In their Comment Giraud and Combescot (GC) [Phys. Rev. A 82, 037603 (2010)] point out that the contribution to the impurity-boson distribution function ${\rho }_{\mathit{bi}}(x-y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but our results for ${\rho }_{\mathit{bi}}$ are highly accurate for large impurity-boson mass ratio $m_i/m$, for all values of $x-y$ and boson-impurity coupling constant.

Optical homodyne detection is examined in view of the joint probability distribution. The usual view is that the relative phase between independent laser fields is localized by photon-number measurements in interference experiments such as homodyne detection. This is why operationally coherent states for laser fields are used in the description of homodyne detection and optical quantum-state tomography. Here, we elucidate these situations by considering the joint probability distribution and the invariance of homodyne detection under the phase transformation of optical fields.

We provide methods for computing the geometric measure of entanglement for two families of pure states with both experimental and theoretical interests: symmetric multiqubit states with non-negative amplitudes in the Dicke basis and symmetric three-qubit states. In addition, we study the geometric measure of pure three-qubit states systematically in virtue of a canonical form of their two-qubit reduced states and derive analytical formulas for a three-parameter family of three-qubit states. Based on this result, we further show that the W state is the maximally entangled three-qubit state with respect to the geometric measure.

The photodetachment dynamics of the atomic oxygen anion ${\mathrm{O}}^{-}$ has been investigated at 266 nm (4.67 eV) by photoelectron detection in a crossed-beam experiment using a magnetic-bottle electron spectrometer. Taking explicit advantage of the Doppler shift imposed by the moving ion beam on the photoelectron energies, we report both the final-state branching ratio and photoelectron angular distributions. After photoabsorption at 266 nm, the formed electron-oxygen scattering state disintegrates, forming either the excited ${}^{1}D$ or the ground ${}^{3}P$ state of oxygen with a partition of ${}^{1}D$:${}^{3}P=0.32$ $\pm$ 0.06. The detachment leading to the production of O(${}^{3}P$) shows an angular distribution of photoelectrons characterized by ${\beta }_P=0.00$ $\pm$ 0.10 mimicking a pure s-wave detachment, while the detachment into excited O(${}^{1}D$) occurs with ${\beta }_D=-0.90\pm 0.10$, giving direct evidence of interference between the outgoing $s$ and $d$ waves.

We consider deflection of polarizable molecules by inhomogeneous optical fields and analyze the role of molecular orientation and rotation in the scattering process. It is shown that molecular rotation induces spectacular rainbowlike features in the distribution of the scattering angle. Moreover, by preshaping molecular angular distribution with the help of short and strong femtosecond laser pulses, one may efficiently control the scattering process, manipulate the average deflection angle and its distribution, and reduce substantially the angular dispersion of the deflected molecules. We study the problem both classically and quantum mechanically and arrive at the same conclusions in both treatments. The effects of strong deflecting field on the scattering of rotating molecules are considered by the means of the adiabatic invariants formalism. The suggested control scheme opens new ways for many applications involving molecular focusing, guiding, and trapping by optical and static fields.

We shall give an alternative Schrödinger-type uncertainty relation for a quantity representing a quantum uncertainty, introduced by Luo [Phys. Rev. A 72, 042110 (2005)]. Our result improves the Heisenberg-type uncertainty relation shown in Luo's paper for a mixed state.

We show a simple relation connecting entangling power and local invariants of two-qubit gates. From the relation, a general condition under which gates have the same entangling power is derived. The relation also helps in finding the lower bound of entangling power for perfect entanglers, from which the classification of gates as perfect and nonperfect entanglers is obtained in terms of local invariants.

We analyze three-body nonadditive interactions and characterize critical points on potential energy surfaces of the lowest $A_{2}B$ ($A,B=\mathrm{Li},\mathrm{Na},\mathrm{K},\mathrm{Rb},\mathrm{Cs}$) quartet states using high-level ab initio calculations. Our calculations indicate that near equilibrium geometries, large nonadditive effects are stabilizing the systems. We also show that trimer formation reactions are always energetically allowed even for low-lying rovibrational states of heteronuclear triplet-$\Sigma$ dimers.

We study the nonequilibrium dynamics of cold atoms held in an optical lattice subjected to a periodic driving potential. The expansion of an initially confined atom cloud occurs in two phases: an initial quadratic expansion followed by a ballistic behavior at long times. Accounting for this gives a good description of recent experimental results and provides a robust method to extract the effective intersite tunneling from time-of-flight measurements.

The observation of quantized nanomechanical oscillations by detecting femtometer-scale displacements is a significant challenge for experimentalists. We propose that a phonon blockade can serve as a signature of quantum behavior in nanomechanical resonators. In analogy to the photon blockade and Coulomb blockade for electrons, the main idea for phonon blockade is that the second phonon cannot be excited when there is one phonon in the nonlinear oscillator. To realize phonon blockade, a superconducting quantum two-level system is coupled to the nanomechanical resonator and is used to induce the phonon self-interaction. Using Monte Carlo simulations, the dynamics of the induced nonlinear oscillator is studied via the Cahill-Glauber $s$-parametrized quasiprobability distributions. We show how the oscillation of the resonator can occur in the quantum regime and demonstrate how the phonon blockade can be observed with the currently accessible experimental parameters.

We consider self-localization of a small number of Bose particles immersed in a large homogeneous superfluid mixture of fermions in three- and one-dimensional space. Bosons distort the density of surrounding fermions and create a potential well where they can form a bound state analogous to a small polaron state. In the three-dimensional volume, we observe the self-localization for repulsive interactions between bosons and fermions. In the one-dimensional case, bosons self-localize as well for attractive interactions, thereby forming, together with a pair of fermions at the bottom of the Fermi sea, a vector soliton. We analyze also thermal effects and show that small nonzero temperature affects the pairing function of the Fermi subsystem and has little influence on the self-localization phenomena.

In a recent paper, Roux [Phys. Rev. A 79, 021608(R) (2009)] argued that thermalization in a Bose-Hubbard system, after a quantum quench, follows from the approximate Boltzmann distribution of the overlap between the initial state and the eigenstates of the final Hamiltonian. We show here that the distribution of the overlaps is in general not related to the canonical (or microcanonical) distribution and, hence, it cannot explain why thermalization occurs in quantum systems.

In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy distribution after a quench is not related to standard statistical ensembles and cannot explain thermalization. The latter is proposed to stem from what he calls the eigenstate thermalization hypothesis and which boils down to the fact that simple observables are expected to be smooth functions of the energy. In this Reply, we show that there is no contradiction or confusion between the observations and discussions of Roux and the expected thermalization scenario discussed by Rigol. In addition, we emphasize a few other important aspects, in particular the definition of temperature and the equivalence of ensemble, which are much more difficult to show numerically even though we believe they are essential to the discussion of thermalization. These remarks could be of interest to people interested in the interpretation of the data obtained on finite-size systems.

Superadditivity effects of communication capacities are known in the case of discrete variable quantum channels. We describe the continuous variable analog of one of these effects in the framework of Gaussian multiple access channels (MACs). Classically, superadditivity-type effects are strongly restricted: For example, adding resources to one sender is never advantageous to other senders in sending their respective information to the receiver. We show that this rule can be surpassed using quantum resources, giving rise to a type of truly quantum superadditivity. This is illustrated here for two examples of experimentally feasible Gaussian MACs.

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user.

We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of long-range forces before they ultimately encounter one another, followed by a probability for the reaction to occur once they do. In this way, the electric-field dependence should be readily parametrized in terms of a pair of fitting parameters (along with a $C_6$ coefficient) for each asymptotic value of partial-wave quantum numbers $|L,M_L\rangle$. From this, the electric-field dependence of the collision rates follows automatically. We present examples for reactive species, such as KRb, and nonreactive species, such as RbCs.

We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is nonthermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.

I show that calibration of the single-photon detector can be performed without knowledge of the signal parameters. Only partial information about the state statistics is sufficient for that. If one knows that the state is the squeezed one or the squeezed one mixed with the incoherent radiation, one can infer both the parameters of the state and the efficiency of the detector. For that one needs only to measure on/off statistics of detector clicks for the number of known absorbers placed before the detector. Thus, I suggest a scheme that performs a tomography of the signal and the measuring apparatus simultaneously.

We study the possibility of suppressing three-body losses in atomic Bose-Einstein condensates via the quantum Zeno effect, which means the delay of quantum evolution by frequent measurements. It turns out that this requires very fast measurements with the rate being determined by the spatial structure of the three-body form factor, i.e., the point interaction approximation ${\delta }^3(\mathbf{r}-{\mathbf{r}}^{\text{'}})$ is not adequate. Since the molecular binding energy $E_b$ provides a natural limit for the measurement rate, this suppression mechanism can only work if the form factor possesses certain special properties.

Factorization of quantum-mechanical potentials has a long history extending back to the earliest days of the subject. In the present article, the nonuniqueness of the factorization is exploited to derive new isospectral nonsingular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such operators for its isospectral partners. The generality of the method is illustrated with a number of examples which may have many possible applications in atomic and molecular physics.