Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite-dimensional subspaces. Entanglement can be fully characterized as a finite-dimensional property, even though in general the truncation of the Hilbert space may cause fake nonclassicality. A generalization for multipartite quantum states is also given.

We present low uncertainty measurements of line parameters for 15 rotation-vibration transitions of water vapor in the wave number range of $7170.27–7183.02{\text{cm}}^{-1}$. These experiments incorporated frequency-stabilized cavity ring-down spectroscopy and a primary standard humidity generator which produced a stable and accurately known amount of water vapor in a nitrogen carrier gas stream. Intensities and line shape factors were derived by fitting high-resolution spectra to spectral models that account for collisional narrowing and speed-dependent broadening and shifting effects. For most transitions reported here, we estimate the relative combined standard uncertainty of the line intensities to be $<0.4\%$, of which approximately one half this value we ascribe to limited knowledge of the line shape. Our measured intensities and broadening parameters are compared to experimental and theoretical literature values. Agreement between our experimental intensity measurements and those derived by recent ab initio calculations of the dipole moment surface of water vapor is within 1.5%.

The generation of isolated attosecond pulses using the polarization gating technique is analyzed considering the single-atom response to an intense pulse with a time-dependent ellipticity. The influence of the carrier-envelope phase of the driving pulses on the characteristics of the harmonic spectra is discussed in combination with the concept of quantum trajectory followed by the electrons. We show that the control of the polarization state of the pulse opens important possibilities for synthesizing particular attosecond pulse wave form.

We describe an ab initio nonperturbative time-dependent $R$-matrix theory for ultrafast atomic processes. This theory enables investigations of the interaction of few-femtosecond and -attosecond pulse lasers with complex multielectron atoms and atomic ions. A derivation and analysis of the basic equations are given, which propagate the atomic wave function in the presence of the laser field forward in time in the internal and external $R$-matrix regions. To verify the accuracy of the approach, we investigate two-photon ionization of Ne irradiated by an intense laser pulse and compare current results with those obtained using the $R$-matrix Floquet method and an alternative time-dependent method. We also verify the capability of the current approach by applying it to the study of two-dimensional momentum distributions of electrons ejected from Ne due to irradiation by a sequence of 2 as light pulses in the presence of a 780 nm laser field.

We present a time-dependent localized Hartree-Fock density-functional linear response approach for the treatment of photoionization of atomic systems. This approach employs a spin-dependent localized Hartree-Fock exchange potential to calculate electron orbitals and kernel functions, and thus can be used to study the photoionization from atomic excited states. We have applied the approach to the calculation of photoionization cross sections of Ne ground state. The results are in agreement with available experimental data and have comparable accuracies with other ab initio theoretical results. We have also extended the approach to explore the photoionization from Ne excited states and obtained some results for the photoionization from outer-shell and inner-shell excited states.

Formation of stationary three-dimensional (3D) wave patterns generated by a small pointlike impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with the three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at the distances from the obstacle equal to a few wavelengths.

We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates (BECs) subject to strong confinement along the axial direction. Starting from the three-dimensional (3D) Gross-Pitaevskii equation (GPE), we proceed to an effective two-dimensional (2D) nonpolynomial Schrödinger equation (NPSE) derived by means of the integration over the axial coordinate. Results produced by the latter equation are in very good agreement with those obtained from the full 3D GPE, including cases when the formal 2D equation with the cubic nonlinearity is unreliable. The 2D NPSE is used to predict the density profiles and dynamical stability of repulsive and attractive BECs with zero and finite topological charges in various planar trapping configurations, including the axisymmetric harmonic confinement and one-dimensional periodic potential. In particular, we find a stable dynamical regime that was not reported before, viz., periodic splitting and recombination of trapped vortices with topological charges 2 or 3 in the self-attractive BEC.

We use the Bogoliubov–de Gennes formalism to analyze the effects of rotation on the ground-state phases of harmonically trapped Fermi gases, under the assumption that quantized vortices are not excited. We find that the rotation breaks Cooper pairs that are located near the trap edge, and that this leads to a phase separation between the nonrotating superfluid (fully paired) atoms located around the trap center and the rigidly rotating normal (nonpaired) atoms located toward the trap edge, with a coexistence (partially paired) region in between. Furthermore, we show that the superfluid phase that occurs in the coexistence region is characterized by a gapless excitation spectrum, and that it is distinct from the gapped phase that occurs near the trap center.

We study the photonic spectrum of a one-dimensional optical lattice possessing a double primitive cell, when the atoms are well localized at the lattice minima. While a one-dimensional lattice with a simple Wigner-Seitz cell always possesses a photonic band gap at the atomic resonance, in this configuration the photonic transmission spectrum may exhibit no, double, or multiple photonic band gaps depending on the ratio between the interparticle distance $\varrho$ inside the cell and the cell size $a$. The transmission spectra of a weak incident probe are evaluated when the atoms are trapped in free space and inside an optical resonator for realistic experimental parameters.

We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-two-dimensional geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to $\sqrt{ϵ/\hslash {\omega }_0}$, where $ϵ$ is the kinetic energy and ${\omega }_0$ is the oscillation frequency of the trapped particles in the confinement potential.

The equation of state of a weakly interacting two-dimensional Bose gas is studied at zero temperature by means of quantum Monte Carlo methods. Going down to as low densities as $n{a}^2\propto {10}^{-100}$ permits us to obtain agreement on beyond mean-field level between predictions of perturbative methods and direct many-body numerical simulation, thus providing an answer to the fundamental question of the equation of state of a two-dimensional dilute Bose gas in the universal regime (i.e., entirely described by the gas parameter $n{a}^2$). We also show that the measure of the frequency of a breathing collective oscillation in a trap at very low densities can be used to test the universal equation of state of a two-dimensional Bose gas.

We discuss experimental situations that consist of multiple preparation and measurement stages. This leads us to an alternative approach to quantum mechanics. In particular, we introduce the idea of multitime quantum states which are the appropriate tools for describing these experimental situations. We also describe multitime measurements and discuss their relation to multitime states. A consequence of our formalism is to put states and operators on an equal footing. Finally we discuss the implications of our approach to quantum mechanics for the problem of the flow of time.

We propose a formalism of quantum subsystems for reduced descriptions of quantum systems. This unifies a number of well-known methods and less common approaches. The main mathematical ingredients are completely positive maps and correlation functions. In this formalism generalized quantum systems can be composed and there is a notion of generalized entanglement. Models of fermionic and bosonic systems and also quantum systems described by the SU(2) symmetry are studied.

We consider soft-photon effects (ir structure of QED) on the construction of physical qubits. Soft photons appear when we build charged qubits from the asymptotic states of QED. This construction is necessary in order to include the effect of soft photons on entanglement measures. The nonexistence of free charged particles (due to the long range of QED interactions) leads us to question the sense of the very concept of free charged qubit. In this work, using the “dressing” formalism, we build physical charged qubits from dressed fields which have the correct asymptotic behavior, are gauge invariant, have propagators with a particle pole structure, and are free from infrared divergences. Finally, we discuss the impact of the soft corrections on the entanglement measures.

Extended superposed quantum-state initialization using disjoint prime implicants is an algorithm for generating quantum arrays for the purpose of initializing a desired quantum superposition. The quantum arrays generated by this algorithm almost always use fewer gates than other algorithms and in the worst case use the same number of gates. These improvements are achieved by allowing certain parts of the quantum superposition that cannot be initialized directly by the algorithm to be initialized using special circuits. This allows more terms in the quantum superposition to be initialized at the same time which decreases the number of gates required by the generated quantum array.

Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed, it is the square of a metric. We consider a family of divergence measures (${\text{JD}}_{\alpha }$ for $\alpha >0$), the Jensen divergences of order $\alpha$, which generalize JD as ${\text{JD}}_1=\text{JD}$. Using a result of Schoenberg, we prove that ${\text{JD}}_{\alpha }$ is the square of a metric for $\alpha ∊\left(0,2\right]$, and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a symmetrized and smoothed version of quantum relative entropy and can be extended to a family of quantum Jensen divergences of order $\alpha$ $\left({\text{QJD}}_{\alpha }\right)$. We strengthen results by Lamberti and co-workers by proving that for qubits and pure states, ${\text{QJD}}_{\alpha }^{1/2}$ is a metric space which can be isometrically embedded in a real Hilbert space when $\alpha ∊\left(0,2\right]$. In analogy with Burbea and Rao’s generalization of JD, we also define general QJD by associating a Jensen-type quantity to any weighted family of states. Appropriate interpretations of quantities introduced are discussed and bounds are derived in terms of the total variation and trace distance.

Recently Boyer et al. [Phys. Rev. Lett. 99, 140501 (2007)] suggested the idea of semiquantum key distribution (SQKD) in which Bob is classical and they also proposed a semiquantum key distribution protocol (BKM2007). To discuss the security of the BKM2007 protocol, they proved that their protocol is completely robust. This means that nonzero information acquired by Eve on the information string implies the nonzero probability that the legitimate participants can find errors on the bits tested by this protocol. The BKM2007 protocol uses four quantum states to distribute a secret key. In this paper, we simplify their protocol by using less than four quantum states. In detail, we present five different SQKD protocols in which Alice sends three quantum states, two quantum states, and one quantum state, respectively. Also, we prove that all the five protocols are completely robust. In particular, we invent two completely robust SQKD protocols in which Alice sends only one quantum state. Alice uses a register in one SQKD protocol, but she does not use any register in the other. The information bit proportion of the SQKD protocol in which Alice sends only one quantum state but uses a register is the double as that in the BKM2007 protocol. Furthermore, the information bit rate of the SQKD protocol in which Alice sends only one quantum state and does not use any register is not lower than that of the BKM2007 protocol.

The deviation of the natural spectral line profile from the Lorentz shape for the optical resonant frequency measurements is considered. This deviation leads to an asymmetry, which is mainly due to nonresonant correction to the resonant Lorentz profile. The nonresonant corrections are studied for the different types of the atomic resonant experiments. The most accurate recent optical resonance experiments are analyzed, i.e., the two-photon $1s\text{−}2s$ resonance excitation of the hydrogen atom with the delayed decay in the external electric field. The description of the nonresonant correction in the latter case requires the employment of QED with different in and out Hamiltonians. The nonresonant corrections for this experiment are investigated and found to be about ${10}^{-5}\text{Hz}$, while the recent experimental uncertainty is 34 Hz and in the near feature is expected to be a few hertz. The projected $1s\text{−}2s$ resonance excitation experiment with the three-photon ionization detection (which is now in progress) is also considered.

We report on an experimental study of the dynamics of the reflection of ultracold atoms from a periodic one-dimensional magnetic lattice potential. The magnetic lattice potential of period $10\mu \text{m}$ is generated by applying a uniform bias magnetic field to a microfabricated periodic structure on a silicon wafer coated with a multilayered TbGdFeCo/Cr magneto-optical film. The effective thickness of the magnetic film is about 960 nm. A detailed study of the profile of the reflected atoms as a function of externally induced periodic corrugation in the potential is described. The effect of angle of incidence is investigated in detail. The experimental observations are supported by numerical simulations.

We investigate exceptional points, which are branch-point singularities of two resonance eigenstates, in spectra of the hydrogen atom in crossed external electric and magnetic fields. A procedure to systematically search for exceptional points is presented, and their existence is proven. The properties of the branch-point singularities are discussed with effective low-dimensional matrix models, their relation with avoided level crossings is analyzed, and their influence on dipole matrix elements and the photoionization cross section is investigated. Furthermore, the rare case of a connection between three resonances almost forming a triple degeneracy in the form of a cubic-root branch point is discussed.