We investigate an atomic three-level Λ system which is exposed to two counterpropagating laser fields (inducing Raman transitions) and which is closed by a magnetic hyperfine field tuned to be in resonance with the transition between the two ground states. The influence of a homogeneous gravitational field is included in a full quantum treatment of the internal and external dynamics of the atom. It is shown that the combined influence of the gravitational field and the lasers lead for specific momentum values with a very high probability to a transition of the Landau-Zener type. This is accompanied by a momentum transfer resulting in an upward kick. For appropriate initial conditions a sequence of up and down motions is obtained. No mirror is needed. A gravito-optical trapping of atoms based on this effect seems to be realizable. © 1996 The American Physical Society.

Using a multidimensional Gaussian approximation of the wave function for the signal and idler light generated by spontaneous parametric down-conversion, we derive analytical expressions for the second-order coherence function and the fourth-order coherence function (which is proportional to the signal-idler photon coincidence rate). The magnitudes of these functions are expressed as products of Gaussian functions of the azimuthal angles, the polar angles, and the time delay. Their widths determine six parameters: the coherence angles and coherence time, and the entanglement angles and entanglement time. We show how these parameters are governed by the pump-beam waist, the pump spectral width, and the crystal length. We thereby derive relations analogous to the van Cittert–Zernike theorem and the Siegert relation for thermal light. We show that the normalized photon coincidence rate decreases sharply as the signal and idler apertures become mismatched or misaligned. We experimentally confirm this latter prediction by using parametrically down-converted light obtained from a ${\mathrm{LiIO}}_3$ crystal pumped by ${\mathrm{Kr}}^{+}$-ion laser radiation at 413 nm. ©1996 The American Physical Society.

The single-mode rate equations for a semiconductor laser subject to optical injection are investigated analytically. We determine the first branch of periodic solutions for low values of the injection field. For larger values of the injection field, we derive a third-order pendulum equation for the phase difference of the laser field of the form ψ‴+ψ′=Λ cos(ψ), where Λ groups all the key laser parameters. This equation captures several aspects of the numerical bifurcation diagram, namely, the fixed amplitude of the period-one solution and the period-doubling bifurcation. Finally, we compute the optical power spectrum utilizing the perturbation solutions of the phase equation before and after the period-doubling transition. We also obtain very good agreement with the numerically computed spectrum. ©1996 The American Physical Society.

We show that light force lenses can be used to focus a thermal beam of neutral atoms with extremely high resolution (∼20 nm) and high contrast (∼10:1), finally making such atom-optical lenses viable for proposed applications. Our (cylindrical) lenses for sodium atoms are created by the dipole force within each period of a standing wave. We determine the spatial distribution of the focused atoms (with nanometer resolution) by allowing the atoms to deposit on a substrate and scanning with a UHV scanning tunneling microscope. We find that the requirements for optimum focusing are very large, positive detuning; short focal lengths; and a well-collimated atomic beam. These dependences can be thoroughly understood from a simple theoretical model. ©1996 The American Physical Society.

We reconsider a variant of the one-atom-maser setup in which the emerging atoms are probed for coherent superpositions of the two Rydberg states of the maser transition. The statistical properties of the corresponding detector clicks contain information about the temporal evolution of the phase of the quantized electromagnetic field inside the resonator. We derive analytical expressions for certain statistical quantities, such as the mean number of successive clicks of the same kind, or the atom-atom and the photon-photon correlation functions. The latter are closely related if the photon-number distribution in steady state is dominated by a single narrow peak. © 1996 The American Physical Society.

In this paper we study propagation of electromagnetic waves in media with an imaginary Kerr-type nonlinearity. We show numerically that the slowly varying envelope approximation can still be used. It is proved that theoretical problems described by this type of differential equations are Hamiltonian systems. This characteristic is used to predict the variation of the electromagnetic field in the nonlinear material. Furthermore, we find a closed expression for the electromagnetic waves in a nonlinear medium with a linear absorption and an imaginary Kerr-type nonlinearity, for both a localized and a diffusive nonlinearity. Calculating the transmission probability of light through a Fabry-Pérot structure shows that the introduction of an imaginary Kerr-type nonlinearity describes an intensity-dependent optical gain or absorption in a nonlinear medium. This system also shows bistable behavior comparable to real Kerr-type nonlinear materials. © 1996 The American Physical Society.

The stability of a two-level laser system with flat end mirrors, operating in a single longitudinal mode, is considered in the case of inhomogeneous pumping. The pumping is assumed to be of a Gaussian type of one transverse variable and spatially slowly varying. This situation is commonly encountered, for instance, in broad-area semiconductor lasers or slab ${\mathrm{CO}}_2$ lasers. We study the transverse structure formation induced by the slow variation of the inhomogeneous pumping near the primary instability. In a linear instability analysis, we show that the absolutely unstable state always sets in through a transversal perturbation near the onset of lasing. The spatiotemporal stability analysis separates local and global instabilities since the latter may have a drastic influence on the subsequent behavior. We determine the threshold and frequency for global transverse unstable modes. These modes are nothing but Hermite modes, which appear as a consequence of the spatial inhomogeneity. These predictions are consistent with the recent near-single-mode operations obtained for slab ${\mathrm{CO}}_2$ lasers. In the weakly nonlinear study, the amplitude equation is derived and appears as a modified Ginzburg-Landau equation with spatially varying coefficients. Numerical investigations are reported to illustrate a possible sequence of convective and absolute instabilities together with global Hopf bifurcations of transverse nonlinear modes. © 1996 The American Physical Society.

We study cooperative properties of the emission spectrum of A two-level atoms interacting with a quantized field in a lossless cavity. We show, in a unified treatment, the system anharmonicity, the fine structure, and size of the spectral bands. Further, we show that for an initially inverted atomic system and a thermal cavity field the atomic cooperativity allows the merging of well-defined sidebands, absent in the single-atom case. Thus the cooperativity reduces the destructive effect of the large dispersion of the blackbody photon distribution. For an increasing number of atoms, the central band is split into a doublet. The dip in the doublet is filled when the cavity field is very strong. Also, the extra sidebands have smaller amplitudes than the time-dependent contributions to the spectrum. © 1996 The American Physical Society.

Lang and Kobayashi equations for a semiconductor laser subject to optical feedback are investigated by using asymptotic methods. Our analysis is based on the values of two key parameters, namely, the small ratio of the photon and carrier lifetimes and the relatively large value of the linewidth enhancement factor. For low feedback levels, we derive a third-order delay-differential equation for the phase of the laser field. We then show analytically and numerically that this equation admits coexisting branches of stable periodic solutions that appear at different and almost constant amplitudes. These amplitudes are proportional to the roots of the Bessel function ${\mathit{J}}_1$(x). The bifurcation diagram of the phase equation is in good agreement with the numerical bifurcation diagram of the original Lang and Kobayashi equations. We interpret the onset of the periodic solutions as the emergence of a new set of external cavity modes with a more complicated time dependence. © 1996 The American Physical Society.

Pattern formation resulting from transverse mode competition has been observed in ${\mathrm{CO}}_2$ lasers with a large transverse section and a stable near-degenerate optical cavity. The pattern properties ruled by transverse hole burning are analyzed experimentally as a function of the Fresnel number, the frequency intermode spacing, and the symmetry breaking induced by the astigmatic cavity. It is shown that mode competition imposes selection rules amid modes belonging to the largest transverse mode family allowed to oscillate. © 1996 The American Physical Society.

The behavior of a three level atom in a cascade configuration with the lower transition coherently driven and also coupled to a narrow bandwidth squeezed vacuum field is studied. A master equation treatment based on dressed atom states is used and expressions for probe absorption spectra are obtained via linear response theory and the quantum regression theorem. The expressions obtained also apply to the broad bandwidth squeezed vacuum case. Numerical studies of the modifications caused by the finite squeezed vacuum bandwidth to the Mollow and Autler-Townes probe absorption spectra are made for the case where the squeezed vacuum field center frequency and the driving laser frequency coincide and where upper transition relaxation terms are ignored. The squeezed vacuum source is assumed to be a degenerate parametric amplifier for the numerical calculations. Cases where the driving laser is resonant and detuned are examined. The spectral features are sensitively dependent on the phase of the squeezed vacuum field for a given driving laser phase. Dispersive features in the Mollow probe absorption spectrum can become absorptive, and vice versa. It is found in the probe absorption spectra that for certain choices of the squeezed vacuum phase lines narrower than for the broadband squeezed vacuum are obtained in the finite bandwidth situation. In both the Mollow and Autler-Townes spectra features narrower than for the normal vacuum case are obtained when the laser field is detuned, and in the Autler-Townes case this occurs for resonance also. © 1996 The American Physical Society.

We consider the spontaneous emission (SE) of radiation by an atom in a one-dimensional cavity which consists of two medium regions and a vacuum region between them. The medium regions are composed of a bulk dielectric material which has a continuous absorption spectrum. We quantize the electromagnetic field as well as the polarization fields of the material, and polaritons composed of infinite number of fields are obtained. Using the polariton solutions, we then study the SE for an atom in such an absorptive and inhomogeneous cavity. The SE rate is shown to depend strongly on the position of the atom, the length l of the vacuum region, and the complex refractive index η+iκ. It is found in particular that the position dependence of the SE rate disappears for some particular values of l, in either of the vacuum or medium region. We also find that unlike the three-dimensional case the SE rate in a homogeneous cavity depends on both η and κ. © 1996 The American Physical Society.

The influence of the normal group-velocity dispersion on anisotropic self-focusing beams in nonlinear Kerr media is studied analytically. It is shown that a light pulse self-focusing in the presence of normal dispersion is split up into several small-scale cells preventing a catastrophic collapse. The theoretical explanation of this splitting process is revealed. © 1996 The American Physical Society.

The quantum harmonic oscillator in a nonuniformly rotating frame is studied. It is shown that squeezed states and particles are generated by inertial effects. The analytic forms of the squeezing and Bogoliubov coefficients are given explicitly in terms of the solutions of the classical equations of motion. The squeezed states have the minumum dispersion allowed by the Robertson uncertainty relations for an arbitrary number of observables (the explicit form of these relations is obtained). The problem of an ‘‘abrupt twist’’ is worked out in detail as an example. The formalism can also be applied to the problem of a charged particle in a Penning trap, where it is shown that squeezed states are produced, with a squeezing frequency of the order of the magnetron frequency. In both examples, analytic expressions for the variances of the position and momentum are obtained. © 1996 The American Physical Society.

A complex order-parameter description of pattern formation in large aspect ratio optical parametric oscillators (OPOs) with flat end reflectors and uniform pumping is presented starting from the mean-field model of the OPO equations [G.-L. Oppo et al., Phys. Rev. A 49, 2028 (1994)]. It is shown that, in the nondegenerate case, the full OPO equations have an exact continuum family of traveling-wave (TW) solutions, which are preferred to standing-wave (SW) states found in the degenerate case. These solutions correspond to an off-axis emission for both signal and idler fields along two symmetric directions to satisfy momentum conservation in the parametric conversion process. Stability of TW versus SW solutions is investigated by deriving two coupled Newell-Whitehead-Segel equations describing the growth of SW or TW close to threshold. Analytical expressions for long-wavelength phase instabilities of the TW states above threshold are obtained from the coefficients of a Cross-Newell phase equation, and are shown to be the same for OPOs with high or low finesse for the pump field. By direct linear stability analysis of the TW solutions, it is also shown that the appearance of amplitude instabilities may reduce the region of stable TW states in the case of OPOs with a high finesse for the pump field. © 1996 The American Physical Society.

We have studied the effects of the fine structure of energy levels on the dynamics of the atom and light field. A significant influence is exhibited in the collapse-revival behavior of atomic inversion, the light squeezing, the phase of the field, and the antibunching of a light beam. When the energy difference between the doublet is large (Δ≥20g, where g is the coupling constant), the dynamics of the atomic inversion becomes identical to that of the usual Jaynes-Cummings model, as expected. However, the fine-structure effects on the phase and the antibunching of the light field exist in a much larger range. In particular, for a strong field, the normally ordered variance of the photon-number operator exhibits complicated collapse and revival patterns and the light displays strong antibunching in each revival envelope. Numerical calculations also show that this model does not produce significant squeezing due to the influence of the fine structure. © 1996 The American Physical Society.

We present multimode model calculations of doubly resonant infrared-visible sum-frequency generation from adsorbed molecules with general harmonic potential surfaces that are valid for finite temperatures. Numerical simulations of spectra recorded versus the frequency of the infrared or the visible sources have been performed on a simple two-mode model with equilibrium position displacements, frequency shifts, and Duschinsky rotation upon electronic excitation. It is argued that quadratic vibronic couplings need to be included if the excited state potential well is to be reliably probed by these techniques. © 1996 The American Physical Society.

We investigate the dynamics of four-wave mixing processes in photorefractive crystals in paraxial approximation, assuming the phase-conjugation condition. By applying an external electric field to the crystal, we observe an onset of instabilities in the phase-conjugate beam, the generation of running transverse waves, their mutual collisions, and a continuous transition to a regime of spatiotemporal chaos. This state appears as irregularly oscillating defectlike patterns in one transverse dimension. Running transverse waves are identified as the basic modes of the system giving rise to a secondary instability. The observed regular and irregular spatiotemporal oscillations are characterized by means of a spatiotemporal cross-correlation function and singular value decomposition. In the extension to two transverse dimensions the possibility of an even greater variety of regular and irregular patterns is observed. © 1996 The American Physical Society.

We propose the reconstruction of the quantum state of light from the homodyne photocounting statistics of a single, realistic photodetector. Contrary to the development of homodyning over the last decade, our approach is based on unbalanced detection with a weak local oscillator. Representing the quantum state in terms of s-parametrized quasiprobability distributions, the method even allows one to determine the Wigner function provided the quantum efficiency of the detector is sufficiently large. We show that perturbing effects due to classical noise of the local oscillator are small. © 1996 The American Physical Society.

We introduce a general strategy for preparation of arbitrary quantum states via optimal control of repeated conditional measurements. The effectiveness of this strategy in generating finite Fock-state superpositions with a high level of confidence from experimentally accessible coherent states is demonstrated for the simple and well known Jaynes-Cummings model dynamics. © 1996 The American Physical Society.