We study the generation of two-mode entanglement in a two-component Bose-Einstein condensate trapped in a double-well potential. The dynamics of the system is shown to be equivalent to that of two coupled harmonic oscillators in the low excitation regime. Strong entanglement between the two components can be achieved if the interspecies interaction is sufficiently strong. In particular, the condensate constitutes a symmetric Gaussian system and hence its entanglement of formation can be measured directly by fluctuations in the quadratures of the two constituent components.

We discuss the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding, respectively, to a classical thermal light source and a quantum two-photon entangled source. Due to the different features in the second-order spatial correlation, the two sources obey different imaging equations. The quantum entangled source behaves as a mirror, whereas the classical thermal source looks like a phase-conjugate mirror in the correlated imaging.

A tomographic process for three-qubit pure states using only pairwise detections is presented.

In this Rapid Communication, we show that a simple process of two-step double ionization taking place in an atom $A$, following the absorption of a single photon, produces a spin-entangled state of two electrons. The degree of entanglement of this state can be tuned to the desired value by selecting appropriate total spin quantum numbers of the electronic states of each of the three atomic species (i.e., $A,A^{+},A^{2+}$) participating in the process in Russell-Saunders coupling. These entangled states are readily characterized by measuring only energies of two emitted electrons, without requiring the entanglement witness, or any other such protocol.

We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-$1∕2$ subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.

A single three-level atom driven by a longitudinal mode of a high-$Q$ cavity is used to implement two-qubit quantum phase gates for the intracavity field. The two qubits are associated with the zero- and one-photon Fock states of each of the two opposite circular polarization states of the field. The three-level atom mediates the conditional phase gate provided the two polarization states and the atom interact in a V-type configuration and the two-photon resonance condition is satisfied. Microwave and optical implementations are discussed with gate fidelities being evaluated against several decoherence mechanisms such as atomic velocity fluctuations or the presence of a weak magnetic field. The use of coherent states for both polarization states is investigated to assess the entanglement capability of the proposed quantum gates.

Using two 500-fs laser pulses and a controlled time delay between them we are able to manipulate the angular distributions of the electrons ejected by autoionization of Ca atoms in the $4p_{3∕2}21s$ and $4p_{3∕2}19d$ states. Subsequent to their isolated core excitation by a 500-fs 393-nm laser pulse, $\mathrm{Ca}4p_{3∕2}21s\left(19d\right)$ Rydberg atoms coherently evolve, via configuration interaction, into the degenerate $4p_{1∕2}ns\left(nd\right)$ states. While in the $4p_{1∕2}ns\left(nd\right)$ states atoms can be de-excited to bound $4sns\left(nd\right)$ levels using a 500-fs 397-nm pulse. Removing these atoms from the autoionizing states leads to a greater fraction of electrons leaving the atom along the direction of the laser polarization than is possible through direct excitation of $4_{3∕2}ns\left(nd\right)$ or $4p_{1∕2}ns\left(nd\right)$ using either the 393- or 397-nm pulse alone.

The electron-ion recombination spectrum of the Li-like ${\mathrm{Na}}^{8+}$ ion in the energy range $0.0–0.5\mathrm{eV}$ is presented. Experimental results obtained by storage-ring techniques are compared with a calculated spectrum, based on a combination of relativistic many-body methods and complex rotation, and the agreement is found to be very good. The deviations between measured and calculated dielectronic recombination resonance energies are usually below about $2\mathrm{meV}$ with a maximum difference at $5.5\mathrm{meV}$, while the theoretical cross sections deviate by at most 20% from the experiment. The recombination spectrum in the investigated energy region is determined by the $2p_{j}7{\ell }_{j^{\prime }}$ Rydberg manifold of dielectronic recombination resonances, comprising 61 states within half an eV above the ground state of ${\mathrm{Na}}^{8+}$. The theoretical resonance parameters of all contributing states are provided.

We present a joint theoretical and experimental investigation of the N $1s$ photoionization of $\mathrm{N}{\mathrm{O}}_2$ in the shape resonance region. The theoretical calculations, based on a single-channel relaxed-core Hartree-Fock approximation, predict that the shape resonance appears only in the $A_1\to B_2$ transition and that the shape resonance energy of the N $1s^{-1}$ ${}^{1}A_1$ channel is about $2.6\mathrm{eV}$ lower in kinetic energy than that of the N $1s^{-1}$ ${}^{3}A_1$ channel, suggesting that the potential for the ${}^{1}A_1$ channel is much more attractive than that for the ${}^{3}A_1$ channel. Symmetry-selected cross sections measured by means of a multiple-ion coincidence imaging prove that the shape resonance appears only in the $A_1\to B_2$ transition, as predicted by the calculation. The experimental partial cross sections for the N $1s^{-1}$ ${}^{1}A_1$ and ${}^{3}A_1$ channels measured by means of conventional electron spectroscopy exhibit the shape-resonance maxima at photon energies of 416.3 and $415.9\mathrm{eV}$, respectively, at corresponding kinetic energies of 3.0 and $3.3\mathrm{eV}$, respectively, implying that the attractive potential for the ${}^{1}A_1$ channel is overestimated in the single-channel approximation. The possible role played by correlation effects on the $K$-shell ionization of $\mathrm{N}{\mathrm{O}}_2$ is discussed in terms of interchannel coupling between the main-line channels and, possibly, with additional excited target states.

We present a detailed investigation of the momentum-dependent self-energy $\Sigma \left(k\right)$ at zero frequency of weakly interacting bosons at the critical temperature $T_c$ of Bose-Einstein condensation in dimensions $3⩽D<4$. Applying the functional renormalization group, we calculate the universal scaling function for the self-energy at zero frequency but at all wave vectors within an approximation which truncates the flow equations of the irreducible vertices at the four-point level. The self-energy interpolates between the critical regime $k⪡k_c$ and the short-wavelength regime $k⪢k_c$, where $k_c$ is the crossover scale. In the critical regime, the self-energy correctly approaches the asymptotic behavior $\Sigma \left(k\right)\propto k^{2-\eta }$, and in the short-wavelength regime the behavior is $\Sigma \left(k\right)\propto k^{2(D-3)}$ in $D>3$. In $D=3$, we recover the logarithmic divergence $\Sigma \left(k\right)\propto \ln (k∕k_c)$ encountered in perturbation theory. Our approach yields the crossover scale $k_c$ as well as a reasonable estimate for the critical exponent $\eta$ in $D=3$. From our scaling function we find for the interaction-induced shift in $T_c$ in three dimensions, $\Delta T_c∕T_c=1.23a{n}^{1∕3}$, where $a$ is the $s$-wave scattering length and $n$ is the density, in excellent agreement with other approaches. We also discuss the flow of marginal parameters in $D=3$ and extend our truncation scheme of the renormalization group equations by including the six- and eight-point vertex, which yields an improved estimate for the anomalous dimension $\eta \approx 0.0513$. We further calculate the constant ${\lim }_{k\to 0}\Sigma \left(k\right)∕k^{2-\eta }$ and find good agreement with recent Monte Carlo data.

Motivated by the experimental observation of collapses and revivals of Bose matter wave field, we investigate correlation functions of cold bosons in an optical lattice. Within a simple model we examine two kinds of states: one that employs the commonly used notion of coherent states, and one that obeys the total number of atoms conservation. We identify rare situations at which these states behave differently. Typically, however, their predictions coincide and so: As a function of “interaction time” the interference pattern in the density undergoes collapse and revival. Exactly at revival times the system mimics the ideal gas case, in which all correlation functions factorize, while in the collapsed phase of the evolution the system effectively behaves as if initially there was no long-range coherence. Even in the latter case though, an interference pattern should be seen in a single experiment. We stress the role of column averaging, which in fact corresponds to an averaged observation of an ensemble of two-dimensional realizations. We also note that, contrary to the common belief, an interference pattern should also be seen in a single observation of a Mott state.

Quantum correlations in pairs and arrays (trains) of bound solitons modeled by the complex Ginzburg-Landau equation (CGLE) are calculated numerically, on the basis of linearized equations for quantum fluctuations. We find strong correlations between the bound solitons, even though the system is dissipative. Some degree of the correlation between the photon-number fluctuations of stable bound soliton pairs and trains is attained and saturates after passing a certain distance. The saturation of the photon-number correlations is explained by the action of nonconservative terms in the CGLE. Photon-number-correlated bound soliton trains offer possibilities to produce multipartite entangled sources for quantum communication and computation.

We measured the dependence of the linewidth of an electromagnetically induced transparency resonance on the angle between coupling and probe beams in an atomic cesium vapor. We observed that the nonparallelism of the beams contributes strongly to a broadening of the coherent resonance, even for small angles on the order of a few milliradians. A numerical calculation that agrees qualitatively with the experimental results is also presented. We discuss a possible application of the observed effect for performing cold-atom velocimetry.

An atom diode, i.e., a device that lets the ground-state atom pass in one direction but not in the opposite direction in a velocity range, is devised. It is based on the adiabatic transfer achieved with two lasers and a third laser potential that reflects the ground state.

A scheme is proposed for generating Greenberger-Horne-Zeilinger (GHZ) entangled states of multiple superconducting quantum-interference device (SQUID) qubits by the use of a microwave cavity. The scheme operates essentially by creating a single photon through an auxiliary SQUID built in the cavity and performing a joint multiqubit phase shift with assistance of the cavity photon. It is shown that entanglement can be generated using this method, deterministic and independent of the number of SQUID qubits. In addition, we show that the present method can be applied to preparing many atoms in a GHZ entangled state, with tolerance to energy relaxation during the operation.

In this paper, we extend our previous works on the generalization of Keldysh’s theory to the photoionization processes of molecules. In particular, we include the Franck-Condon factors into our photoionization rate formulas which are based on the use of the molecular orbital theory to describe the electronic degrees of freedom. The inclusion of Franck-Condon factors leads to the proper treatment of the molecular vibrational degrees of freedom. All of our formulas consist of the preexponential and exponential factors, and have explicit laser frequency dependence in the same manner as the original atomic Keldysh theory. The latter fact facilitates the exploration of the laser frequency dependence of the photoionization rate, which is more advantageous than the popular Ammosov-Delone-Krainov formulas. As a result, our analytical expressions turn out to be quite instructive to deduce physical meanings of the photoionization processes of molecules. As an illustrative example, we have applied our formulas to the photoionization process of ${\mathrm{H}}_2$ molecules and found that our formulas reproduce the numerical results reported in the literature quite well. Without the Franck-Condon factors, our formulas cannot fit the numerical results well, which implies the importance of including properly the Franck-Condon factors for the tunneling photoionization processes of molecules. The results also indicate that the exponential factors which depend on the nuclear equilibrium state play a key role in determining the photoionization rates of the spatially aligned molecules. Comparing the Condon and non-Condon approximations shows that the Condon approximation is usually appropriate for the case of the laser polarization perpendicular to the molecular axis, while it is not necessarily true for the parallel case. Our theoretical results are also applied to analyze the experimental data of Urbain et al. [Phys. Rev. Lett. 92, 163004 (2004)] for the photoionization process of ${\mathrm{H}}_2$ molecules.

The notion of genuine three-particle nonlocality introduced by Svetlichny [Phys. Rev. D 35, 10, 3066 (1987)] is discussed. Svetlichny’s inequality, which can distinguish between genuine three-particle and three-particle nonlocality that is based on underlying two-particle nonlocality, is analyzed by reinterpreting it as a frustrated network of correlations. Its quantum-mechanical maximum violation is derived and a situation is presented that produces the maximum violation. We show that recent beautiful experiments to demonstrate nonlocality for a three-party state by the GHZ paradox, although demonstrating nonlocality, do not allow any violation of the Svetlichny inequality. However, we show that with only minor modifications to the measurements performed, the experiments would be far more powerful and able to demonstrate genuine three-party nonlocality.

The incoherent inelastic part of the resonance fluorescence spectrum of a laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. Starting from this level of description, we discuss theoretical foundations of high-precision spectroscopy using the resonance fluorescence light of strongly laser-driven atoms. Specifically, we evaluate the leading relativistic and radiative corrections to the Mollow spectrum, up to the relative orders of ${\left(Z\alpha \right)}^2$ and $\alpha {\left(Z\alpha \right)}^2$, respectively, and Bloch-Siegert shifts as well as stimulated radiative corrections involving off-resonant virtual states. Complete results are provided for the hydrogen $1S\text{−}2P_{1∕2}$ and $1S\text{−}2P_{3∕2}$ transitions; these include all relevant correction terms up to the specified order of approximation and could directly be compared to experimental data. As an application, the outcome of such experiments would allow for a sensitive test of the validity of the dressed-state basis as the natural description of the combined atom-laser system.

In the context of nonrelativistic quantum mechanics, we obtain several upper and lower limits on the mean square radius applicable to systems composed of two bodies bound by a central potential. A lower limit on the mean square radius is used to obtain a simple criterion for the occurrence of $S$-wave quantum halo sates.

We propose a scalable quantum-computing architecture based on cold atoms confined to sites of a tight optical lattice. The lattice is placed in a nonuniform magnetic field and the resulting Zeeman sublevels define qubit states. Microwave pulses tuned to space-dependent resonant frequencies are used for individual addressing. The atoms interact via magnetic-dipole interactions allowing implementation of a universal controlled-NOT gate. The resulting gate operation times for alkalis-metals are on the order of milliseconds, much faster then the anticipated decoherence times. Single qubit operations take about $10\mathrm{\mu s}$. Analysis of motional decoherence due to NOT operations is given. We also comment on the improved feasibility of the proposed architecture with complex open-shell atoms, such as Cr, Eu, and metastable alkaline-earth atoms with larger magnetic moments.