Nonclassicality and entanglement are notions fundamental to quantum-information processes involving continuous variable systems. That these two notions are intimately related has been intuitively appreciated for quite some time. An aspect of considerable interest is the behavior of these attributes of a state under the action of a noisy channel. Inspired by the notion of entanglement-breaking channels, we define the concept of nonclassicality-breaking channels in a natural manner. We show that the notion of nonclassicality breaking is essentially equivalent—in a clearly defined sense of the term “essentially”—to the notion of entanglement breaking, as far as bosonic Gaussian channels are concerned. This is notwithstanding the fact that the very notion of entanglement breaking requires reference to a bipartite system, whereas the definition of nonclassicality breaking makes no such reference. Our analysis rests on our classification of channels into nonclassicality-based, as against entanglement-based, types of canonical forms. Our result takes ones intuitive understanding of the close relationship between nonclassicality and entanglement a step closer.

A uniformly coupled double-quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission for an arbitrary Hamiltonian including this one. By calculating the eigenvalues and eigenvectors of a unitary operator obtained from the free evolution plus an exchange operator, we find that the double-quantum Hamiltonian spin chain will support a three-spin initial encoding that will transfer along the chain with remarkably high fidelity. The fidelity is also found to decrease very slowly with increasing chain length. In addition, we are able to explain previous results showing exceptional transfer using this method.

The nonrelativistic three-body Schrödinger equation of the heteronuclear molecular ion HD${}^{+}$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states $v=0–3$ are calculated for total orbital momenta from 0 to 47. Energies are given with an accuracy from about 12 digits for the lowest vibrational level to at least nine digits for the third vibrational excited level. With a simple calculation using the corresponding wave functions, accurate dipole transition probabilities per time unit between those levels are given over the whole $v=0–3$ rotational bands. Results are presented with six significant figures.

We present a method for performing quantum state holography, with which we completely characterize the amplitude and phase of an attosecond electron wave packet. Our approach is an extension of a recent publication [J. Mauritsson et al.,  Phys. Rev. Lett. 105, 053001 (2010)] in which we demonstrated experimentally that the energies and amplitudes of an attosecond electron wave packet can be characterized using attosecond electron interferometry. Here we show theoretically that attosecond electron interferometry can be extended to retrieve the phases of all the states that make up the wave packet. We demonstrate the feasibility of our method by analyzing a wave packet created by a shake-up process. We show that our method can successfully retrieve arbitrary phases and/or lifetimes added to the component eigenstates.

The existence of a Cooper minimum in the experimentally measured photoionization cross sections for the 7$s$ ${}^2$$S_{1/2}$ excited state of potassium has been reported using a two-step laser excitation technique in conjunction with a time-of-flight mass spectrometer. The photoionization cross sections for the 7$s$ ${}^2$$S_{1/2}$ state have been determined as $(9.78\pm 0.01)\times {10}^{-2}$, $(3.30\pm 0.49)\times {10}^{-4},(5.47\pm 0.82)\times {10}^{-3}$, and $(2.06\pm 0.30)\times {10}^{-2}$ Mb at the ionizing laser wavelengths 1064, 700, 532, and 355 nm, respectively, that validate the presence of a Cooper minimum at ≅1.25 eV above the first ionization threshold. The number density has been determined as $N_0=2\times {10}^{11}$ cm${}^{-3}$. The experimentally determined absolute values of the cross sections are in qualitative agreement with the theoretical predictions.

We study the dynamical properties, with special emphasis on mobility, of quantum lattice compactons (QLCs) in a one-dimensional Bose-Hubbard model extended with pair-correlated hopping. These are quantum counterparts of classical lattice compactons (localized solutions with exact zero amplitude outside a given region) of an extended discrete nonlinear Schrödinger equation, which can be derived in the classical limit from the extended Bose-Hubbard model. While an exact one-site QLC eigenstate corresponds to a classical one-site compacton, the compact support of classical several-site compactons is destroyed by quantum fluctuations. We show that it is possible to reproduce the stability exchange regions of the one-site and two-site localized solutions in the classical model with properly chosen quantum states. Quantum dynamical simulations are performed for two different types of initial conditions: “localized ground states” which are localized wave packets built from superpositions of compactonlike eigenstates, and SU(4) coherent states corresponding to classical two-site compactons. Clear signatures of the mobility of classical lattice compactons are seen, but this crucially depends on the magnitude of the applied phase gradient. For small phase gradients, which classically correspond to a slow coherent motion, the quantum time scale is of the same order as the time scale of the translational motion, and the classical mobility is therefore destroyed by quantum fluctuations. For a large phase instead, corresponding to fast classical motion, the time scales separate so that a mobile, localized, coherent quantum state can be translated many sites for particle numbers already of the order of 10.

We propose and analyze nonlinear optomechanical protocols that can be implemented by adding a single atom to an optomechanical cavity. In particular, we show how to engineer the environment in order to dissipatively prepare the mechanical oscillator in a superposition of Fock states with fidelity close to 1. Furthermore, we demonstrate that a single atom in a cavity with several mechanical oscillators can be exploited to realize nonlinear many-partite systems by stroboscopically driving the mechanical oscillators. This can be used to prepare nonlinear many-partite states by applying either coherent protocols or engineering dissipation. The analysis of the protocols is carried out using a perturbation theory for degenerate Liouvillians and numerical tools. Our results apply to other systems where a qubit is coupled to a mechanical oscillator via a bosonic mode, e.g., in cavity quantum electromechanics.

Recent advances in micro- and nanofabrication techniques have led to corresponding improvement in the performance of optomechanical systems, which provide a promising avenue towards quantum-limited metrology and the study of quantum behavior in macroscopic mechanical objects. One major impediment to reaching the quantum regime is thermal excitation, which can be overcome for a sufficiently high mechanical quality factor $Q$. Here, we propose a method for increasing the effective $Q$ of a mechanical resonator by stiffening it via the optical spring effect exhibited by linear optomechanical systems and show how the associated quantum-radiation-pressure noise can be evaded by sensing and feedback control. In a parameter regime that is attainable with current technology, this method allows for realistic quantum cavity optomechanics in a frequency band well below that which has been realized thus far.

We propose a method for generation of single-cycle squeezed light by parametric down-conversion in a chirped quasi-phase-matched nonlinear crystal. We find an exact quantum solution for this process valid for an arbitrary parametric gain (under an assumption of nondepleted pump), and discover an ultrabroadband squeezing in the down-converted light with a flat squeezing spectrum comprising the full optical octave. We describe a scheme for observation of this kind of squeezing using second-harmonic generation as an ultrafast correlator.

It is shown that conventional one-photon and two-photon absorption processes can be made subject to nonlinear optical control, in each case significantly modifying the efficiency of absorption, through the effect of a secondary, off-resonant stimulus laser beam. The mechanistic origin of these laser-modified absorption processes, in which the stimulus beam emerges unchanged, is traced to higher-order terms in standard perturbation treatments. These normally insignificant terms become unusually prominent when the secondary optical stimulus is moderately intense. Employing a quantum formulation, the effects of the stimulus beam on one-photon and two-photon absorption are analyzed, and calculations are performed to determine the degree of absorption enhancement, and the form of spectral manifestation, under various laser intensities. The implications of differences in selection rules are also considered and exemplified, leading to the identification of dark states that can be populated as a result of laser-modified absorption. Attention is also drawn to the possibility of quantum nondemolition measurements, based on such a form of optical nonlinearity.

We analytically solve the higher-order nonlinear Schrödinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and obtain results for bright and dark solitary wave solutions. The functional form of these solutions are different from the traditional sech and tanh bright and dark solitons. Periodic wave solutions are also presented. Going over to the traveling coordinate, we reduce the complicated HNLS equation to the Hamiltonian form and treat the resulting equations by the dynamical systems theory. The results of our study demonstrate that the equation can, in general, support both soliton (bright and dark) and periodic solutions. We estimate the size of the derivative non-Kerr nonlinear coefficients. The results are in good agreement with those of the waveguide made of highly nonlinear optical materials. Our calculated values can be used as model parameters for sub-10 fs pulse propagation.

The effect of an external continuous wave (cw) on the motion of solitons of the complex Ginzburg-Landau (CGL) equation is investigated. It is shown that soliton motion, which is prevented by a strong braking due to finite gain bandwitdh, can be induced by the cw. Then the effect of the cw on the collective behavior of a large number of dissipative solitons is considered. Starting from a soliton crystal, we demonstrate that the soliton motion is induced by the cw, so that either the soliton gas, liquid, or crystal can be obtained depending on the intensity and the frequency of the cw.

We study an unextendible maximally entangled basis in arbitrary bipartite spaces. A systematic way of constructing a set of $d^2$ orthonormal maximally entangled states in ${\mathbb{C}}^d⨂{\mathbb{C}}^{d^{\prime }}(\frac{d^{\prime }}{2}<d<d^{\prime })$ is provided. The complementary space of the set of these $d^2$ orthonormal maximally entangled states contains no maximally entangled states that are orthogonal to all of them. Furthermore, we investigate mutually unbiased bases in which all the bases are unextendible maximally entangled ones. We present two unextendible maximally entangled bases in ${\mathbb{C}}^2⨂{\mathbb{C}}^3$ which are mutually unbiased.

We consider a photonic crystal fiber resonator pumped by a coherent injected beam. We show that temporal cavity solitons exhibit a motion with a constant velocity. This regular drift is induced by a broken reflection symmetry mediated by a third-order dispersion. We focus the analysis on dark temporal cavity solitons. They consist of asymmetric moving dips in a uniform background of the intensity profile. The number of the moving dips and their temporal distribution are determined solely by the initial conditions. We characterize this motion by computing the velocity of the dark temporal cavity soliton. Without fourth-order dispersion, dark cavity solitons do not exist.

We report the experimental violation of Leggett-type inequalities for a hybrid entangled state of spin and orbital angular momentum of a single photon. These inequalities give a physical criterion to verify the possible validity of a class of hidden-variable theories, originally named “crypto nonlocal,” that are not excluded by the violation of Bell-type inequalities. In our case, the tested theories assume the existence of hidden variables associated with independent degrees of freedom of the same particle, while admitting the possibility of an influence between the two measurements, i.e., the so-called contextuality of observables. We observe a violation of the Leggett inequalities for a range of experimental inputs, with a maximum violation of seven standard deviations, thus ruling out this class of hidden-variable models with a high level of confidence.

We study the dynamical behavior of a quantum cellular automaton which reproduces the Dirac dynamics in the limit of small wave vectors and masses. We present analytical evaluations along with computer simulations, showing that the automaton exhibits typical Dirac dynamical features, such as the Zitterbewegung and, considering the scattering from potential, the so-called Klein paradox. The motivation is to show concretely how pure processing of quantum information can lead to particle mechanics as an emergent feature, an issue that has been the focus of solid-state, optical, and atomic-physics quantum simulators.

The evaluation method of the one-loop self-energy of the electron bound in a Coulomb field is described. The method combines the relativistic multipole expansion with the free-particle approximation in the virtual states without breaking any integrations of pieces. The relativistic multipole expansion is based on a single assumption: except for the part of the time component of the electron four-momentum corresponding to the electron rest mass, the exchange of four-momentum between the virtual electron and photon can be treated perturbatively. This assumption holds very well, except for the electron virtual states with very high three-momentum. It is shown that for such virtual states one can always rearrange the pertinent expression in a way that allows the electron to be treated as free. The fraction of the free-particle approximation contained in the relativistic multipole expansion carried out to a given order is precisely determined. Furthermore, it is pointed out that in the virtual states with very large wave numbers the electron ceases to feel the Coulomb force from the nucleus for arbitrarily strong fields. This results in a simple scaling behavior of the integrals over the large electron wave numbers. This in turn enables us to avoid a decomposition of convergent integrals into the sum of divergent integrals encountered earlier. By taking the method up to the ninth order and estimating the remainder of the series, the result obtained for the ground state of the hydrogen atom differs from the other result of comparable accuracy by two parts in ${10}^9$. This amounts to the difference of 18 Hz for $2s-1s$ transition in hydrogen. This is by four orders smaller than the uncertainty in determination of the proton radius. With an increasing nuclear charge $Z$, the rate of convergence of the expansion slows down. Nonetheless, the obtained results are in very good agreement with the results obtained by partial wave expansion up to $Z=90$.

In this paper we describe a few phenomena that may affect the linewidth and/or the line shape of Ramsey fringes observed in an alkali-metal vapor cell with buffer gas. Experiments are performed on a vapor-cell–microwave-cavity arrangement in which ${}^{87}\mathrm{Rb}$ atoms successively experience laser pumping preparation (through a $D_2$ line), microwave interrogation with a couple of coherent pulses, and clock signal detection by means of laser absorption. We show that the linewidth of the Ramsey central fringe is influenced by the Rabi pattern produced by a single microwave pulse. Moreover, cycle memory and atomic density effects can modify the shape of the Ramsey central fringe from the common sinusoidal behavior. A simple three-level model well reproduces the experimental observations.

The correlated electron momentum distribution for nonsequential double ionization (NSDI) of Ne in a strong linearly polarized laser field is studied by quantum $S$-matrix and semiclassical theories. At low intensity, where the single-return-collision NSDI process dominates, a good agreement between two theories is found. However, at high intensity, two theories are inconsistent with each other, and the semiclassical calculation is qualitatively in agreement with the experimental observation. Our analysis shows that this can be attributed to the neglect of the ion potential in the present $S$-matrix theory, and hence the multiple-return-collision NSDI process, which becomes important at high intensity, is underestimated in the current $S$-matrix theory.

We study the pair-creation process due to spatially localized but nonoverlapping electric fields and examine the role of quantum mechanical tunneling for fermionic and bosonic systems. While for small distances between the pulses the rates are significantly different, in the tunneling regime where the separations are large the fermionic and bosonic pair-creation rates scale similarly. As long as the distance between two adjacent electric fields is less than a characteristic tunneling length, each subcritical pulse can generate particle pairs. We design a multifield configuration to make use of quantum tunneling to lower the threshold of pair creation.