We study the Loschmidt echo and Berry phase in a nonlinear system transported around a double and a triple degeneracy. The nonlinearity of the system makes this Berry phase different from that in linear systems. We propose a witness of nonlinearity for the nonlinear system and show its dependence on the parameters of the system, taking the standard Landau-Zener model as an example. We calculate the Loschmidt echo (LE) or quantum fidelity in the quantum dynamics under perturbations around the degeneracy, and establish a connection between the LE and the witness of nonlinearity. These phases can be observed with current experimental technology in a nonlinear resonator.

We describe an algorithm to simulate time evolution using the multiscale entanglement renormalization ansatz and test it by studying a critical Ising chain with periodic boundary conditions and with up to $L\approx {10}^6$ quantum spins. The cost of a simulation, which scales as $L{\text{log}}_2\left(L\right)$, is reduced to ${\text{log}}_2\left(L\right)$ when the system is invariant under translations. By simulating an evolution in imaginary time, we compute the ground state of the system. The errors in the ground-state energy display no evident dependence on the system size. The algorithm can be extended to lattice systems in higher spatial dimensions.

We analyze the effect of local decoherence of two qubits on their entanglement and the Bell-inequality violation. Decoherence is described by Kraus operators, which take into account dephasing and energy relaxation at an arbitrary temperature. We show that in the experiments with superconducting phase qubits the survival time for entanglement should be much longer than for the Bell-inequality violation.

A continuous positive operator-valued measurement (POVM) is described for the polarization state of a single photon propagating in a known spatiotemporal mode. This POVM is shown to be the maximum-likelihood quantum measurement for estimating that polarization state. Moreover, the maximum-likelihood polarization estimate derived from this POVM enables uniformly optimal measure-and-prepare state transmission via classical communication—at the $\overline{F}=2/3$ classical limit on average teleportation fidelity—for any pure state of polarization. When two continuous-POVM polarimeters are used to detect the singlet state of a pair photons that are in distinct spatial modes, the conditional probability density for one polarimeter’s output given the other’s encompasses the quantum interference patterns seen in standard singlet-state polarization analysis. For single-photon illumination, a $1:M$ optical splitter followed by a collection of $M$ projective polarization measurements, whose bases are uniformly distributed over the Poincaré sphere, yields observation statistics that converge in distribution to those of the continuous-POVM polarimeter as $M\to \infty$.

High-order harmonic signals from aligned molecules subject to a dissipative medium is studied theoretically using a density matrix formalism. Rotations are taken into account exactly, through an extension of a recently developed theory [S. Ramakrishna and T. Seideman, Phys. Rev. Lett. 99, 113901 (2007)], leading to an expression for the harmonic signal in terms of a series of rotational expectation values that are determined by the geometry of the experiment and the symmetry of the molecular ground electronic state. A multilevel Bloch model is used to illustrate the imprint of rotational decoherence and relaxation in the harmonic emission. It is shown that the harmonic intensities can be decomposed into two components, each of which carries a different physical interpretation and information content. The usefulness of the decomposition scheme in unraveling the interplay between the different dipole moment components that make the signal, and in relating the observable time dependence of the signal to the underlying electronic-rotational dynamics, is delineated. Finally, we show that the phase of the harmonic signal contains unique information regarding the phases of the electronic dipole matrix elements and hence the underlying electronic continuum.

An efficient and straightforward approach is proposed to produce extreme ultraviolet frequency combs by using high-order harmonic generation from diatomic molecules driven by surface-enhanced high-repetition-rate femtosecond pulses. For a nonpolar molecule, the maximum (minimum) energy conversion efficiency is observed as the molecule is oriented at an angle of $27°$ $\left(108°\right)$ relative to the surface. For a polar molecule, the frequency components of the generated ultraviolet frequency combs are doubled as both odd- and even-order harmonics are generated, which shows different orientation dependence and shifts from the nonpolar molecule. The generated ultraviolet frequency combs are mainly emitted with angles smaller than $30°$ close to the surface, while there is a noticeable emission probability around the directions perpendicular to the surface when the molecules are oriented with large angles.

In this Brief Report, we prove that an analytically solvable two-qubit entanglement monotone introduced by Zhang et al. [Phys. Rev. A 76, 032306 (2007)] is no greater than the square of concurrence. This proof is based on the equivalence between Zhang et al.'s monotone and an observable entanglement measure for mixed states suggested by Mintert and Buchleitner [Phys. Rev. Lett. 98, 140505 (2007)]. Our result may clarify the connections between several recently defined entanglement measures and help understand their possible applications in quantum-information theory.

The ionization of Mg $2p$ by electron impact has been studied at about 400 and 1000 eV incident energy and small momentum transfer via $\left(e,2e\right)$ experiments. Two kinematical conditions have been chosen in order to study the coincidence angular distribution in the case where either only the direct $2p$ ionization contributes or the decay of the $2p$ core hole plays a role, too. The results have been compared with distorted-wave Born approximation calculations.

Systems of coupled photonic cavities have been predicted to exhibit quantum phase transitions by analogy with the Hubbard model. To this end, we have studied topologies of few (up to six) photonic cavities each containing a single two-level system. Quantum phase space diagrams are produced for these systems, and compared to mean-field results. We also consider finite effective temperature, and compare this to the notion of disorder. We find the extent of the Mott lobes shrink analogously to the conventional Bose-Hubbard model.

In this Rapid Communication we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily connected or they are incomparable. There exists an infinite number of deterministically locally inequivalent classes of pure bipartite states in the same Schmidt rank (starting from three) having the same amount of entanglement. Further, if there exists incomparable states with the same entanglement in higher Schmidt ranks (greater than three), then they should differ in at least three Schmidt coefficients.

We present the theory of a method to slow a linearly polarized probe pulse as it propagates through a duplicated two-level system driven by an orthogonally polarized control field. The method makes use of Zeeman coherence oscillations that arise in the atomic system because of the spatial and temporal modulation of the total polarization. This method exhibits properties similar to those that rely on electromagnetically induced transparency but without the existence of any trapping dark state. We demonstrate also the propagation of a polariton in the medium.

We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that each eigenvalue of the measured object observable is tied up with a specific pointer deflection. Different pointer positions mutually decohere under the influence of a bath. Object-pointer entanglement and decoherence of distinct pointer readouts proceed simultaneously. Mixtures of macroscopically distinct object-pointer states may then arise without intervening macroscopic superpositions. Initially, object and apparatus are statistically independent while the latter has pointer and bath correlated according to a metastable local thermal equilibrium. We obtain explicit results for the object-pointer dynamics with temporal coherence decay in general neither exponential nor Gaussian. The decoherence time does not depend on details of the pointer-bath coupling if it is smaller than the bath correlation time, whereas in the opposite Markov regime the decay depends strongly on whether that coupling is Ohmic or super-Ohmic.

Many protocols for long distance quantum communication require interferometric phase stability over long distances of optical fibers. In this paper we investigate the phase noise in long optical fibers both in laboratory environment and in installed commercial fibers in an urban environment over short time scales (up to hundreds of $\mu \text{s}$). We show that the phase fluctuations during the travel time of optical pulses in long-fiber loops are small enough to obtain high visibility first-order interference fringes in a Sagnac interferometer configuration for fiber lengths up to 75 km. We also measure phase fluctuations in a Mach-Zehnder interferometer in installed fibers with arm length 36.5 km. We verify that the phase noise respects Gaussian distribution and measure the mean phase change as a function of time difference. The typical time needed for a mean phase change of 0.1 rad is of order of $100\mu \text{s}$, which provides information about the time scale available for active phase stabilization. Our results are relevant for future implementations of quantum repeaters in installed optical fiber networks.

We have numerically examined optimization of the experimentally achievable shapes of mid-infrared femtosecond laser pulses to construct elementary quantum gates using molecular rovibrational states of a single molecule. Instead of optimizing the electric field by optimal control theory, the method generally used in theoretical studies of coherent control, the transmittance and the phase shift of conventional pulse shapers were optimized in the frequency domain by a genetic algorithm. The target molecular system we examined was the rotation-vibration states of CO in the $X\left({{}^1\Sigma }^{+}\right)$ ground electronic state. Although the existence of the rotational degrees of freedom makes the quantum gate operation complicated, high fidelity of over 0.95 was achieved for one-rovibrational-qubit systems, which indicates that a molecular quantum computer may be feasible for at least one-qubit calculations on a diatomic molecule. On the other hand, two-qubit calculations are more difficult to achieve in a single CO molecule using rotational and vibrational degrees of freedom as different qubits. The importance of the control of the rotational in addition to the vibrational wave packet in order to realize a molecular quantum computer is discussed.

The security of a standard bidirectional “plug-and-play” quantum key distribution (QKD) system has been an open question for a long time. This is mainly because its source is equivalently controlled by an eavesdropper, which means the source is unknown and untrusted. Qualitative discussion on this subject has been made previously. In this paper, we solve this question directly by presenting the quantitative security analysis on a general class of QKD protocols whose sources are unknown and untrusted. The securities of standard Bennett-Brassard 1984 protocol, $\text{weak}+\text{vacuum}$ decoy state protocol, and one-decoy state protocol, with unknown and untrusted sources are rigorously proved. We derive rigorous lower bounds to the secure key generation rates of the above three protocols. Our numerical simulation results show that QKD with an untrusted source gives a key generation rate that is close to that with a trusted source.

The multichannel quantum-defect theory is used to investigate the role of the numerous couplings between rovibrational states in the dissociative recombination and superelastic collisions of $\text{H}_2{}^{+}$ with low-energy electrons, within different molecular electronic symmetries. All the paths accessible are considered. In the case of the singlet gerade symmetry of the neutral system, for example, not only the dominant path, ${{}^1\Sigma }_g^{+}$, is taken into account, but also ${{}^1\Pi }_g^{+}$, rotationally coupled to ${{}^1\Sigma }_g^{+}$, via a frame transformation from the interaction region to the external one. The initial vibrational states investigated are $v_i^{+}=0–4$. The final rate coefficients are obtained as weighted sums including the so-called ortho-para effect, at room temperature, over all the relevant rotational initial states $N_i^{+}$, which vary from 0 to 12. The results show that the consideration of rotational effects give a much better overall agreement of the dissociative recombination rate coefficients with experiment, and that, for superelastic collisions, these effects can be used to account, at least partly, for the discrepancies between our former calculations and experiment, which showed a strong vibrational relaxation of $\text{H}_2{}^{+}$.

Si x-ray and backscattering yields have been measured as a function of the ${\text{C}}^{+}$ and ${\text{C}}_2^{+}$ entrance angle along the Si $⟨100⟩$ channel in an energy interval between 900 and 2200 keV/atom. A significant enhancement of the x-ray production has been observed for the well-aligned ${\text{C}}_2^{+}$ beam in comparison with the monoatomic case. It is shown that this effect results from the Coulomb explosion of the molecule during the channeling motion. By combining the Rutherford backscattering channeling (RBS-C) and the x-ray results we were able to determine the value of the transverse energy transfer as a function of the beam energy due to the break up process (Coulomb heating). This energy increases monotonically from 14 eV for 900 keV/atom up to 30 eV for 2200 keV/atom. In addition, we were able to predict the theoretical Coulomb heating values by combining calculations and simulations, the theoretical-experimental agreement, within the experimental errors, being quite reasonable.

We report a first study of the depolarization behavior of spin polarized ${}^3\text{H}\text{e}$ in a mixture of ${}^3\text{H}\text{e-}{}^4\text{H}\text{e}$ at a temperature below the ${}^4\text{H}\text{e}$ $\lambda$ point in a deuterated tetraphenyl butadiene-doped deuterated polystyrene (dTPB-dPS) coated acrylic cell. In our experiment the measured ${}^3\text{H}\text{e}$ relaxation time is due to the convolution of the ${}^3\text{H}\text{e}$ longitudinal relaxation time, $T_1$, and the diffusion time constant of ${}^3\text{H}\text{e}$ in superfluid ${}^4\text{H}\text{e}$ since depolarization takes place on the walls. We have obtained a ${}^3\text{H}\text{e}$ relaxation time of $\sim 3000\text{s}$ at a temperature around 1.9 K. We have shown that it is possible to achieve values of wall depolarization probability on the order of $\left(1–2\right)\times {10}^{-7}$ for polarized ${}^3\text{H}\text{e}$ in the superfluid ${}^4\text{H}\text{e}$ from a dTPB-dPS coated acrylic surface.

Nonperturbative analytical quantum treatments of strong-field laser-atom interaction are essentially based on the assumption that binding forces are negligible once the electron is emitted because the further dynamics are considered as being dominated by the laser field. In this work we introduce a Coulomb-corrected strong-field theory of photoionization based on quantum trajectories and show how binding forces lead to strong qualitative effects in above-threshold ionization of atoms. We examine the theory by comparing experimental data for elliptically polarized laser fields and results from the ab initio solution of the time-dependent Schrödinger equation with our theoretical predictions. The comparison shows good quantitative agreement with the ab initio results and reasonable agreement with the data. For ground states with nonzero angular momentum we show a strong circular dichroism in the high-energy (rescattering) part of photoelectron spectra.

We investigated the two-dimensional electron momentum distributions of atomic negative ions in an intense laser field by solving the time-dependent Schrödinger equation (TDSE) and using the first- and second-order strong-field approximations (SFAs). We showed that photoelectron energy spectra and low-energy photoelectron momentum distributions predicted from SFAs are in reasonable agreement with the solutions from the TDSE. More importantly, we showed that accurate electron-atom elastic scattering cross sections can be retrieved directly from high-energy electron momentum spectra of atomic negative ions in the laser field. This opens up the possibility of measuring electron-atom and electron-molecule scattering cross sections from the photodetachment of atomic and molecular negative ions by intense short lasers, respectively, with temporal resolutions in the order of femtoseconds.