Momentum flow in electromagnetic wave systems has become a topic of considerable importance in recent years with the development of optical tweezers and spanners. Although momentum conservation has been explored for deterministic wave fields, the corresponding laws for partially coherent wave fields have yet to be completely determined. In this paper we derive the frequency-domain representation for the Maxwell stress tensor for partially coherent fields and sources.

A generalized model of the quantum measurement process is considered, in which the relaxation of the detector system interacting with an environment can be treated. When the effect of the environment on the detector system is described by the quantum Markovian process, the model can be solved exactly. The time evolution of the particle and detector is investigated in detail. It is shown that the decay of quantum coherence of the particle becomes negligible when the relaxation time of the detector system is sufficiently short. Furthermore the stochastic model is found, which is equivalent to the proposed model with respect to the particle state.

We investigate the entanglement dynamics of a generic multimode Gaussian state interacting with a common environmental noise by means of the characteristic function method and the defined operators. We find that such operators obey the rather simple commutation relations. This enables us to exactly solve the Fokker-Planck equation and to establish the general form of the input and output covariance matrices of this state. As an application, we consider the separability and entanglement of three-mode squeezed Gaussian state in the common thermal and squeezed thermal bath.

By using the algebraic separability criterion of Simon, we present an explicit determination of squeezing parameters for which the $P$-representation condition saturates the $\text{Sp}\left(2,R\right)\otimes \text{Sp}\left(2,R\right)$ invariant separability condition for continuous variable two-party Gaussian systems. We thus give the explicit analytic formulas of squeezing parameters which establish the equivalence of the separability condition with the $P$-representation condition. The implications of our algebraic analysis on some of the past related works are discussed.

A complete experiment of pulse compression mediated by femtosecond filaments is numerically simulated. Spatiotemporal distortions experienced by a filament formed in an argon cell with subsequent propagation inside the exit glass window and an air path are examined. Millimeter propagation ranges in silica preserve the spatial shape of the filament. However, the pulse duration strongly broadens due to the combination of high dispersion in glass and Kerr nonlinearity. We show that, despite this harmful broadening, on-axis pulse compression can be restored in the final stage of atmospheric propagation and can even be reestablished in vacuum. The key process for refocusing the beam is the introduction of an intensity-dependent spatial curvature in the pulse phase accumulated inside the silica window.

We present a study of the effects of dispersion on the properties of photon pairs generated by type-II collinear spontaneous parametric down-conversion. Specifically, we take into consideration the effects of a chirped pump, as well as of dispersive propagation of the photon pairs. We present expressions for the joint amplitude both in the spectral and temporal domains, as well as for the chronocyclic Wigner function of heralded single photons, which fully characterizes the single-photon spectral (temporal) properties. On the one hand, we show that unwanted effects of pump chirp in terms of the heralded single-photon duration can be suppressed for states designed to be factorable and spectrally elongated. On the other hand, we show that pump chirp constitutes an effective tool for the control of the degree of photon-pair entanglement. We show that when frequency-entangled photon pairs propagate through a dispersive medium, entanglement can “migrate” between the modulus and phase of the joint temporal amplitude.

We have numerically calculated the resonance curve and the region of existence of high-energy dissipative solitons in systems governed by the complex cubic-quintic Ginzburg-Landau equation. The calculations are carried out for negative reactive quintic nonlinearity. This choice allows the resonance curve to be continued into the region of positive net dispersion, thus showing that high-energy pulses can also be generated by lasers operating in the anomalous dispersion regime.

We discuss a protocol for efficient and quick transfer of population between nearly one-dimensional Rydberg states by a chirped train of half-cycle pulses. The chirp refers both to the time interval and relative strength between subsequent pulses. The most spectacular result obtained by the use of this protocol is the transfer of over 10% of the initial population from the high-Rydberg state of $n=50,80$ to much lower ones of $n^{\prime }\approx 10$ in a short time of the order of 1 ns.

We have investigated multiple ionization of Xe clusters by 61-nm ${10}^{11}–{10}^{12}\text{W}/{\text{cm}}^2$ extreme-ultraviolet light pulses at the free-electron laser facility, SPring-8 Compact SASE Source test accelerator, in Japan, using a dead-time-free three-dimensional momentum spectrometer. It was found that the average kinetic energy of atomic ${\text{Xe}}^{+}$ ions increases when increasing the laser power density and the cluster size. For these experimental conditions significant frustration of the cluster photoionization occurs but no indication for heating mechanisms other than sequential photoabsorption by individual atoms in the cluster was found.

A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite-dimensional quantum states, with the covariance matrix playing the role of the density matrix and homodyne detection providing Stern-Gerlach-like projections. The major difference stems from a different character of relevant noises: while the statistics of Stern-Gerlach-like measurements is governed by binomial statistics, the detection of quadrature variances corresponds to ${\chi }^2$ statistics. For Gaussian and near Gaussian states the suggested method provides, compared to standard tomography techniques, more stable and reliable reconstructions. In addition, by putting together reconstruction methods for Gaussian and arbitrary states, we obtain a tool to detect the non-Gaussian character of optical signals.

Photons cannot be localized in a sharply defined region. The expectation value of their energy density and the photon number density can only be approximately localized, leaving an exponential tail. We show that one may sharply localize either electric or magnetic (but not both) footprints of photons and only momentarily. In the course of time evolution this localization is immediately destroyed. However, the coherent states, like their classical counterparts, can be localized without any limitations. The main tool in our analysis is a set of space-dependent photon creation and annihilation operators defined without any reference to the mode decomposition.

We investigate the possibility of the existence of different types of thermal entanglement in the two-spin Heisenberg $XY$ model, which are distinguished by the behavior of the concurrence as a function of the model parameters. Singularities in the temperature threshold for thermal entanglement and in the ground-state energy as a function of the model parameters are used to construct diagrams containing boundary lines separating the several types of thermal entanglement in the system, showing an unexpected rich structure. We discuss a procedure to extract a pure quantum component from the spin-correlation function at arbitrary temperatures, by using the explicit form of the decomposition that minimizes the concurrence, and show that it is highly sensitive to the different patterns of thermal entanglement.

In this paper, we find subspaces that have no locally distinguishable orthonormal bases. For a $C^m\otimes C^n$ $\left(m,n\ge 3\right)$ bipartite tensor system, we show that the orthogonal complement of the space spanned by a Schmidt rank-3 maximally entangled state is such a subspace. We further demonstrate that, when both parties’ dimensions are greater than three, the orthogonal complement of the space spanned by any entangled state whose Schmidt rank is greater than three has no locally distinguishable orthonormal bases. Although derived using a scheme simpler than previous methods, our results are much more general than known before.

Polynomially large ground-state energy gaps are rare in many-body quantum systems, but useful in quantum information and an interesting feature of the one-dimensional quantum Ising model. We show analytically that the gap is generically polynomially large not just for the quantum Ising model, but for one-, two-, and three-dimensional interaction lattices and Hamiltonians with certain random interactions. We extend the analysis to Hamiltonian evolutions and we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. These results also yield a new perspective on the one-dimensional cluster state.

We consider a spin-1/2 anisotropic $XY$ model with time-dependent spin-spin coupling as means of creating long-distance entanglement. We predict the emergence of significant entanglement between the first spin and the last spin whenever the ac part of the coupling has a frequency matching the Zeeman splitting. In particular, we find that the concurrence assumes its maximum with a vanishing dc part. Mapping the time-dependent Hamiltonian within a rotating-wave approximation to an effective static model provides qualitative and quantitative understanding of this entanglement resonance. Numerical results for the duration of the entanglement creation and its length dependence substantiate the effective static picture.

We present a general method to construct a set of local rectilinear vibrational coordinates for a nonlinear molecule whose reference structure does not necessarily correspond to a stationary point of the potential-energy surface. We show both analytically and with a numerical example that the vibrational coordinates satisfy Eckart’s conditions. In addition, we find that the Watson Hamiltonian provides a fairly robust description even of highly excited vibrational states of triatomic molecules, except for a few states of large amplitude motion sampling the singular region of the Hamiltonian. These states can be identified through slow convergence.

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers $\left(\ge -1\right)$ of all the interparticle distances $r_{ij}$, multiplied by an exponential containing an arbitrary linear combination of all the $r_{ij}$. These integrals are generalizations of those encountered using Hylleraas basis functions and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill plus some easily evaluated three-body “boundary” integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.

An approach is developed for high-accuracy calculations of the $2p$ state decay width in the hydrogenlike atoms. The relativistic recoil correction to the $2p$ state decay width of the relative order ${\left(Z\alpha \right)}^{2}m/M$, which is responsible for the uncertainty of the total width calculation, is obtained in the frame of the two-body formalism. Numerical results for total widths of the $2p$ state of some medium-$Z$ muonic atoms are presented. As additional applications of the developed technique, the relativistic recoil correction to the electric dipole matrix element for the $2p-1s$ transition is obtained and that for the bound $g$ factor of $ns$ states is reproduced.

The recombination of a free electron into a bound state of bare, heavy nucleus under simultaneous production of bound-electron–free-positron pair is studied within the framework of relativistic first-order perturbation theory. This process, denoted as “negative-continuum dielectronic recombination” leads to a formation of not only the ground but also the singly and doubly excited states of the residual heliumlike ion. The contributions from such an excited state capture to the total as well as angle-differential cross sections are studied in detail. Calculations are performed for the recombination of (initially) bare uranium ${\text{U}}^{92+}$ ions and for a wide range of collision energies. From these calculations, we find almost 75% enhancement of the total recombination probability if the excited ionic states are taken into account.

We use an optically dense anisotropic magneto-optical trap to study recoil-induced resonances (RIRs) in the transient high-gain regime. We find that two distinct mechanisms govern the atomic dynamics: the finite, frequency-dependent atomic response time and momentum-space population redistribution. At low input probe intensities, the residual Doppler width of the atoms, combined with the finite atomic response time, result in a linear transient hysteretic effect that modifies the locations, widths, and magnitudes of the resulting gain spectra depending on the sign of the scan chirp. When larger intensities (i.e., greater than a few $\mu \text{W}/{\text{cm}}^2$) are incident on the atomic sample for several $\mu \text{s}$, hole burning in the atomic sample momentum distribution leads to a coherent population redistribution that persists for approximately $100\mu \text{s}$. We propose using RIRs to engineer the atomic momentum distribution to enhance the nonlinear atom-photon coupling. We present a numerical model and compare the calculated and experimental results to verify our interpretation.