In this article we present a simple and unified procedure to solve various nonlinear two-level Jaynes-Cummings models. By establishing their similarity to the model describing a spin- particle in a magnetic field, we obtain the standardized forms, appropriate uniformly for all Jaynes-Cummings models, of eigenvalues, eigenstates, evolution, and atomic inversion operators. In this way, we show that the analytical solution of any single-mode and two-mode nonlinear Jaynes-Cummings model can easily be obtained. We also apply this procedure to a three-mode Jaynes-Cummings model.

We have observed a strong anticorrelation between the photocurrent fluctuations of two laser outputs from symmetric low-Q cavity laser diodes (LDs) driven far above the threshold in a constant-current mode. The degree of correlation is highly dependent on the mirror reflectivities of the cavity:nn-66% for the conventional LD with cleaved facets, and -90% for the antireflection-coated LD with residual mirror reflectivities of 5%. In the case of a cleaved LD, the sum of the photocurrent fluctuations of both laser outputs exhibits 2.8 dB noise reduction below the shot-noise level. This is the first observation of subshot-noise photocurrent fluctuations symmetric cavity LDs.

We present a simple geometrical-optics model for the excess-noise factor of a hard-edged unstable-resonator laser. When we ad hoc incorporate the numerically calculated diffraction losses in this model we find similar behavior to results from the more complex mode-nonorthogonality theory. Under certain conditions the predictions of our model are in reasonable agreement with mode-nonorthogonality theory; phenomena such as the resonant behavior of the excess-noise factor with Fresnel number and the dependence of the excess-noise factor on the transverse resonator symmetry are recovered. However, in the general case there is no quantitative agreement between the two approaches. We confirm this with an experiment on an unstable-cavity He-Xe laser. Severe deviations occur for values of the round-trip magnification close to unity or much larger than unity and for higher-order modes. This illustrates the profound consequences of mode-nonorthogonality theory, which are apparently much more subtle than can be described by a model directly based on losses.

The excess noise factor due to the nonorthogonality of the transverse modes of a geometrically stable cavity subject to large diffraction losses is calculated. This calculation is based on an exact determination of the transverse field distribution of the cavity fundamental eigenmode. It is shown that when the modes become essentially determined by diffraction, the transverse modes are far from being orthogonal, leading to the appearance of a large excess noise factor that must multiply the standard Schawlow-Townes linewidth. Moreover, in the presence of two diffracting apertures, the excess noise factor is shown to exhibit a resonant behavior reminiscent of the one observed in unstable cavities. We estimate that, in the case of circular apertures, excess noise factors as large as 100 can be experimentally measured using a high-gain gas microlaser.

We analyze transient properties of light amplification in a coherently coupled three-level Λ-type system and study the system evolution from the transient regime into the steady state. From the time evolution of the atomic coherence and population distribution, we discuss the transient light amplification mechanism with and without population inversion. We also solve the density-matrix equations in the steady state and derive the conditions for the existence of specific light amplification mechanisms, such as light amplification without inversion in any standard state basis, light amplification by stimulated Raman scattering, and light amplification from population inversion in the dressed states.

The radiation generated in the soft-x-ray domain by spontaneous emission and amplified while propagating in a plasma column is investigated in the Maxwell-Bloch (MB) formalism. The MB theory is especially appropriate to describe the interaction between the medium and the lasing radiation in the saturation regime, and asymptotically yields the commonly used theory of the small-signal gain coefficient. We have examined the effect of spontaneously created magnetic fields on gain coefficients, integrated intensity, and steady-state population of quantum states. Our calculations are applied to the 0-1 and 2-1 radiations at 196 and 236 Å, respectively, in collisionally pumped Ne-like germanium lasers. For these radiations and in our range of plasma parameters the Voigt function—accounting for the Zeeman splitting of the various sublevels associated with a given multiplet—provides accurate line shapes.

Highly entangled states of more than one quantum system are necessary for tests of local hidden-variable theories and of quantum mechanics itself. We show how to produce field states, which are located in several cavities and are highly entangled, by sending apropriately prepared atoms through the cavities. We discuss both a two-cavity and a three-cavity state in which either each cavity is in a one-photon number state or each is in the vacuum state. Finally, a test of quantum mechanics using the two-cavity state is presented.

Various energy functionals in density-functional theory must possess the form of 〈${\mathrm{{\rm B}}}^{3+\mathrm{\mu }}$f(ζ,η,${\xi }_1$,${\xi }_2$,…,${\xi }_{\mathrm{n}}$)〉, if one assumes that they can be expressed as 〈g(λ,r,ρ(r),${\mathrm{\rho }}^{\mathrm{}\left(1\right)\mathrm{}}$,${\mathrm{\rho }}^{\mathrm{}\left(2\right)\mathrm{}}$,…,${\mathrm{\rho }}^{\mathrm{}\left(\mathrm{n}\right)\mathrm{}}$)〉. Here ρ(r) and ${\mathrm{\rho }}^{\mathrm{}\left(\mathrm{m}\right)\mathrm{}}$ are the electron density and its mth-order gradient; f and g are proper analytic functions of their variables; μ is 2 when the functionals are ${\mathrm{T}}_{\mathrm{s}}$[ρ], ${\mathrm{T}}_{\mathrm{c}}^{\lambda }$[ρ], and ${\mathrm{T}}^{\lambda }$[ρ] (otherwise it equals 1); λ is the electron-electron interaction coupling constant in the adiabatic connection formulation; and {Β,ζ,η,${\xi }_1$,${\xi }_2$,…,${\xi }_{\mathrm{n}}$} is a set of independent variables (called natural variables) in place of {λ,r,ρ,${\mathrm{\rho }}^{\mathrm{}\left(1\right)\mathrm{}}$,${\mathrm{\rho }}^{\mathrm{}\left(2\right)\mathrm{}}$,…,${\mathrm{\rho }}^{\mathrm{}\left(\mathrm{n}\right)\mathrm{}}$}. These variables are defined as {Β(r)=${\mathrm{\rho }}^{1\mathrm{/}3}$(r), ζ=Β/λ, η=rΒ, ${\xi }_{\mathrm{m}}$=${\mathrm{\rho }}^{\mathrm{}\left(\mathrm{m}\right)\mathrm{}}$/${\mathrm{{\rm B}}}^{3+\mathrm{m}}$|m=1,2,…,n}. Generalizations to more complex functional forms are also discussed. Some exact relationships are derived that should be useful for developing density functionals of the weighted-density approximation type.

In this paper we show how the fault-tolerant quantum error-correction scheme recently proposed by DiVincenzo and Shor [Phys. Rev. Lett. 77, 3260 (1996)] can be made more efficient. Our scheme, unlike the earlier one, can deal with a single error between the quantum gate operations that are required for the implementation of the quantum error correction without repeated generation of error syndromes. For errors during gate operations we have to produce fewer error syndromes as we generate them conditionally on the previous one. We show how to generalize the method to arbitrary error-correcting codes.

We report an investigation of the ${\mathrm{b}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$(v=0)←${\mathrm{X}}^3$${\mathrm{\Sigma }}_{\mathrm{g}}^{\mathrm{-}}$(v=0) band of ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}_2^{}{}_{}{}^{}$. The weak magnetic-dipole transitions around 761 nm were observed using a high-sensitivity absorption spectroscopy apparatus based on a DFB diode laser source and a multipass absorption cell. We accurately measured the wavelength of several lines and deduced the rotational constants for the ${\mathrm{b}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$(v=0) electronic state. We also studied the line broadening in the presence of different isotopic species and determined the pressure broadening coefficients. We discuss the interest of these data in view of a possible test of the symmetrization postulate for ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ nuclei.

Although the density-gradient expansion for the noninteracting fermion kinetic energy is known through sixth order, numerical tests and applications of it have so far only been made through fourth order because its sixth-order term (${\mathrm{T}}_6$) diverges in the exponentially decaying tail of the electron density for a finite system. We show that ${\mathrm{T}}_6$ provides a useful correction to the density functional ${\mathrm{T}}_0$+${\mathrm{T}}_2$+${\mathrm{T}}_4$ for a problem in which the density n(r) is everywhere bounded from below: the formation energy of a monovacancy in jellium. Thus the sixth-order expansion may be useful in condensed-matter physics or perhaps more generally via convergent resummation. We also suggest that the most important terms of the series may be those involving |∇n${\mathrm{|}}^2$ and ${\mathrm{\nabla }}^2$n, but no other derivative.

We present the general quantum-mechanical formula for the photodetachment cross section of ${\mathrm{H}}^{\mathrm{-}}$ in the electric and magnetic fields with any orientation and the comparison of the quantum-mechanical cross sections to the cross sections calculated from the closed-orbit theory.

The response of a hydrogen atom to a perturbative electric field is presented from a classical viewpoint. We find classical energy shifts in the hydrogen atom in situations that correspond to both the linear and quadratic Stark effects. We then compare these energy shifts to the exact quantum-mechanical values for the Stark effect. We find that the linear Stark effect can be accurately reproduced classically (given the correct initial conditions). In contrast, quantum-mechanical results for the quadratic Stark effect cannot be accurately reproduced classically, except in the correspondence principle limit of large principal quantum numbers n.

Electron capture from ${\mathrm{H}}_2^{+}$ by fast positron impact is studied theoretically by using a model of two molecular scattering centers. Differential cross sections are obtained within the first Born approximation. The influence of the orientation angle of the molecular axis on the reaction is analyzed. Analogy with Young's interference experiment is established. Comparison with proton impact is made.

A calculational procedure is formulated for extracting differential cross sections in the ejected energy from a time-dependent wave-packet method for the electron ionization of hydrogen. The procedure is applied to an s-wave model for electron-hydrogen scattering. In contrast to recent time-independent methods, the differential cross sections are found to be smooth and symmetric.

We present a rate equation model to account for the trapping mechanism in the sodium type-II magneto-optical trap (MOT). A key feature of the model is that excitation from the ground F=1 state to both excited states ${\mathrm{F}}^{|\mathrm{I}\mathrm{H}}$=1 and ${\mathrm{F}}^{|\mathrm{I}\mathrm{H}}$=0—possible in sodium because of the small excited state separation—is confirmed to be crucial in avoiding the optical pumping that otherwise inhibits steady-state trapping. Furthermore, we calculate that the mixed polarization typically present in a three-dimensional trapping arrangement gives substantially better one-dimensional trapping performance than pure circular polarization, and that the active role of repumping in the trapping process is important. The model is also applied to the type-I (F=2 to ${\mathrm{F}}^{|\mathrm{I}\mathrm{H}}$=3) MOT and comparisons are made with experiment in both cases. The possibility of blue-detuned Sisyphus cooling in the F=1 to ${\mathrm{F}}^{|\mathrm{I}\mathrm{H}}$=1 and 0 transition scheme is considered.

We consider above-threshold ionization of inert gases within the framework of the Keldysh-Faisal-Reiss model. However, we represent the state of the ionized electron by a more precise Coulomb-Volkov wave function. Thus we find sidelobes in the angular distribution of the emitted electrons at about the right high nonlinear orders and in the correct angular range as found experimentally for inert gases.

We reconsider the state reconstruction of a completely unpolarized light beam from measured homodyne data. We show that the measurement of the quadrature distribution of any linearly polarized component of the light field is sufficient to determine the quantum state of completely unpolarized light. As a result we reveal the close connection to the reconstruction algorithm in the single-mode case.

In a previous paper [Phys. Rev. A 54, R1789 (1996)], we reported the observation of a laserlike transition in a single GaAs quantum well microcavity and gave the interpretation as spontaneous buildup of coherent exciton-polariton population via stimulated polariton-phonon emission. In this Brief Report, we present new experimental data and correct our previous interpretation for the microcavity polariton system at high density. We observe a continuous transition from a microcavity polariton emission to a bare photon laser. This conclusion is based on the measurements of the angular resolved photoluminescence, linewidth, and intensity of the lasing line as well as the reflection spectrum under cw pumping.

An approach to the decay of a two-state quantum system coupled to a resonant environment is developed in terms of exact (nonperturbative) master equations. Starting from a quantum optical model of a two-level system coupled to a heatbath, it is shown that the effect of the bath can be replaced by one or more pseudomodes. This description is valid for a wide class of analytic density-of-state functions and it leads to exact master equations which fully describe the non-Markovian decay of the quantum system without the use of perturbation theory, the Born approximation, or the Markov approximation. Two examples are given: a simple model of a density-of-states gap which has two poles, and a non-Lorentzian resonance.