We present a multimode model to describe an arbitrary $N$-photon state with a wide spectral range and some arbitrary temporal distribution. In general, some of the $N$ photons are spread out in time while others may overlap and become indistinguishable. From this model, we find that the temporal (in)distinguishability of photons is related to the exchange symmetry of the multiphoton wave function. We find that simple multiphoton detection scheme gives rise to a more general photon bunching effect with the famous two-photon effect as a special case. We then send this $N$-photon state into a recently discovered multiphoton interference scheme. We calculate the visibility of the multiphoton interference scheme and find that it is related to the temporal distinguishability of the $N$ photons. Maximum visibility of one is achieved for the indistinguishable $N$-photon state whereas the visibility degrades when some of the photons are separated and become distinguishable. Thus we can identify an experimentally measurable quantity that may quantitatively define the degree of indistinguishability of an $N$-photon state. This presents a quantitative demonstration of the complementary principle of quantum interference.

We examine the tripartite entanglement properties of an optical system using interlinked ${\chi }^{\left(2\right)}$ interactions, recently studied experimentally in terms of its phase-matching properties by Bondani et al. [Opt. Express 14, 21, 9838 (2006)]. We show that the system produces output modes at three distinct frequencies which are genuinely tripartite entangled, and analyze this entanglement in terms of different measurable correlations. We show that, due to the asymmetry of the process, the detection of this entanglement depends crucially on the correlation functions that are measured. We find that some of the correlations found in the literature fail to register the entanglement, in contrast to symmetric systems, for which the actual choice of correlation to be measured makes little difference.

We have developed a full multimode theory of a synchronously pumped type-I optical parametric oscillator. We calculate the output quantum fluctuations of the device and find that, in the degenerate case (coincident signal and idler set of frequencies), significant squeezing is obtained when one approaches threshold from below for a set of well-defined “supermodes,” or frequency combs, consisting of a coherent linear superposition of signal modes of different frequencies which are resonant in the cavity.

Schrodinger equation for a charged particle interacting with the plane-wave electromagnetic field is solved exactly. The exact analytic solution and the perturbative solution up to second order are compared.

Relativistic energy shifts of atomic excitation energies, showing the dependence of these energies on the value of the fine-structure constant $\alpha$, are needed to extract past changes in $\alpha$ from spectra of distant quasars. These shifts are calculated by the Fock-space coupled cluster method and its extrapolated intermediate Hamiltonian extension, which allow high-accuracy treatment of electron correlation. The accuracy of the method is tested by comparing 33 transition energies in heavy atoms (obtained with the laboratory $\alpha$) with experiment; the average error is $258{\mathrm{cm}}^{-1}$, and the largest error is $711{\mathrm{cm}}^{-1}$. This may be compared with an average error of $432{\mathrm{cm}}^{-1}$ and a maximum error of $2150{\mathrm{cm}}^{-1}$ in the work of Dzuba et al., who reported most of the available energy shift calculations. The enhanced accuracy is due to more extensive inclusion of electron correlation. To obtain the energy shifts, we repeated the calculations with different values of $\alpha$ (within 0.1% of the current value). Our shifts differ by up to 30% from the values given by Dzuba et al., with an average difference of 9%. Based on the better quality of the present-day excitation energies, we believe the energy shifts reported here are more accurate than earlier work.

The intervals between hyperfine levels of high $ns$ and $nd$ $(n=68–76)$ Rydberg states of ${}^{83}\mathrm{Kr}$ have been determined by millimeter-wave spectroscopy. The hyperfine structure of the Rydberg states has been analyzed using multichannel quantum defect theory. Improved eigenquantum defects for the $ns$ and $nd$ Rydberg series and quantitative information about the $s\text{−}d$ interaction at the energy of the ${}^{2}P_{3∕2}$ threshold have been obtained, and improved values of the hyperfine structure of the ${}^{2}P_{3∕2}$ ground state of ${}^{83}\mathrm{Kr}^{+}$ have been derived.

We have investigated the electron emission by the RNA uracil base $\left({\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}_2{\mathrm{O}}_2\right)$ due to collisions with protons in the $25\mathrm{keV}–100\mathrm{keV}$ energy range. Electron spectroscopy was performed at 35° with respect to the beam direction and absolute values for the double-differential cross section were obtained. Our results show preferential emission of low-energy electrons that are responsible for damage in biological material through dissociative electron attachment [Boudaïffa et al., Science 287, 1658 (2000)]. Experimental results are compared to calculations that used the classical trajectory Monte Carlo method, and a reasonable agreement is obtained.

The self-trapping phenomenon of Bose-Einstein condensates (BECs) in optical lattices is studied by numerically solving the Gross-Pitaevskii equation. Our numerical results reproduce the self-trapping that was observed in a recent experiment [Anker et al., Phys. Rev. Lett. 94, 020403 (2005)]. However, we do not find that the appearance of the steep edges on the boundaries of the wave packet is the critical signal of the self-trapping. More importantly, we discover that the self-trapping breaks down at long evolution times; that is, the self-trapping in optical lattices is only temporary and has a lifetime. This temporariness is caused by the tunneling of atoms at the edge of the BEC wave packet towards outside wells. Our analysis shows that the phenomena observed numerically can all be understood by regarding the optical lattice as a train of double-well potentials.

We study the correlation properties of the ground states of few ultracold bosons, trapped in double wells of varying barrier height in one dimension. Extending previous results on the signature of the transition from a Bose-condensed state via fragmentation to the hard-core limit, we provide a deeper understanding of that transition by relating it to the loss of coherence in the one-body density matrix and to the emerging long-range tail in the momentum spectrum. These are accounted for in detail by discussing the natural orbitals and their occupations. Our discussion is complemented by an analysis of the two-body correlation function.

Experimental demonstration of record optical quality factor of $(6.3\pm 0.8)\times {10}^{10}$ corresponding to cavity ring-down time of $\tau \simeq 36\mu \mathrm{s}$ is made possible by avoiding nonlinear effects in a crystalline whispering gallery mode resonator. We discuss various loss mechanisms in $\mathrm{Ca}{\mathrm{F}}_2$ cavities and ways of achieving higher quality factors. Possible applications in quantum optics and photonics are discussed.

We have experimentally studied the propagation behaviors of light pulses in an electromagnetically induced transparency (EIT) medium. Both phase variation in different parts of a pulse and distortion of the pulse shape are observed. The consistency between the experimental data and theoretical predictions is satisfactory. Our study explains the physical origins of the phase variation and the shape distortion, shows that the phase variation should be taken into consideration in applications utilizing the EIT scheme in which two-photon detuning must exist, and provides better understanding of the propagation behavior of the slow light.

We investigate resonances of spin-1 bosons in a three-dimensional magnetic quadrupole field. Complementary to the well-known positive energy resonances it is shown that there exist short-lived, i.e., broad, negative energy resonances. The latter are characterized by an atomic spin that is aligned antiparallel to the local magnetic field direction. In contrast to the positive energy resonances the lifetimes of the negative energy resonances decrease with increasing total magnetic quantum number. We derive a mapping of the two branches of the spectrum.

We describe a method to perform two-qubit measurements and logic operations on pairs of qubits which each interact with a harmonic oscillator degree of freedom (the bus), but do not directly interact with one another. Our scheme uses only weak interactions between the qubit and the bus, homodyne measurements, and single-qubit operations. In contrast to earlier schemes, the technique presented here is extremely robust to photon loss in the bus mode, and can function with high fidelity even when the rate of photon loss is comparable to the strength of the qubit-bus coupling.

The position-representation wave function for multiphoton states and its equation of motion are introduced. A major strength of the theory is that it describes the complete evolution (including polarization and entanglement) of multiphoton states propagating through inhomogeneous media. As a demonstration of the two-photon wave function’s use, we show how two photons in an orbital-angular-momentum entangled state decohere upon propagation through a turbulent atmosphere.

We investigated the hydrogen atom problem with deformed Heisenberg algebra leading to the existence of a minimal length. Using modified perturbation theory developed in our previous work [Stetsko and Tkachuk, Phys. Rev. A 74, 012101 (2006)] we calculated the corrections to the arbitrary $s$ levels for the hydrogen atom. We obtained a simple relation for the estimation of the minimal length. We also compared the estimation of minimal length obtained here with the results obtained in previous investigations.

We investigate the multiparticle quantum superposition and the persistence of bipartite entanglement of the output field generated by the quantum injected high-gain optical parametric amplification of a single photon. The physical configuration based on the optimal universal quantum cloning has been adopted to investigate how the entanglement and the quantum coherence of the system persists for large values of the nonlinear parametric gain $g$.

The $3d^{-1}$ photoionization and subsequent $M_{4,5}{N}_{2,3}{N}_{2,3}$ Auger electron spectra of free initially laser-excited rubidium atoms have been investigated. The rubidium atoms were excited from the ground state $\left[\mathrm{Kr}\right]5s_{1∕2}$ to the $\left[\mathrm{Kr}\right]5p_{1∕2}$ and $\left[\mathrm{Kr}\right]5p_{3∕2}$ states. Emphasis was put on the changes in coupling and electron correlation between the three different initial states. The ground state $3d$ photoelecton spectrum of free Rb atoms was interpreted in detail. The binding energies for $3d_{3∕2,5∕2}$ orbitals of initially ground-state and laser-excited Rb atoms were obtained. Extensive multiconfiguration Dirac-Fock calculations performed in the relativistic $jj$ coupled basis were compared to the experimental photoelectron and Auger electron spectra.

We present a theory of ionization of diatomic molecules by a strong laser field. A diatomic molecule is considered as a three-particle system, which consists of two heavy atomic (ionic) centers and an electron. After the separation of the center-of-mass coordinate, the dynamics of this system is reduced to the relative electronic and nuclear coordinates. The exact $S$-matrix element for ionization is presented in a form in which the laser-molecule interaction is emphasized. This form is useful for application of the molecular strong-field approximation (SFA). We introduced two forms of the molecular SFA, one with the field-free and the other with the field-dressed initial molecular bound state. We relate these two forms of our modified molecular SFA to the standard molecular SFAs, introduced previously using the length gauge and the velocity gauge. Numerical examples of the ionization rates of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ molecules are shown and compared for all four versions of the molecular SFA and we suggest that our modified molecular SFA should be used instead of the standard molecular SFA.

We develop an analytic theory for the harmonic generation of symmetric diatomic molecular ions beyond the two-level model, emphasizing the influence of the charge-resonance (CR) states that are strongly coupled to electromagnetic fields for the case of large internuclear distances. Taking into account the continuum states that are ignored in the two-level model and become important for the intense laser case, our model is capable of producing the spectrum for the whole range of harmonic orders that consists of a molecular plateau due to the CR transition and an atomiclike plateau for long-wavelength excitation. Our analytic results are in good agreement with the numerical results from directly solving the Schrödinger equation. Our theory also identifies the crucial role of the CR states in the fine structure of the harmonic spectrum and shows that harmonic generation in molecular systems can be effectively controlled by adjusting the internuclear distance.

We theoretically demonstrate that optical measurements of electron spin noise can be a spectroscopic probe of the entangled quantum states of ultracold fermionic atom gases and unambiguously reveal the detailed nature of the underlying interatomic correlations. Different models of the effective interatomic interactions predict entirely new sets of resonances in the spin noise spectrum. Once the correct effective interatomic interaction model is identified, the detailed noise line shapes of the spin noise can be used to constrain this model. We estimate the magnitude of spin noise signals expected in ultracold fermionic atom gases via noise measurements in classical alkali vapors, which demonstrate the feasibility of this approach.