By examining balanced homodyne defectors (BHDs) from the general quantum-field-theoretical point of view we derive a number of generalizations of the standard analysis of their response. In particular, by allowing for interactions restricted in time (by a smooth function) we present general expressions for BHD output (in which the usual, simplifying limits can but need not be taken). Moreover, we point out the need for nonstrictly monochromatic local oscillators (i.e., the need for “pulsed” ones) in order to have well-defined quantum-field-theory (QFT) observables (the products of which, e.g., have finite vacuum expectation values). Furthermore, we show how the analysis of the detectors generalize to situations with BHDs in waveguides, Casimir cavities, or other time-independent but inhomogeneous $ϵ$ and $\mu$. The general treatment also allows us to comment on important QFT features of the detector observables such as locality (i.e., commuting for causally separated measurements) and non-null vacuum response. This leads to the conclusion that balanced homodyne-type detectors (and not single photodiodelike ones) are the appropriate tools in testing intriguing QFT predictions such as negative (subvacuum) energy densities. Finally, by recalling results on field-autocorrelation functions for QFT in Casimir cavities we show that interesting effects (large reductions of fluctuations) are to be expected if a version of BHDs were to be placed in such cavities.

It is known that the states in an unextendible product basis (UPB) cannot be distinguished perfectly when the parties are restricted to local operations and classical communication (LOCC). Previous discussions of such bases have left open the following question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In this paper, I present protocols which use entanglement more efficiently than teleportation to distinguish certain classes of UPB’s. The ideas underlying my approach to this problem offer rather general insight into why entanglement is useful for such tasks.

We show that bipartite concurrence for rank-2 mixed states of qubits is written by an observable which can be exactly and directly measurable in experiment by local projective measurements, provided that four copies of the composite quantum system are available. In addition, for a tripartite quantum pure state of qubits, the 3-tangle is also shown to be measurable only by projective measurements on the reduced density matrices of a pair of qubits conditioned on four copies of the state.

We report results of ab initio calculations of excited states of the fullerene molecule using the configuration-interaction approach with singly excited determinants (SCI). We have used both experimental geometry and the geometry optimized by the density functional method and worked with basis sets at the correlation-consistent polarization valence triple-$\zeta$ (cc-pVTZ) and augmented cc-pVTZ levels. In contrast to the early SCI semiempirical calculations, we find that the two lowest ${{}^{1}T}_{1u}\leftarrow {{}^{1}A}_g$ electron optical lines are situated at relatively high energies of $\sim 5.8\text{eV}$ (214 nm) and $\sim 6.3\text{eV}$ (197 nm). These two lines originate from two ${{}^{1}T}_{1u}\leftarrow {{}^{1}A}_g$ transitions: from the highest occupied molecular orbital (HOMO) to one above the lowest unoccupied molecular orbital $\left(\text{LUMO}+1\right)$ $\left(6h_u\to 3t_{1g}\right)$ and from $\left(\text{HOMO}-1\right)$ to LUMO $\left(10h_g\to 7t_{1u}\right)$. The lowest molecular excitation, which is the $1{{}^{3}T}_{2g}$ level, is found at $\sim 2.5\text{eV}$. Inclusion of doubly excited determinants leads only to minor corrections to this picture. We discuss possible assignment of absorption bands at energies smaller than 5.8 eV (or $\lambda$ larger than 214 nm).

We formulate the quantization rule $n_{\mathrm{th}}-n=F\left(E_n\right)$ for bound-state energies $E_n$ in a deep potential well with a long-range attractive tail for an extended range of near-threshold energies. This makes it possible to accurately read off the scattering length $a$ from the energy of a high-lying (not necessarily the highest-lying) bound state via $a=\overline{a}+b∕\tan \left[\pi F\right(E_n\left)\right]$. For a potential tail proportional to $-1∕r^{\alpha }$, $\alpha >3$, the constants $\overline{a}$ and $b$ are known and an explicit and universally valid expression for the function $F\left(E\right)$ is given analytically.

Measurements of differential cross sections (DCSs) for electron-impact excitation of the $a^{″}{}^1\Sigma _g^{+}$, $b{}^1\Pi _u$, $c_3{}^1\Pi _u$, $o_3{}^1\Pi _u$, $b^{\prime }{}^1\Sigma _u^{+}$, $c_4^{\prime }{}^1\Sigma _u^{+}$, $G{}^3\Pi _u$, and $F{}^3\Pi _u$ states in ${\mathrm{N}}_2$ from the $X{}^1\Sigma _g^{+}(v^{″}=0)$ ground level are presented. The DCSs were obtained from energy-loss spectra in the region of $12\text{to}13.82\mathrm{eV}$ measured at incident energies of 17.5, 20, 30, 50, and $100\mathrm{eV}$ and for scattering angles ranging from 2° to 130°. The analysis of the spectra follows a different algorithm from that employed in a previous study of ${\mathrm{N}}_2$ for the valence states [Khakoo et al. Phys. Rev. A 71, 062703 (2005)], since the ${}^1\Pi _u$ and ${}^1\Sigma _u^{+}$ states form strongly interacting Rydberg-valence series. The results are compared with existing data.

We analyze the ground-state phases of two-component $(\sigma \equiv \{\uparrow ,\downarrow \})$ population- and mass-balanced ($N_{\uparrow }=N_{\downarrow }$ and $m_{\uparrow }=m_{\downarrow }$) but trap-imbalanced $({\omega }_{\uparrow }\ne {\omega }_{\downarrow })$ fermion mixtures as a function of interaction strength from the weak attraction Bardeen-Cooper-Schrieffer (BCS) to the strong attraction Bose-Einstein condensation (BEC) limit. In the BCS limit, we find that the unpolarized superfluid (UPS) fermions exist away from the central core of the trapping potentials, and are surrounded by partially $\sigma$-polarized normal $\left(\mathrm{P}\sigma \mathrm{PN}\right)$ fermions. As the interactions increase towards unitarity, we find that the central $\mathrm{P}\sigma \mathrm{PN}$ core first transitions to a UPS, and then expands towards the edges until the entire mixture becomes a UPS in the BEC limit.

We study a model for ultracold, spinless atoms in quasi-one-dimensional optical lattices and subjected to a tunable tilting force. Statistical tests are employed to quantitatively characterize the spectrum of the Floquet-Bloch operator of the system along the transition from the regular to the quantum chaotic regime. Moreover, we perturbatively include the coupling of the one-band model to the second energy band. This allows us to study the Landau-Zener interband tunneling within a truly many-body description of ultracold atoms. The distributions of the computed tunneling rates provide an independent and experimentally accessible signature of the regular-chaotic transition.

The Casimir effect between two left-handed-material (LHM) slabs is investigated. For the LHM described by dispersive permittivity and permeability of Drude-Lorentz type, the structure of dispersion curve over negative refraction frequency band is determined by material characteristic frequencies. The bandwidth of the negative refraction characterizes the reflection property, and thus influences the Casimir effect between the slabs. Furthermore, a comparison of the Casimir forces for LHM and ordinary dielectric slabs, which have the opposite values of refractive indices at the chosen frequency, is shown. Generally, the force for LHM with sufficiently large bandwidth of negative refraction is greater than the force for ordinary dielectrics.

We determine the superfluid transition temperatures $T_c$ and the ground states of the attractive Hubbard model and find unusual insulating phases associated with noninteger filling at sufficiently strong pairing attraction $\mid U\mid$. These states, distinct from the band-and Mott-insulating phases, derive from pair localization; pair hopping at large $\mid U\mid$ and high densities is impeded by intersite, interpair repulsive interactions. The best way to detect the breakdown of superfluidity is by using fermionic optical lattices, which should reveal these unusual forms of “bosonic” order, reflecting ground-state pairing without condensation.

Many schemes to realize quantum state transfer in spin chains are not robust to random fluctuations in the spin-spin coupling strength. In efforts to achieve robust quantum state transfer, an adiabatic quantum population transfer scheme is proposed in this study. The proposed scheme makes use of a slowly moving external parabolic potential and is qualitatively explained in terms of the adiabatic following of a quantum state with a moving separatrix structure in the classical phase space of a pendulum analogy. Detailed aspects of our adiabatic population transfer scheme, including its robustness, is studied computationally. Applications of our adiabatic scheme in quantum information transfer are also discussed, with emphasis placed on the usage of a dual spin chain to encode quantum phases. The results should also be useful for the control of electron tunneling in an array of quantum dots.

Stark widths and shifts of 35 singly charged krypton ion spectral lines have been measured in a pulsed discharge lamp, where electron density ranges from $0.35–0.8\times {10}^{23}{\mathrm{m}}^{-3}$ and electron temperature ranges from $15000–27000\mathrm{K}$. This work extends a previous one [A. de Castro et al., J. Phys. B: At. Mol. Opt. Phys. 34, 3275 (2001)] already published by our laboratory. Intramultiplet and intratransition nonregularities have been found and have been explained by considering the perturbing levels effect on the Stark parameters for each one of the measured spectral lines.

We give a detailed account on our semiempirical calculations of the forbidden electric tensor polarizability ${\alpha }_2^{\left(3\right)}$ of the ground state of free Cs atoms and of Cs atoms implanted in a solid ${}^4\mathrm{He}$ matrix. The results are compared with measurements of ${\alpha }_2^{\left(3\right)}$ in the free atoms [Europhys. Lett. 76, 1074 (2006)] and in He-trapped atoms [Phys. Rev. A 75, 042505 (2007)]. Features with respect to calculations by other authors are the inclusion of off-diagonal hyperfine interactions and an analysis of contributions from continuum states, which turn out to be negligible. For both samples the results of the calculations are in good agreement with the experimental values, thereby settling a long-standing discrepancy.

State-selective electron-capture processes in low-energy collisions of ${\text{O}}^{3+}$ recoil ions with He, Ar, ${\text{D}}_2$, ${\text{O}}_2$, ${\text{H}}_2\text{O}$, and ${\text{CO}}_2$ at impact energies between 0.3 and 1.2 keV and scattering angles between $0°$ and $6°$ have been studied using a differential energy-gain spectrometer, capable of measuring simultaneously the energy-gain and the scattering angle of projectile products in ion-atom and -molecule collisions. The energy-gain spectra show that the dominant reaction channels are due to capture into excited states of the projectile product ${\text{O}}^{2+}$. In this work, no clear evidence of the processes involving long-lived metastable state ${\text{O}}^{3+}$ $\left(2s2p^2{}^{4}P\right)$ was observed. The energy-gain spectra are interpreted qualitatively in terms of the reaction windows, which are calculated using the single-crossing Landau-Zener model and the extended version of the classical over-the-barrier model. The energy dependence of cross sections for electron capture are also measured and found to be nearly constant with changing collision energy. The data are also compared with available measurements and calculations and theoretical results based on the multichannel Landau-Zener model.

The mathematical term for the mean flow velocity in supersonic beams of ideal gases is extended to include real gas properties. This procedure yields an explicit dependence of the flow velocity on pressure, as observed in recent experiments of free jet expansions. Applied to stagnation conditions slightly above the critical point, the model suggests that seeded high-pressure jet expansions might be suitable for slowing down virtually any molecule with maximum efficiency. Moreover, we discuss the consequence of a pressure-dependent flow velocity $v_0$ for the speed ratio $S=v_0/\Delta v_{\parallel }$ with respect to collisional cooling and suggest to use the velocity spread $\Delta v_{\parallel }$ as a more nonambiguous measure of translational temperature in high-pressure jet expansions.

We study the nonlinear dynamics of the splitting of a doubly quantized vortex in a trapped Bose-Einstein condensate. The dynamics is studied in detail by solving the Gross-Pitaevskii equation. The main dynamical features are explained in terms of a nonlinear three-level system, to which we find an analytical solution. This result is compared to linear Bogoliubov analysis and to the full numerical time evolution. It is concluded that the time scale for the splitting is mainly determined by the instability of the linearized system, and nonlinear effects contribute logarithmically.

We show the possibility of directional guided superradiance from a linear array of distant atoms separated by one or several wavelengths in a line parallel to the axis of a nanofiber. We find that the rate and efficiency of channeling of emission from the atoms into the fiber are cooperatively enhanced by the guided modes.

We consider the problem of whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on $n$ qubits that involve at most two-body interactions, we show that no $n$-qubit graph state can be the exact, nondegenerate ground state. We determine for any graph state the minimal $d$ such that it is the nondegenerate ground state of a $d$-body interaction Hamiltonian, while we show for $d^{\prime }$-body Hamiltonians $H$ with $d^{\prime }<d$ that the resulting ground state can only be close to the graph state at the cost of $H$ having a small energy gap relative to the total energy. When allowing for ancilla particles, we show how to utilize a gadget construction introduced in the context of the $k$-local Hamiltonian problem, to obtain $n$-qubit graph states as nondegenerate (quasi)ground states of a two-body Hamiltonian acting on $n^{\prime }>n$ spins.

Controlled generation and manipulation of photon states encoded in their spatial degrees of freedom is a crucial ingredient in many quantum-information tasks exploiting higher-than-two dimensional encoding. Here, we prove the impossibility to arbitrarily modify $d$-level state superpositions (qudits) for $d>2$, encoded in the transverse modes of light, with optical components associated to the group of symplectic transforms (Gaussian operations). Surprisingly, we also provide an explicit construction of how non-Gaussian operations acting on mode subspaces do enable one to overcome the limit $d=2$. In addition, this set of operations realizes the full SU(3) algebra.

We provide a detailed analysis of our previously proposed scheme [J. Ruostekoski, G. V. Dunne, and J. Javanainen, Phys. Rev. Lett. 88, 180401 (2002)] to engineer the profile of the hopping amplitudes for atomic gases in a one-dimensional optical lattice so that the particle number becomes fractional. We consider a constructed system of a dilute two-species gas of fermionic atoms where the two components are coupled via a coherent electromagnetic field with a topologically nontrivial phase profile. We show both analytically and numerically how the resulting atomic Hamiltonian in a prepared dimerized optical lattice with a defect in the pattern of alternating hopping amplitudes exhibits a fractional fermion number. In particular, in the low-energy limit we demonstrate the equivalence of the atomic Hamiltonian to a relativistic Dirac Hamiltonian describing fractionalization in quantum field theory. Expanding on our earlier argument [J. Javanainen and J. Ruostekoski, Phys. Rev. Lett. 91, 150404 (2003)] we show how the fractional eigenvalues of the particle number operator can be detected via light scattering. In particular, we show how scattering of far-off resonant light can convey information about the counting and spin statistics of the atoms in an optical lattice, including state-selective atom density profiles and atom number fluctuations. Optical detection could provide a truly quantum mechanical measurement of the particle number fractionalization in a dilute atomic gas.