We study the performance of initial product states of $n$-body systems in generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear $k$-body $\left(k\ll n\right)$ Hamiltonian. We obtain the theoretical lower bound on the uncertainty in the estimate of the parameter. For arbitrary initial states, the lower bound scales as $1/n^k$, and for initial product states, it scales as $1/n^{k-1/2}$. We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian $\left(k=2\right)$, implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the $O\left(n^{-3/2}\right)$ scaling for $k=2$; the model shows that the entanglement generated by the quadratic Hamiltonian does not play a role in the enhanced sensitivity scaling. We show that phase decoherence does not affect the $O\left(n^{-3/2}\right)$ sensitivity scaling for initial product states.

Squeezing of a thermal bath introduces features absent in an open quantum system interacting with an uncorrelated (zero squeezing) thermal bath. The resulting dynamics, governed by a Lindblad-type evolution, extends the concept of a generalized amplitude damping channel, which corresponds to a dissipative interaction with a purely thermal bath. Here we present the Kraus representation of this map, which we call the squeezed generalized amplitude damping channel. As an application of this channel to quantum information, we study the classical capacity of this channel.

Symmetry-resolved ion-yield spectroscopy of vibrationally excited ${\mathrm{N}}_2\mathrm{O}$ in the vicinity of the $\mathrm{O}1s$ ionization threshold has been carried out using an angle-resolved ion detection technique. The spectral intensity of the $\mathrm{O}1s\to ns\sigma$ Rydberg series, which has ${\sigma }^{*}$ valence character, is significantly reduced by the excitation of the bending vibration in the electronic ground state. Using an ab initio analysis of the electronic part of the second moment $⟨r^2⟩$, this suppression is interpreted as being due to a decrease in the mixing of the valence character in the $ns\sigma$ Rydberg states with decreasing bond angle.

We have studied the effects of spontaneous emission (SE) on a single-state time domain atom interferometer (AI) that uses trapped Rb atoms. The AI uses two standing wave pulses separated by time $T$ to produce an echo signal at time $2T$ due to interference between momentum states. We find that SE influences both the shape of the echo signal and its periodic time-dependent amplitude in a manner consistent with theoretical predictions. The results show that the time-dependent signal from the AI is related to the effective radiative decay rate of the excited state. We also present results that test theoretical predictions for several properties of the echo formation such as the variation in momentum transfer due to the change in the angle between the traveling wave components of the excitation pulses, strength of the atom-field interaction, and the effect of spatial profile of the excitation beams. These studies are important for realizing precision measurements of the atomic fine structure constant and gravity using this interferometer.

We study the properties of Bose-Einstein condensates in a one-dimensional ring with periodically modulated interaction strength. We demonstrate that within the semiclassical mean-field theory, a condensate can undergo a quantum phase transition between a solitonlike state and a spatially periodic condensate that matches the scattering length modulation. However, we show via exact diagonalization of the full many-body Hamiltonian that the solitonic ground states do not exist in the true quantum treatment. Instead, the system is driven into an entangled macroscopic-quantum-superposition-like state and the semiclassical soliton state may be regarded as a decohered macroscopic quantum superposition state. We investigate how the properties of the quantum ground state scales with the total number of atoms. Our work elucidates how semiclassical properties emerge from quantum behavior.

We calculate the Casimir force between slabs of finite thickness made of intrinsic and doped silicon with different concentration of carriers and compare the results to those obtained for gold slabs. We use the Drude and the plasma models to describe the dielectric function for the carriers in doped Si. We discuss the possibility of experimentally testing the appropriateness of these models. We also investigate the influence of finite thickness on ${\text{VO}}_2$, which has recently been proposed for Casimir effect measurements testing the metal-insulator transition.

We report on experimental results revealing the important role of linear diffraction in multiple filamentation of intense laser pulses propagating in air. We show that during the early stages of propagation the transverse energy redistribution is governed by the laws of classical optics, defining the initial conditions for subsequent filamentary breakup of the beam. This is done by introducing a smoothly varying transverse phase, resulting in deterministic multiple filamentation. The observations presented here indicate precise wave-front shaping as a way to control the highly nonlinear and otherwise turbulent aforesaid process, which is a prerequisite for a number of applications.

We study the quantum brachistochrone problem for a spin-1 system in a magnetic field of constant absolute value. Such a system gives us the possibility to examine in detail the statement that the state vectors realizing evolution with the minimal time of passage evolve along the subspace spanned by the initial and final state vectors [Carlini et al., Phys. Rev. Lett. 96, 060503 (2006); Brody and Hook, J. Phys. A 39, L167 (2006)]. Considering an explicit example, we show the existence of a quantum brachistochrone with the minimal possible time; however, the state vector we study leaves the subspace spanned by the initial and final state vectors during evolution. This is the result of our choice of a more constrained Hamiltonian than the one assumed in the general quantum brachistochrone problem. It is worth noting that such an evolution, being more complicated, is time optimal but with larger time than in the general case. This might be important for experiments, where a general Hamiltonian with all the allowed parameters is difficult to implement, but a constrained one, depending on the magnetic field, can be realized. However, for the preconstrained Hamiltonian not all final states are accessible. The present result does not contradict the general statement of the quantum brachistochrone problem, but gives additional insight into possible realization of the time-optimal passage.

The effect of the Pauli exclusion principle on double ionization of He atoms by strong, linearly polarized laser pulses is analyzed. We show that correlated electron escape, with electron momenta symmetric with respect to the field polarization axis, is suppressed if atoms are initially prepared in the metastable state ${}^{3}S$. The effect is a consequence of selection rules for the transition to the appropriate outgoing two-electron states. We illustrate the suppression in numerical calculations of electron and ion momentum distributions within a reduced dimensionality model.

We propose a scheme for the generation of a two-mode field squeezed state in cavity QED. It is based on two-channel Raman excitations of a beam of three-level atoms with random arrival times by two classical fields and two high-$Q$ resonator modes. It is shown that by suitably choosing the intensities and detunings of fields the dynamical processes can be selective and two-mode squeezing between the cavity modes can be generated at steady state. This proposal does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay.

We analyze the connections between entanglement dynamics and classical trajectories in a semiclassical regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on classical invariant tori and such phenomenon is closely related to the power spectra of classical trajectories. Classical power spectrum with a larger number of frequency components corresponds to larger entanglement. We introduce a frequency entropy to describe the classical frequency distribution. It is found that there is good correspondence between the classical frequency entropies and the maximum von Neumann entropies.

We formulate the accuracy of a quantum measurement for a qubit (spin-1/2) system in terms of a $3\times 3$ matrix. This matrix, which we refer to as the accuracy matrix, can be calculated from a positive operator-valued measure (POVM) corresponding to the quantum measurement. Based on the accuracy matrix, we derive trade-off relations between the measurement accuracy of two or three noncommuting observables of a qubit system. These trade-off relations offer a quantitative information-theoretic representation of Bohr’s principle of complementarity. They can be interpreted as the uncertainty relations between measurement errors in simultaneous measurements and also as the trade-off relations between the measurement error and back-action of the measurement. A no-cloning inequality is derived from the trade-off relations. Furthermore, our formulation and the results obtained can be applied to analyze quantum-state tomography. We also show that the accuracy matrix is closely related to the maximum-likelihood estimation and the Fisher information matrix for a finite number of samples; the accuracy matrix tells us how accurately we can estimate the probability distributions of observables of an unknown state by a finite number of quantum measurements.

We outline a proposal for a method of preparing an encoded two-state system (logical qubit) that is immune to collective noise acting on the Hilbert space of the states supporting it. The logical qubit is comprised of three photonic three-state systems (qutrits) and is generated by the process of spontaneous parametric down conversion. The states are constructed using linear optical elements along with three down-conversion sources, and are deemed successful by the simultaneous detection of six events. We also show how to select a maximally entangled state of two qutrits by similar methods. For this maximally entangled state we describe conditions for the state to be decoherence-free which do not correspond to collective errors.

We present a complete characterization for the local distinguishability of orthogonal $2\otimes 3$ pure states except for some special cases of three states. Interestingly, we find there is a large class of four or three states that are indistinguishable by local projective measurements and classical communication (LPCC), but can be perfectly distinguished by LOCC. That indicates the ability of LOCC for discriminating $2\otimes 3$ states is strictly more powerful than that of LPCC, which is strikingly different from the case of multiqubit states. We also show that classical communication plays a crucial role for local distinguishability by constructing a class of $m\otimes n$ states which require at least $2\min \{m,n\}-2$ rounds of classical communication in order to achieve a perfect local discrimination.

The electron affinity for neodymium is determined from relativistic configuration interaction calculations to be 169 meV, and six additional bound excited states are also predicted. These $6p$ attachments to the $4f^{4}6s^2$ neutral ground-state configuration are carefully analyzed with respect to approximate $LS$ of the total configuration and $LSJ$ of the $4f^4$ subgroup. This analysis is used to drastically reduce the basis size of the calculations and preselect channels for potentially large photodetachment partial cross sections. Estimations of the effects of the mixing of resonance states in the partial cross-section calculations suggest that for incident photon energies $\sim 2.0\text{eV}$ or larger, $6s$ detachments to excited $4f^{4}6s6p$ thresholds will represent the dominant channels of the total cross section.

A semiclassical model is devised to shed light on the role of asymptotic transitions around conical intersections in the dynamics of ion-diatom collisions. We consider the fundamental ${\text{H}}^{+}+{\text{H}}_2$ case, with vibrationally excited target, in the impact velocity range ${10}^{-4}\le v\le {5.10}^{-2}\text{a}\text{.u}\text{.}$ The reliability of the sudden approximation for vibration and trajectory-surface-hopping method is analyzed with respect to the model results. The consistency in the application of the adiabatic theorem at extremely low $v$ is also considered.

We investigate the phase diagram of a two-species Bose-Hubbard model including a conversion term, by which two particles from the first species can be converted into one particle of the second species, and vice versa. The model can be related to ultracold atom experiments in which a Feshbach resonance produces long-lived bound states viewed as diatomic molecules. The model is solved exactly by means of quantum Monte Carlo simulations. We show that an “inversion of population” occurs, depending on the parameters, where the second species becomes more numerous than the first species. The model also exhibits an exotic incompressible “super-Mott” phase where the particles from both species can flow with signs of superfluidity, but without global supercurrent. We present two phase diagrams, one in the chemical potential, conversion plane, the other in the chemical potential, detuning plane.

We experimentally and theoretically investigate the second order nonlinear optical response of metallodielectric multilayer structures composed of Ag and ${\mathrm{Ta}}_2{\mathrm{O}}_5$ layers, deposited by magnetron sputtering. Second harmonic generation measurements were performed in reflection mode as a function of incidence angle, using femtosecond pulses originating from a Ti:sapphire laser system tuned at $\lambda =800\mathrm{nm}$. The dependence of the generated signal was investigated as a function of pump intensity and polarization state. Our experimental results show that the conversion efficiency from a periodic metallodielectric sample may be enhanced by at least a factor of 30 with respect to the conversion efficiency from a single metal layer, thanks in part to the increased number of active surfaces, pump field localization, and penetration inside the metal layers. The conversion efficiency maximum shifts from 70° for the single silver layer down to approximately 55° for the stack. The experimental results are found to be in good agreement with calculations based on coupled Maxwell-Drude oscillators under the action of a nonlinear Lorentz force term.

We analyze the transverse shift (Imbert-Fedorov shift) of a focused beam upon reflection at stratified (doubly dispersive) metamaterials. In deriving analytical expressions for the reflection of a focused beam at such an interface this shift can be quantitatively forecast. Solely based on symmetry considerations of the vectorial reflection coefficient we analyze potential geometries where such a shift occurs. Contrary to the common belief, this shift is observable for a linearly polarized beam at total internal reflection. Furthermore, we predict a giant Imbert-Fedorov shift if light is partially reflected at impedance-matched media.

Using Nelson’s stochastic mechanics, quantum motion of electrons in the double-slit experiment is studied numerically. It is found that not only the distribution of arrival positions but also that of arrival times at the screen forms an interference pattern. It is demonstrated that the presence time and arrival time are well interpreted in terms of stochastic mechanics.