A theory of deep laser cooling of atoms by counterpropagating circular polarized laser waves in multilevel interaction schemes is developed. Using a (3+5)-level atom as an example, we show that in multilevel interaction schemes two-photon processes are responsible for creating a narrow structure near zero velocity in the ground-state atomic coherence. This structure is in turn responsible for narrow velocity structures in atomic populations and optical coherences. A Fokker-Planck-type kinetic equation is derived for a model of a (3+5)-level interaction scheme. It is found that two-photon coherent processes considerably enhance the radiation force at low velocities and the friction produced by the force at a negative detuning, and considerably decrease the diffusion coefficient. Two-photon processes in multilevel interaction schemes are identified as the basic physical mechanism responsible for deep laser cooling of atoms. The temperature of laser-cooled atoms is derived for a model (3+5)-level atom, and found to be in good agreement with the experimentally observed temperature for laser-cooled cesium atoms.

We demonstrate control of high-harmonic generation (HHG) by a linearly polarized laser field using uniform static magnetic and electric fields parallel to the laser polarization. We show that the harmonic intensity can be considerably increased for particular values of the magnetic field. The maximum values of the harmonic intensity correspond to such values of magnetic induction for which an integer multiple of the classical cyclotron period of the electron’s motion perpendicular to the magnetic field is equal to the return time of the ionized electron wave packet to the nucleus under the influence of the laser field (and static electric field, if present). While a static magnetic field (for the strengths we are considering) only affects the cutoff position slightly, a static electric field can introduce additional plateaus and cutoffs. A properly chosen combination of the static electric and magnetic fields can increase both the harmonic intensity and the harmonic order. For the case of a magnetic field only, the present work expands upon a brief account recently given elsewhere [D. B. Milošević and A. F. Starace, Phys. Rev. Lett. $82,$ 2653 (1999)]. For both a static B field and for parallel static B and E fields, the present work provides further confirmation of the so called “three-step” model for interpreting quantum-mechanical predictions of HHG.

We analyze photoassociation theoretically by treating the dissociation continuum of a molecule as a quasicontinuum (QC) of discrete states. In this manner, free-bound transitions are reduced to a few-level problem. The correct continuum limit is deduced from an explicit analysis of the density of QC states. Besides giving the usual photoassociation rate, the QC model facilitates the analysis of the steady-state molecular yield. Moreover, complications such as velocity redistribution and line broadening due to atom-atom collisions may be treated basically in the same way as in connection with the customary two-level atom. Next we adapt the standard three-level quantum optics to describe free-bound-bound photoassociation for both continuous-wave and pulsed two-color excitation. For a quantum degenerate gas of atoms, a proper two-photon resonant scheme may transform atoms to ground state molecules with near-unit efficiency even in the presence of spontaneous losses from the intermediate state.

The dynamics of atom lasers with a continuous output coupler based on two-photon Raman transitions is investigated. With the help of the time-convolutionless projection operator technique the quantum master equations for pulsed- and continuous-wave (cw) atom lasers are derived. In the case of the pulsed atom laser the power of the time-convolutionless projection operator technique is demonstrated through comparison with the exact solution. It is shown that in an intermediate coupling regime where the Born-Markov approximation fails, the results of this algorithm agree with the exact solution. To study the dynamics of a continuous-wave atom laser a pump mechanism is included in the model. Whereas the pump mechanism is treated within the Born-Markov approximation, the output coupling leads to non-Markovian effects. The solution of the master equation resulting from the time-convolutionless projection operator technique exhibits strong oscillations in the occupation number of the Bose-Einstein condensate. These oscillations are traced back to a quantum interference which is due to the non-Markovian dynamics and which decays slowly in time as a result of the dispersion relation for massive particles.

We report on the realization of various nine-wave atom polarization interference experiments using pulsed magnetic fields. Diabatic transitions by rapid changes in the applied magnetic-field direction are used to coherently manipulate the spin coherences of cold cesium atoms. A large number of high-contrast sharply peaked fringes are obtained by state-selecting the outcoming cloud. Atom optical components similar to crystal wave plates are implemented. The spin dynamics is studied under various experimental procedures. When the applied field is homogeneous, the nondispersive character of the phase shift is evidenced. Fringe blurring related to inhomogeneous effects is discussed.

We study the nonequilibrium time evolution of the Bose-Einstein condensate of interacting bosons confined in a leaky box, when its number fluctuation is initially $\mathrm{}(t=0\mathrm{})\mathrm{}$ suppressed. We take account of quantum fluctuations of all modes, including $\mathbf{k}=0,$ of the bosons. As the wave function of the ground state that has a definite number N of interacting bosons, we use a variational form $|N,\mathbf{y}〉,$ which is obtained by operating a unitary operator $e^{iG\left(\mathbf{y}\right)}$ on the number state of free bosons. Using $e^{iG\left(\mathbf{y}\right)},$ we identify a “natural coordinate” $b_0$ of the interacting bosons, by which many physical properties can be simply described. The $|N,\mathbf{y}〉$ can be represented simply as a number state of $b_0;$ we thus call it the “number state of interacting bosons” (NSIB). To simulate real systems, for which if one fixes N at $t=0\mathrm{}$ N will fluctuate at later times because of a finite probability of exchanging bosons between the box and the environment, we evaluate the time evolution of the reduced density operator $\hat{\rho }\mathrm{}\left(t\right)\mathrm{}$ of the bosons in the box as a function of the leakage flux J. We concentrate on the most interesting and nontrivial time stage, i.e., the early time stage for which $\mathrm{Jt}\ll N,$ much earlier than the time when the system approaches the equilibrium state. It is shown that the time evolution can be described very simply as the evolution from a single NSIB at $t<\mathrm{}0,$ into a classical mixture, with a time-dependent distribution, of NSIBs of various values of N at $t>\mathrm{}0.\mathrm{}$ Using $b_0,$ we successfully define the cosine and sine operators for interacting many bosons, by which we can analyze the phase fluctuation in a fully quantum-mechanical manner. We define a new state $|\xi ,N,\mathbf{y}〉$ called the “number-phase-squeezed state of interacting bosons” (NPIB), which is characterized by a complex parameter $\xi .$ It is shown that $\hat{\rho }\mathrm{}\left(t\right)\mathrm{}$ for $t>\mathrm{}0\mathrm{}$ can be rewritten as the phase-randomized mixture (PRM) of NPIBs. Among many possible representations of $\hat{\rho }\mathrm{}\left(t\right),$ this representation is particularly convenient for analyzing the phase fluctuations and the order parameter. We study the order parameter according to a few typical definitions, as well as their time evolution. It is shown that the off-diagonal long-range order (ODLRO) does not distinguish the NSIB and NPIB. Hence, the order parameter $\Xi$ defined from ODLRO does not distinguish them, either. On the other hand, the other order parameter $\Psi ,$ defined as the expectation value of the boson operator $\hat{\psi }$, has different values among these states. In particular, for each element of the PRM of NPIBs, we show that $\Psi$ evolves from zero to a finite value very quickly. Namely, after the leakage of only two or three bosons, each element acquires a full, stable, and definite (nonfluctuating) value of $\Psi .$

We develop a theory of dissipative dynamics of a kink state in a finite-temperature Bose-condensed gas. We find that, due to the interaction with the thermal cloud, the kink state accelerates towards the velocity of sound and continuously transforms to the ground-state condensate. We calculate the lifetime of a kink state in a trapped gas and discuss possible experimental implications.

We predict the possibility of sharp, high-contrast resonances in the optical response of a broad class of systems, wherein interference effects are generated by coherent perturbation or interaction of dark states. The properties of these resonances can be manipulated to design a desired atomic response.

The interaction of two-level atoms with two modes of a resonator, formed by two weakly coupled cavities, is investigated. The first atom, passing through one of the two cavities, excites the two field modes. The second atom then, passing through the other cavity, tests the excitation. Since the photon generated by the first atom may be in the first or the second cavity, quantum interference phenomena are observed. Furthermore, the setup can be used to generate maximum entangled pairs of atoms.

We study the generation of high-order harmonics during the ionization process for atoms described by relativistic classical mechanics with a special focus on retardation and Doppler shifts. We will then extend the discussion to a regime for which the atom-laser interaction takes place in a static homogeneous magnetic field. We demonstrate theoretically the possibility to tune the strength of the magnetic field to relativistic resonances to enhance the frequency components in the scattered light harmonic signal.

We describe theoretically the enhanced generation and propagation of attosecond pulses in a gas medium irradiated by sub-10-fs laser pulses. Both classical and quantum calculations reveal a significant increase in the energy of the attosecond pulse as a result of quasiphase matching in a tapered structured hollow-core fiber. The increasing laser field into the fiber reduces the dependence of the harmonic spectrum on the dispersive phase of the laser pulse and ensures generation and propagation of a single attosecond pulse in a highly ionized transient plasma. For the attosecond pulse radiation this design acts as a phase-locked traveling-wave x-ray laser.

We theoretically investigate the generation of spatial patterns in intracavity second-harmonic generation. We consider a cavity with planar mirrors that is resonant at the fundamental frequency, but not at the second-harmonic frequency. A mean-field model is derived that describes the resonant fundamental field, and its coupling to a pair of nondegenerate parametric fields. The parametric fields are driven by the nonresonant second-harmonic field. Analysis indicates the existence of transverse instability of the pump field alone, as well as the possibility of simultaneous instability of the pump and the parametric fields. A range of spatial structures including periodic planforms as well as spatially localized states are found numerically. The simplicity of the singly resonant cavity makes it well suited for experimental studies. Estimates of experimental parameters necessary for observation of spatial structures are given.

A two-photon correlator has been constructed and successfully operated in measuring the true two-photon correlation of synchrotron radiation in the soft-x-ray region. The strong influence of the nonstationary features of the optical field, which is the so-called accidental correlation induced by the systematic bunched structure of the stored current in a storage ring, has been removed by a coherence time modulation technique. The explicit bunching effect of the measured two-photon correlation shows that synchrotron radiation is a chaotic rather than coherent radiation, indicating a chaotic nature of the stored current. This experimental method provides a way to measure the instantaneous emittance with the time scale of the coherence time ${\tau }_c,$ and to characterize the coherence property of incomplete free-electron lasers, such as self-amplified spontaneous emission.

We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as β, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for β are $0.01<\mathrm{}\beta <\mathrm{1.0.}\mathrm{}$ We find that for large enough β, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as β is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with β values in the range considered here. As β is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results.

When a fast free electron is subjected to a high intensity plane-wave laser field propagating in the same direction as that of its initial motion, none of the harmonics of order higher than $n=1\mathrm{}$ are scattered in the forward and backward directions if the field is circularly polarized. Moreover, backscattering of harmonics of odd integer order only occurs in the case of a linearly polarized laser field. However, in the presence of a uniform magnetic field oriented parallel to the common directions of laser propagation and initial electron motion, richer forward and backscattered spectra may arise. In this paper, the results of analytic and numerical investigations of these spectra will be presented. In particular, it will be shown that forward scattering at exactly two frequencies will occur in both cases of polarization, while the backscattered spectra will be shown to consist of many lines whose frequencies depend upon the laser-field intensity, the magnetic-field strength, and the initial electron speed. Analytic derivation of the relativistic backscattered spectra will be carried out fully in both cases of laser-field polarization.

We present theoretical and experimental results on the quantum noise performances of vertical-cavity-surface-emitting-lasers (VCSELs). Using a semiclassical laser noise approach, we demonstrate that the ratio $M=\overline{S}/\overline{P}$ of the powers in the two polarization modes of the laser is one of the essential parameters governing the VCSELs quantum noise behavior. The generation of amplitude squeezed states of light is only possible for two well-selected cases which are the ideal two-polarization-mode laser $\left(M\approx 1\right)$ and the ideal single-polarization-mode laser $\left(M\approx 0\right),$ respectively. Furthermore, we show that gain suppression, as well as other relevant semiconductor parameters, have also to be taken into account to model realistically the VCSEL’s quantum noise. These theoretical investigations are very well supported by our experimental results. We demonstrate experimentally that indeed there exists a direct link between the parameter M and the shot noise normalized amplitude noise. In a two-polarization-mode laser as, e.g., represented by a large diameter air-post VCSEL, squeezed states could not be generated because of insufficiently low values of M even though a strong anticorrelation between the two modes exists. With a single-polarization-mode laser, as realized with small diameter oxide confined VCSELs, we have been able to demonstrate the generation of single-mode squeezed light with a VCSEL. A squeezing level of 0.9 dB has been measured, which with the detection efficiency corrected, results in 1.3 dB at the VCSEL upper facet.

We study broadcasting of entanglement where we use universal quantum cloners (in general less optimal) to perform local cloning operations. We show that there is a lower bound on the fidelity of the universal quantum cloners that can be used for broadcasting. We prove that an entanglement is optimally broadcast only when optimal quantum cloners are used for local copying. We also show that broadcasting of entanglement into more than two entangled pairs is forbidden using only local operations.

Expansion of the internuclear Born-Oppenheimer potential for diatomic systems, in the form of a continued fraction, has been investigated. This function satisfies all criteria applicable to a real potential curve of molecules in a stable electronic state; it asymptotically approaches a finite value in the dissociation limit, exhibits a minimum energy at the equilibrium internuclear separation, and approaches a positive value greater than a dissociation energy as the separation decreases. The proposed expansion is applied in quantitative analysis of the infrared, microwave, and Raman spectra of BrCl, NaCl, and ${\mathrm{N}}_2.$ The observed transitions are reproduced within experimental errors by making use of fewer fitted parameters than in the approach that employs a power expansion of the potential-energy function.

Relativistic configuration-interaction results have been obtained for the ${(3d}_{3/2}{)}^3{3d}_{5/2}$ $J=\overrightarrow{3}J=2\mathrm{}$ transition in ${\mathrm{W}}^{52+}$ and ${\mathrm{Bi}}^{61+}.$ If prior work on ${\mathrm{Gd}}^{42+},$ ${\mathrm{Nd}}^{38+},$ ${\mathrm{Ba}}^{34+},$ and ${\mathrm{Xe}}^{32+}$ is a guide, the accuracy of our results should be in the 1–2 % range. Both these species have recently been under active experimental study. The transition itself is thought to provide a very useful plasma diagnostic tool because it lies in the optical region, and is remarkably constant with Z.

Order ${\alpha }^2$ contribution to the orthopositronium decay rate due to one-photon virtual annihilation is found to be ${\delta }_{\mathrm{ann}}{\Gamma }^{\mathrm{}\left(2\right)\mathrm{}}=(\alpha /\pi {)}^2[{\pi }^2\ln \alpha -0.8622\left(9\right)]{\Gamma }_{\mathrm{LO}}.$