The problem of generating discrete superpositions of coherent states in the process of light propagation through a nonlinear Kerr medium, which is modelled by the anharmonic oscillator, is discussed. It is shown that under an appropriate choice of the length (time) of the medium the superpositions with both even and odd numbers of coherent states can appear. Analytical formulae for such superpositions with a few components are given explicitly. General rules governing the process of generating discrete superpositions of coherent states are also given. The maximum number of well distinguished states that can be obtained for a given number of initial photons is estimated. The quasiprobability distribution Q(α, α * , t) representing the superposition states is illustrated graphically, showing regular structures when the component states are well separated.

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We discuss a system with two discrete levels embedded in one continuum, which, after Fano diagonalization, gives a double Fano profile with two zeros. The second zero, which is located between the two levels, does not disappear even when the asymmetry parameter q goes to infinity. The spectrum of photoelectrons from such a system is calculated for any strength of the exciting field.), Vol = (IVradll), V 0 2 = (0l'Vradl2), VO(M = (01radlw)-(3b) (3c) (3d) (3e) According to Fano, it is possible to diagonalize that part of the Hamiltonian expression (1) that includes configuration interaction, that is, FL = il + f 2 + ,, + VCou1T Introducing a new eigenbasis

The problem of squeezing and its graphical representations in the anharmonic oscillator model is considered. Explicit formulas for squeezing, principal squeezing, and the quasiprobability distribution (QPD) function are given and illustrated graphically. Approximate analytical formulas for the variances, extremal variances, and QPD are obtained for the case of small nonlinearities and large numbers of photons. The possibility of almost perfect squeezing in the model is demonstrated and its graphical representations in the form of variance lemniscates and QPD contours are plotted. For large numbers of photons the crescent shape of the QPD contours is hardly visible and quite regular ellipses are obtained.

First measurements of double-photon elastic scattering performed on liquids with centrosymmetric molecules yield good agreement with statistical molecular theory of nonlinear light scattering. Studies of this new scattering are shown to allow determination of the third-order molecular polarizability as well as its anisotropy, and to promise information on the structure of short-range molecular ordering and electric properties of molecules.Terhune, Maker, and Savage 1 performed the first observation of second-harmonic laser light scattering (SHLS) in liquids whose molecules lack a center of symmetry. This communication reports first measurements of double-photon elastic scattering (DPES or SHLS) by liquids consisting of molecules having a center of symmetry in their ground state. The possibility of destroying the molecular center of inversion, owing to time and space fluctuations of the molecular electric field F, led us to predict this new scattering. This is particularly predictable in the case of liquids with molecules having permanent electric quadrupole or hexadecapole moments capable of causing very strong fluctuating molecular fields in regions of shortest-range ordering in the liquid. 2 Such regions in general do not possess a center of symmetry and thus cause SHLS. This is uniquely cooperative scattering by neighboring molecules whose positions and orientations are correlated. 2 ' 3 Theoretical considerations. -Consider a laser light wave of frequency w L and propagation vector k L incident on such a liquid. The electric dipole moment M induced in the medium of volume V at frequency 2u> L is 2 ' 3is the tensor 6f third-order nonlinear polarizability induced in a molecule p at the frequency 2(x) L by the squared electric field of the light wave E UL in the presence of the molecular field ¥ ( -p) due to the AT-1 molecules surrounding molecule p with the radius vector f^.With the light beam plane polarized, propagating at velocity c along y and oscillating vertically, the intensity components of light elastically scattered at frequency 2w L with horizontal (along y) and vertical (along z) oscillations, respectively, can be written in the forms (observation along x) / y /^=#/^+i(2c^^ (2) /./"*=7^=£(2w L^^ (3 ) where I L is the incident intensity, and £=1 Q=lIn Eqs. (5) and (6) we have Ak = k 2 -2k x , where k 2 is the wave vector of the scattered second-harmonic wave and r />a = r a -"f /) is the vector connecting the centers of the two scattering molecules p and q.From Eqs.(2) and (3), we define the depolarization ratio of second-harmonic scattering byIt is obvious from the shape of the scattering factors (5) and (6) that only cooperative SHLS is present since, in the absence of molecular correlation, S 2(JJL and R 2U)L vanish. This is an important distinction with regard to SHLS by liquids consisting of molecules without centers of symmetry for which we have both a noncooperative part (isolated molecules) and a cooperative one. 2 ' 3 1295

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The equal-time intensity correlation function and variances of the in-phase and out-of-phase components of the electric field radiated by a system of two interacting atoms in the process of resonance fluorescence are calculated analytically for arbitrary values of the field strength, interatomic interaction, and detuning and are illustrated graphically. It is shown that not only photon antibunching but also squeezing can occur in two-atom resonance fluorescence. The influence of dipole-dipole interaction between the atoms on both nonclassical effects is discussed. It is shown that a considerable amount of photon antibunching and squeezing can be obtained for finite detuning of the laser frequency from atomic resonance, especially when the detuning and dipole-dipole interaction parameters cancel out mutually. The maximum value of squeezing for interacting atoms is shown to be less, however, than that for noninteracting atoms. Very strong dipole-dipole interaction reduces the squeezing effect to zero.