We demonstrate numerically that efficient and lasting squeezed light can be achieved due to a constructive two-photon interference. Even if large phase fluctuations occur, the dispersion in one of the two quadrature components of the light field can still be reduced below the standard quantum limit set by the symmetric distribution of the vacuum state. Experimental observation of squeezed light in this system is possible by generalizing the recent techniques of Ou’s group [L. J. Lu and Z. Y. Ou, Phys. Rev. Lett. 88, 023601 (2002)].

A Raman scheme for optical-pulse group-velocity reduction in a pure lifetime broadened system is studied. We show that this nonelectromagnetically induced transparency (NEIT) scheme has many advantages over the conventional method that critically relies on the transparency window created by an EIT process. Significant reduction of the group velocity, probe field loss, and pulse distortion are reported. In addition, rich dynamics of the propagation process are studied.

Using the inverse of the Hamiltonian, we introduce the inverse Schrödinger equation (ISE) that is equivalent to the ordinary Schrödinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem.

The semiclassical dynamics of Rydberg electronic wave packets in diatomic molecules is investigated using a sum over classical trajectories method, which is based on the semiclassical form of Feynman’s path integral. Our approach allows us to calculate intramolecular energy redistribution rates based on averaging of coupling parameters over classical trajectories associated with time-dependent parts of the overall system that exhibit different periodicities. The accuracy of our method is tested against perturbation theory and good agreement is obtained. A resonance structure in the computed autocorrelation function has also been observed in the case of rotating nuclei, when the periods of the classical trajectories of the electron match an integer multiple of the rotational period. This has previously been called the “stroboscopic” effect.

A polar molecule experiences a force in an inhomogeneous electric field. Using this force, neutral molecules can be decelerated and trapped. It is shown here that this can in principle be done without loss in phase-space density. Using a series of 64 pulsed inhomogeneous electric fields a supersonic beam of ammonia molecules ${(}^{14}{\mathrm{NH}}_3,$ ${}^{14}{\mathrm{ND}}_3,$ ${}^{15}{\mathrm{ND}}_3)$ is decelerated. Subsequently, the decelerated molecules are loaded into an electrostatic quadrupole trap. Densities on the order of ${10}^7\hspace{0.5em}{\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$ at a temperature of 25 mK are obtained for ${}^{14}{\mathrm{ND}}_3$ and ${}^{15}{\mathrm{ND}}_3$ separately and simultaneously. This corresponds to a phase-space density in the trap of $2\times {10}^{-13},$ 50 times less than the initial phase-space density in the beam.

The recent evolution toward resonant conditions of the two-color resonant four-wave-mixing (TC-RFWM) spectroscopy has been dictated by the high sensitivity required experimentally. While some models have been used in different contexts such as light pressure forces in strong polychromatic fields, magnetically assisted Sisyphus effect, or multiphoton resonances in Λ atoms, the existence in molecules of additional processes such as nonradiative transitions and rotational or vibrational dephasings requires the extension of previous models. For this reason, we give here a general description of the internal dynamics for a molecule undergoing two strong grating beams, acting either on two different transitions sharing a common level or on the same transition, and one weak probe beam to reproduce the ground-state grating and stimulated emission pumping configurations of TC-RFWM spectroscopy. By combining high spectral resolution and strong grating beams, we show that the TC-RFWM spectrum is very sensitive to the transition constants, dephasing constants, as well as to the transverse velocity of the molecules in the jet. The last case corresponding to a bichromatic field acting on a single transition is used to explain the origin of the line-shape asymmetry observed experimentally on jet-cooled molecules.

We present results of computer simulations showing dramatic increases in the production and intensity of high-order harmonics (in the cutoff region) produced by 20-fs pulse with counterpropagating pulse in rare gases. Using two different models for the gas medium (i.e., classical anharmonic oscillators representing Ne, Ar, Kr and quantum oscillators representing ${\mathrm{Ne}}^{+},$ ${\mathrm{Ar}}^{+},$ ${\mathrm{Kr}}^{+}),$ we demonstrate an efficiency increase of four and six orders of magnitude for the respective models. This suggests a notable improvement over other methods.

We suggest and analyze the concept of a semiconductor laser device that incorporates two basic ideas: (i) dual-wavelength generation of two optical fields on the interband transitions with independent control of each field in a three-terminal “transistor” scheme, and (ii) generation of infrared radiation in the 3–300 μm range due to nonlinear wave mixing of the above optical fields in the same laser cavity. Due to inversionless nature of the difference frequency generation and inherently low threshold current, the laser can be capable of continuous room-temperature operation in the mid/far-infrared and THz range.

A measurement strategy is developed for a different kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given nonorthogonal quantum states occurring with given a priori probabilities. A general analytical solution is obtained for N states that are restricted to a two-dimensional subspace of the Hilbert space of the system. The result for the special case of three arbitrary but linearly dependent states is applied to a variety of sets of three states that are symmetric and equally probable. It is found that, in this case, the minimum-error probability for distinguishing one of the states from the other two is only about half as large as the minimum-error probability for distinguishing all three states individually.

We present exact ab initio quantum results for harmonic generation (HG) by a weakly bound electron interacting with a strong monochromatic laser field. The analytic structure of the HG amplitude resulting from the multiphoton detachment thresholds is demonstrated. Our numerical results show that the HG spectrum is sensitive primarily to the distance in energy from the thresholds, thereby opening new possibilities for control of HG.

In this paper two fundamental questions in the contracted Schrödinger equation (CSE) approach are considered by using Lipkin’s quasispin model: 1-1 mapping between the second-order reduced density matrix (2-RDM) and the wave function of an excited state, and the uniqueness of the solution of CSE under incomplete N-representability conditions. We present some examples of the wave functions that give the same 2-RDM as the excited state. Thus 2-RDM of an excited state does not determine the wave function uniquely, and it alone cannot be used as basic variable for excited states of the density-matrix theory. Under the incomplete representability constraints the solution of the second-order CSE contains all the exact 4-RDMs together with the spurious ones. We examined the distribution of the solutions as a function of energy, and found that the solutions are well separated from each other under the P- and G-representability conditions of 4-RDM in the low-energy region, but with moderate interaction, or in the higher-energy region, there exist spurious solutions for almost all energies. Thus the G condition of 4-RDM is not sufficient to solve the excited states, although it gives accurate results for the ground state of Lipkin’s model.

We study the robustness of multiparty entanglement under local decoherence, modeled by partially depolarizing channels acting independently on each subsystem. Surprisingly, we find that the robustness of (GHZ) entanglement increases with the number of qubits. An n-qubit Greenberger-Horne-Zeilinger (GHZ) state can stand more than 55% local depolarization in the limit $\overrightarrow{n}\infty .$ GHZ states are more robust than other generic states of three and four qubits. We also study spin-squeezed states in the limit $\overrightarrow{n}\infty$ and find that they too can stand considerable local depolarization.

Using the weakest-bound-electron potential model, an eight-parameter formula is derived for the 153 ionization potentials of atomic or ionic systems with $Z=2\mathrm{}–18,$ $N=2\mathrm{}–18$ yielding results departing from experimental ones by no more than 0.65 eV.

The behavior of the ejected electron spectra resulting from low-energy ion-atom collisions relevant to momentum imaging experiments is explored and the origin of the oscillatory structures these spectra display as a function of collision energy is discussed. This is aided by consideration of the time-dependent, electronic Schödinger equation that is solved at a fixed impact parameter for 1–25 keV proton impact of atomic hydrogen utilizing the lattice, Fourier collocation technique and split-operator time propagation. At a large internuclear separation after the collision the bound states of the target and projectile are projected out for $n<\mathrm{}4\mathrm{}$ and the resulting continuum wave function is examined. Techniques, such as multigridding, are investigated to extend the propagation of the wave function to significantly larger final distances.

We investigated ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ fragment production from the dissociation of ${\mathrm{HeH}}^{+}$ ions in collision with a He target. This occurs through either the ${\mathrm{He}}^{+}+\mathrm{H}$ or the $\mathrm{He}+{\mathrm{H}}^{+}$ channel. We also investigated ${\mathrm{He}}^{2+}$ and ${\mathrm{H}}^{-}$ production, which are three orders of magnitude smaller than those for ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}.$ The ${\mathrm{He}}^{+}/\mathrm{H}$ channel seems to be favored over the ${\mathrm{H}}^{+}/\mathrm{He}$ channel at all acceleration energies as well as at all ion source pressures. The ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ cross sections appear to be independent of the acceleration energy while they show significant dependence on ion source pressures. The center of mass energy distribution for both ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ shows a kinetic energy release of near zero eV. Our results suggest that the initial state of the parent ${\mathrm{HeH}}^{+}$ molecular ions is that of a mixture of ground electronic state as well as metastable excited states with the $a{}^3{\Sigma }^{+}$ dominant.

Studies of electron transfer from a molecule $\left({\mathrm{CH}}_4\right)$ to a negative ion $\left({\mathrm{C}}_{60}{\mathrm{F}}_{36}^{-}\right)$ at low-ion collision energies (4 to 10 keV) are reported. The center-of-mass energy threshold for the reaction ${\mathrm{C}}_{60}{\mathrm{F}}_{36}^{-}+{\mathrm{CH}}_4\to {\mathrm{C}}_{60}{\mathrm{F}}_{36}^{-2}+{\mathrm{CH}}_4^{+}$ is found to be ∼60 eV, which is well above the estimated thermodynamic endoergicity $\left[V_i\right({\mathrm{CH}}_4{)-A}_e\left({\mathrm{C}}_{60}{\mathrm{F}}_{36}^{-}\right)\sim 10\mathrm{eV}].$ Dissociative charge transfer to produce ${\mathrm{C}}_{60}{\mathrm{F}}_{35}^{-}$ and ${\mathrm{C}}_{60}{\mathrm{F}}_{34}^{-}$ is also observed but much less probable. Collisions of other negative ions with neutral molecules (notably ${\mathrm{C}}_{84}^{-})$ did not result in a detectable signal of doubly charged negative ions.

Scattering of electron wave packets by large-size targets is considered. In the “no-spreading” approximation the general expression for the electron distribution function after scattering is found. An alternative regime of scattering, different from both the first-order Born approximation and classical limit, is found to exist in the case of narrow (compared to a target) nonspreading wave packets. In this regime, the average angle of scattering is shown to differ from the classical one and, counterintuitively, the difference is shown to be greater, the narrower the wave packets are. Physical reasons of this effect are discussed.

We present a general formalism for an efficient treatment of a broad range of electron-nucleus laser processes. The interaction with the laser beam is taken into account by transforming the system into an oscillating frame, called the Henneberger picture. General expressions for the transition probability per unit time are given in the weak laser field and in the n photonic cases, and connection to previous methods is demonstrated in the appropriate limits. As an example, the transition probability per unit time of laser-induced internal conversion (IC) processes is presented. The conservation of angular momentum in the multiphoton process can be traced well in our calculation. Numerical values of the IC coefficient of the energetically forbidden IC process in case of ${}^{99m}\mathrm{Tc}$ ignited by the absorption of up to three soft-x-ray laser photons are also given. The increase in the rate of IC decay is found comparable to or greater than the natural decay rate of the isomer in case of appropriate intensity and photon energy of the laser. Hard UV laser-induced internal conversion coefficients (ICCs) are also calculated for energetically forbidden shells of ${}^{107}{\mathrm{Ag}}^m$ $(K$ shell, $E3,$ $25.47\hspace{0.5em}\mathrm{keV}),$ ${}^{90}{\mathrm{Nb}}^m$ ${(L}_2$ shell, $M2+E3,$ $2.3\hspace{0.5em}\mathrm{keV}),$ ${}^{183}{\mathrm{W}}^m$ ${(N}_1$ shell, $E1,$ $544\hspace{0.5em}\mathrm{eV}$ and $M_5$ shell, $E2,$ $1.79\hspace{0.5em}\mathrm{keV}),$ ${}^{188}{\mathrm{Re}}^m$ ${(M}_2$ shell, $M3+E4,$ $2.63\hspace{0.5em}\mathrm{keV}),$ ${}^{205}{\mathrm{Pb}}^m$ ${(M}_5$ shell, $E2,$ $2.4\hspace{0.5em}\mathrm{keV}),$ and ${}^{235}{\mathrm{U}}^m$ ${(O}_4$ and $O_5$ shells, $E3,$ $73.5\hspace{0.5em}\mathrm{eV}).\mathrm{}$ Measurable induced ICCs are found in case of available intensities and photon energies of the laser beam for the above isomers. Experiments, that may demonstrate the effect and may be tools for determination of nuclear transition energies, are also suggested.

We use the nonperturbative linear $\delta$ expansion method to evaluate analytically the coefficients $c_1$ and $c_2^{″}$ that appear in the expansion for the transition temperature for a dilute, homogeneous, three-dimensional Bose gas given by $T_c{=T}_0({1+c}_1{\mathrm{an}}^{1/3}+[c_2^{\prime }\ln {(an}^{1/3}{)+c}_2^{″}\left]a^2{n}^{2/3}{+O(a}^{3}n\right)),$ where $T_0$ is the result for an ideal gas, a is the s-wave scattering length, and n is the number density. In a previous work the same method has been used to evaluate $c_1$ to order ${\delta }^2$ with the result $c_1=\mathrm{3.06.}\mathrm{}$ Here, we push the calculation to the next two orders obtaining $c_1=2.45\mathrm{}$ at order ${\delta }^3$ and $c_1=1.48\mathrm{}$ at order ${\delta }^4.$ Analyzing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the $1/N$ approximations. At the same orders we obtain $c_2^{″}=101.4,$ $c_2^{″}=98.2,$ and $c_2^{″}=\mathrm{82.9.}\mathrm{}$ Our analytical results seem to support the recent Monte Carlo estimates $c_1=1.32\mathrm{}\pm 0.02$ and $c_2^{″}=75.7\mathrm{}\pm \mathrm{0.4.}$

Based on the similarity of the coupled nonlinear Schrödinger equations with and without external potentials, a relation is established between their solutions. The external potentials are assumed to modify both amplitudes and phases together with the spatial and temporal variables appearing in the transformation relation. With examples of trap potentials depending linearly and quadratically on the spatial coordinate it is demonstrated how the transformation ansatz works in practice for obtaining atomic solitons of Bose-Einstein condensates consisting of sodium and rubidium atoms when one starts from the known optical soliton solution of the nonlinear Schrödinger equation without potential.