurement, but according to our condition, cannot be optimally discriminated by LOCC. These examples nicely illustrate the usefulness of the present results, since our earlier necessary condition, which the present result generalizes, is not strong enough to reach a conclusion in any of these cases.

A physical realization of self-correcting quantum code would be profoundly useful for constructing a quantum computer. In this theoretical work, we provide a partial solution to major challenges preventing self-correcting quantum code from being engineered in realistic devices. We consider a variant of Kitaev's toric code coupled to propagating bosons, which induce a ranged interaction between anyonic defects. By coupling the primary quantum system to an engineered dissipation source through resonant energy transfer, we demonstrate a “rate barrier” which leads to a potentially enormous increase in the system's quantum-state lifetime through purely passive quantum error correction, even when coupled to an infinite-temperature bath. While our mechanism is not scalable to infinitely large systems, the maximum effective size can be very large, and it is fully compatible with active error-correction schemes. Our model uses only on-site and nearest-neighbor interactions and could be implemented in superconducting qubits. We sketch one such implementation at the end of this work.

With the local resonant interaction between a nitrogen-vacancy-center ensemble (NVE) and a superconducting coplanar resonator, and the single-qubit operation, we propose two protocols for the state transfer between two remote NVEs and for a fast controlled-phase (cphase) gate on these NVEs, respectively. This hybrid quantum system is composed of two distant NVEs coupled to separated high-$Q$ transmission line resonators (TLRs), which are interconnected by a current-biased Josephson-junction superconducting phase qubit. The fidelity of our state-transfer protocol is about $99.63\%$ within the operation time of $70.60$ ns. The fidelity of our cphase gate is about $98.15\%$ within the operation time of $93.87$ ns. Furthermore, using the cphase gate, we construct a two-dimensional cluster state on NVEs in a $n\times n$ square grid based on the hybrid quantum system for the one-way quantum computation. Our protocol may be more robust, compared with the one based on the superconducting resonators, due to the long coherence time of NVEs at room temperature.

We study the problem of remote one-qubit mixed state creation using a pure initial state of two-qubit sender and spin-1/2 chain as a connecting line. We express the parameters of creatable states in terms of transition amplitudes. We show that the creation of a complete receiver's state space can be achieved only in the chain engineered for the one-qubit perfect state transfer (PST) (for instance, in the fully engineered Ekert chain); the chain can be arbitrarily long in this case. As for the homogeneous chain, the creatable receiver's state region decreases quickly with the chain length. Both homogeneous chains and chains engineered for PST can be used for the purpose of selective state creation, when only the restricted part of the whole receiver's state space is of interest. Among the parameters of the receiver's state, the eigenvalue is the most hard to create and therefore deserves special study. Regarding the homogeneous spin chain, an arbitrary eigenvalue can be created only if the chain is of no more than 34 nodes. The alternating chain allows us to increase this length to up to 68 nodes.

Energy levels, radiative transition probabilities, and autoionization rates for $\text{[Ar]}3d^{10}4l^{\prime }nl (n=4–12, l\le n-1), \text{[Ar]}3d^{10}5l^{\prime }nl (n=5–8, l\le n-1)$, and $\text{[Ar]}3d^{9}4l^{\prime }4l^{\prime \prime }nl (n=4–5, l\le n-1$) states in Zn-like tungsten (${\mathrm{W}}^{44+}$) are calculated using the relativistic Hartree-Fock method (cowan code), the multiconfiiguration relativistic Hebrew University Lawrence Livermore Atomic Code (hullac code), and the relativistic many-body perturbation theory method (rmbpt code). Autoionizing levels above the thresholds $\text{[Ar]}3d^{10}4s$ are considered. It is found that configuration mixing $\left[4sns+4pnp+4dnd+4fnf\right], \left[4snp+4pns+4pnd+4dnp+4fns+4fnd\right]$ plays an important role for all atomic characteristics. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the first excited odd- and even-parity states. It is shown that the contribution of the highly excited states is very important for the calculation of total DR rates. Contributions to DR rate coefficients from the excited $\text{[Ar]}3d^{10}4l^{\prime }nl$ states with $n>12$ and $\text{[Ar]}3d^{10}5l^{\prime }nl$ states with $n>8$, and additionally from core-excited $\text{[Ar]}3d^{9}4l^{\prime }4l^{\prime \prime }nl$ states with $n>5$, are estimated by extrapolation of all atomic parameters. The orbital angular momentum quantum number $l$ distribution of the rate coefficients shows two peaks at $l=2$ and $l=5$. The total DR rate coefficient is derived as a function of electron temperature. The dielectronic satellite spectra of ${\mathrm{W}}^{44+}$ are important for $M$-shell diagnostic of very high-temperature laboratory plasmas such as those found in future tokamaks.