We investigate the phase-locking phenomena of two weakly coupled Bose-Einstein condensates in a double-well potential subject to a high-frequency periodic driving field. The conditions for the existence of the phase-locked solutions in this system are derived. The parameter ranges of phase locking are found analytically and confirmed numerically.

We analyze the rate of two-photon absorption in tapered optical fibers with diameters less than the wavelength of the incident light. The rate of two-photon absorption is shown to be enhanced due to the small mode volume of the tapered fiber and the relatively large overlap of the evanescent field with an atomic vapor that surrounds the tapered region. The two-photon absorption rate is optimized as a function of the diameter of the tapered region.

By using extended bosonic coherent states, a technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in the literature. Finite-size scaling for several observables, such as the ground-state energy, Berry phase, and concurrence, is analyzed. A scaling exponent for ground-state energy is found. An existing discrepancy in the scaling exponent of the concurrence is reconciled.

Cold atomic ensembles can mediate the generation of entanglement between pairs of photons. Photons with specific directions of propagation are detected, and the entanglement can reside in any of the degrees of freedom that describe the whole quantum state of the photons: polarization, spatial shape, or frequency. We show that the direction of propagation of the generated photons determines the spatial quantum state of the photons and, therefore, the amount of entanglement generated. When photons generated in different directions are combined, this spatially distinguishing information can degrade the quantum purity of the polarization or frequency entanglement.

We compute the entropy of entanglement of two blocks of $L$ spins at a distance $d$ in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size $L=1$ and 2. In the general case, the critical entropy is shown to be additive when $d\to \infty$. Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both $L$ and $d$. This formula is in excellent agreement with numerical results.

We investigate entanglement of solitons in the continuum limit of the nonlinear Frenkel-Kontorova chain. We find that the entanglement of solitons manifests particlelike behavior as they are characterized by localization of entanglement. The von Neumann entropy of solitons mixes critical with noncritical behaviors. Inside the core of the soliton the logarithmic increase of the entropy is faster than the universal increase of a critical field, whereas outside the core the entropy decreases and saturates the constant value of the corresponding massive noncritical field. In addition, two solitons manifest long-range entanglement that decreases with the separation of the solitons more slowly than the universal decrease of the critical field. Interestingly, in the noncritical regime of the Frenkel-Kontorova model, entanglement can even increase with the separation of the solitons. We show that most of the entanglement of the so-called internal modes of the solitons is saturated by local degrees of freedom inside the core, and therefore we suggest using the internal modes as carriers of quantum information.

We present measurements of a photoelectron circular dichroism in photoionization from O and C $1s$ core levels, of the $R$ enantiomer of glycidol $\left({\mathrm{C}}_3{\mathrm{H}}_6{\mathrm{O}}_2\right)$ in the gas phase. This dichroism emerges from a forward-backward asymmetry in the angular distribution of electrons created on ionization with circularly polarized synchrotron radiation and is already fully present in the pure electric dipole approximation. Asymmetry factors obtained for the core levels in this study range up to a few percent, but it is likely that these values are limited by a failure to resolve photoemission from individual atomic sites. Theoretical modeling is provided to examine possible differences between these alternative atomic photoemission sites, and between different conformational structures of glycidol. The calculated chiral angular distribution parameters that support the circular dichroism display a much enhanced sensitivity to the molecular conformation compared to the conventional photoionization cross section and the $\beta$ parameter. Likely conformer structures can be suggested after comparison with the experiment.

The Young-type interference arising due to the spatial coherence has been investigated in the electron emission spectrum from fast electron impact ionization of the inversion symmetric homonuclear diatomic molecule ${\mathrm{H}}_2$. The evidence of the interference effect in the angular distribution of the double differential spectrum of the secondary electron is found. The signature of constructive interferences has been identified in the soft-collision regions as well as in binary encounters. The observed oscillation in the forward-backward asymmetry parameter is explained in terms of the Cohen-Fano-type interference coupled with the angular dependence of oscillation frequency. A comparative study indicates a marked difference between the angular asymmetry in the case of fast heavy ion $\left({\mathrm{F}}^{9+}\right)$ and electron collisions with ${\mathrm{H}}_2$ at a similar velocity.

High-energy electron-impact excitation cross sections are directly proportional to the generalized oscillator strengths (GOS’s) of the target (an atom or molecule). In the present work, the GOS’s for the Na $3s\text{−}3p$ and $2p\text{−}3s$ transitions are calculated by using the updated $R$-matrix codes. The present results for the $3s\text{−}3p$ transition are in good agreement with the experimental measurements at $1\mathrm{keV}$ incident energy. For the $2p\text{−}3s$ resonance transition, the present results are larger than the measurements at $1\mathrm{keV}$ incident energy. The difference is discussed. The important role of the inner shell electron correlations is elucidated. The positions of the first and second GOS minimums and maximums for these two transitions are reported. The dependence of the GOS minimum and maximum positions on the increasing incident energies are discussed.

We show that quantum beating appears in the intensity of Stokes and uv radiation generated via hyper-Raman scattering (HRS) and four-wave mixing (FWM), respectively, when a large number of close-lying upper states of atoms or molecules is excited by two-photon interaction with consecutive ultrashort laser pulses. The quantum beating at frequencies correlated with the energy difference between atomic states results from a Ramsey-like interference of atomic wave packets created by the pump and probe laser fields. We reveal that the destructive interference between HRS and FWM is superimposed on the wave packet interference, leading to substantial enhancement of the beating fringe visibility. We examine the effect of laser phase fluctuations and show that they strongly limit the number of beating modes. An analytical solution of transient Maxwell-Bloch equations is obtained, and the oscillatory dependence of uv emission on the delay between two laser pulses is revealed, allowing atomic wave packets to be detected optically. A comparison to available pump-probe experiments is made.

We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta functions, a fully analytical solution is obtained for symmetric, antisymmetric, and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on both direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta functions. In the general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.

The asymptotic form of the wave functions describing a freely expanding Lieb-Liniger gas is derived by using a Fermi-Bose transformation for time-dependent states, and the stationary phase approximation. We find that asymptotically the wave functions approach the Tonks-Girardeau (TG) structure as they vanish when any two of the particle coordinates coincide. We point out that the properties of these asymptotic states can significantly differ from the properties of a TG gas in a ground state of an external potential. The dependence of the asymptotic wave function on the initial state is discussed. The analysis encompasses a large class of initial conditions, including the ground states of a Lieb-Liniger gas in physically realistic external potentials. It is also demonstrated that the interaction energy asymptotically decays as a universal power law with time, $E_{\mathrm{int}}\propto t^{-3}$.

We explore the Bose condensed phases of an atomic gas on the molecular side of a Feshbach resonance. In the absence of atom-molecule and molecule-molecule scattering, we show that the atomic condensate is either a saddle point of the free energy with energy always exceeding that of the molecular condensate, or has a negative compressibility (hence unstable to density fluctuations). Therefore no phase transition occurs between the atomic and molecular condensates. We also show that a repulsive molecule-molecule scattering can stabilize a sufficiently dense atomic condensate, leading to the possibility of a phase transition. We caution that three-body processes may render this transition unobservable.

Based on the nonlinear coupling equations, the process of third-harmonic generation (THG) is investigated theoretically in temporal and frequency domains and a set of analytical expressions is derived under the plane-wave and pump undepletion approximations. The explicit formula characterizing the group-velocity-matching relationship in the process of THG is obtained. The group-velocity-matching relationship appears to be dependent on the pulse-duration ratio of fundamental (FH) to second-harmonic (SH) pulses. The THG mixing process in KDP crystals with input Gaussian pulses is numerically simulated, and the obtained results show that the conversion efficiency and conversion bandwidth can reach maximum when the formula is satisfied (i.e., zero group-velocity mismatch), and both will decrease rapidly when the formula is unsatisfied. Numerical results confirm the validity of our formula. Furthermore, with the increasing of the pulse-duration ratio of FH to SH pulses, the maximum bandwidth of generated TH pulses increases while maximum THG conversion efficiency decreases.

We offer a general treatment of electromagnetically induced transparency (EIT) in a five level system consisting of four metastable ground states. Two additional rf-microwave fields coherently couple the two ground states of the standard EIT $\Lambda$ atom to a pair of additional hyperfine states in the ground state manifold, generating two sets of dressed states that interact via the probe and control lasers, which couple to the electronic excited state. These new hyperfine dressed states manifest themselves in the linear optical susceptibility of the probe as new resonances in addition to the Autler-Townes doublet characteristic of EIT. In particular, we show that the existence of two new narrow resonances, whose width are limited only by ground state decoherence, appear inside the normal EIT transparency window. We show that by controlling the intensity of these rf-microwave fields, one can engineer both the position and width of these narrow resonances and thereby exercise additional control over both the dispersion and group velocity of the probe.

A recent paper [J. Schirmer and A. Dreuw, Phys. Rev A. 75, 022513 (2007)] challenges exact time-dependent density-functional theory (TDDFT) on several grounds. We explain why these criticisms are either irrelevant or incorrect, and that TDDFT is both formally exact and predictive.

In the preceding Comment, Maitra, van Leeuwen, and Burke (MLB) [Phys. Rev. A 78, 056501 (2008) attempt to refute our criticism of the foundations of time-dependent density functional theory [see J. Schirmer and A. Dreuw, Phys. Rev. A 75, 022513 (2007)]. However, their arguments miss the essence of our position. This is partly due to an ambiguity concerning the present status of the time-dependent (TD) Kohn-Sham (KS) equations. Based on the first Runge-Gross (mapping) theorem, the TD KS equations have to be established as a fixed-point iteration scheme for potential functionals (PF-FPI). Here, however, the convergence of the FPI is not assured. On the other hand, time propagation of the TD KS equations in their PF-FPI form fails because these equations do not represent physical equations of motion. MLB present a construction of the exact exchange-correlation potential, apparently contradicting one of our findings. We explain that their construction is explicitly based on the solution of the TD Schrödinger equation and, for this reason, does not address our objections, let alone refute them.

We study the relation between the sudden death and revival of the entanglement of two qubits in a common squeezed bath and the decoherence. By getting “close” to the decoherence free subspace, we show that the death time shows a decrease and subsequent increase until the sudden death disappears and the concurrence goes to its steady-state value asymptotically.

The $\mathcal{P}\mathcal{T}$-symmetric (PTS) quantum brachistochrone problem is re-analyzed as a quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as a subsystem of a larger Hermitian system, we find nonunitary operator equivalence classes (conjugacy classes) as natural ingredients which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.