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We report on the observation of a strong optical dipole force which is exerted on atoms in a bichromatic standing light wave as a result of nonlinear wave-mixing processes. This force can substantially exceed the upper limit of the spontaneous light force and, in contrast to the dipole force in monochromatic standing-wave fields, acts with constant sign on a macroscopic spatial scale. PACS numbers: 32.80.Pj, 42.50.VkThe induced dipole force can strongly affect the motion of atoms in inhomogeneous light fields. 1,2 In standing-wave laser fields, which have been the subject of extensive studies, 3 " 6 a very strong dipole force can occur, greatly exceeding the principal upper limit of the spontaneous force. ] In a single monochromatic standing wave, however, the application of this possibly strong force to manipulate the motion of atoms is restricted by the fact that the force spatially oscillates on the optical wavelength scale: Here the dipole force cannot effectively act on a macroscopic spatial scale as it vanishes in a wavelength average.Recently, very interesting effects were considered in the works of Kazantsev and Krasnov, 7 Voitsekhovich et 0A, 8 and Javanainen: 9 Long-wavelength dipole forces are predicted to occur in bichromatic standing-wave fields as a result of a "rectification," being due to nonlinear wave-mixing processes. Different rectification schemes were investigated for two-level atoms 7,8 and a A-type three-level system. 9 A relatively weak rectified dipole force may have already been observed in an experiment; 10 here, however, it at least remains unclear which rectification scheme was realized.It is the aim of this Letter to present the first clear experimental demonstration of a strong rectified dipole force for the elementary case of two-level atoms in a bichromatic standing light wave (BSLW). Before discussing our experiment, let us explain the basic physics of the rectification effect in a simple comprehensible picture; a detailed theoretical description has already been given 7 but an illustrative explanation has not been provided up to now.We consider the dipole force exerted on two-level atoms in a bichromatic light field under the following condition, 7 allowing for a relatively easy theoretical description. We assume that one frequency component (co\) of the field is strongly detuned from resonance, so that the corresponding detuning A| greatly exceeds all other relevant parameters of all points of the field: |A,|»ai(r),a 0 (r),|Ao|,/;(1) here n 0 (r) and Cl\(r) denote the space-dependent optical Rabi frequencies of the two field components, AQ represents the detuning of the other field component (coo), and y is the natural transition linewidth (HWHM). We furthermore neglect all effects induced by the atomic motion, like, e.g., friction forces. 4,5 This approximation is justified as long as all Doppler shifts occurring in the bichromatic field remain small compared with the natural transition linewidth. We use a Fourier expansion of the optical Bloch equations to calculate the indu...

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A theory is developed to model the excitations in a dimerized, spin-1/2 system with a magnetically ordered ground state and where the dimer exchange constant is antiferromagnetic. This method starts by considering the energy levels of a single dimer in the effective, staggered magnetic field due to the mean-field ordering of the surrounding dimers. Pseudo-boson operators are introduced which create and annihilate these excitations, and the Hamiltonian of the magnetic system can be rewritten in terms of these operators and then diagonalized to yield one doubly degenerate transverse mode and a longitudinal singlet mode for each non-equivalent dimer in the magnetic unit cell. The dimer theory has been used to model the measured dispersion relations in the antiferromagnetically ordered phase of the alternating-chain compound CuWO 4 . It provides a good fit to the data and is as successful as spin-wave theory in accounting for the transverse excitations although with different values of the exchange constants. In addition the transition temperature and the size of the reduced moment at T = 0 K calculated in the dimer theory are closer to the experimental values of CuWO 4 than those calculated by spinwave theory. An important difference between these two models lies in their predictions of the longitudinal excitations: whereas in spin-wave theory these are regarded as two-magnon events resulting in a continuum of scattering, in the dimer theory one well defined mode is expected. An experimental measurement of the longitudinal excitations should distinguish between these models.B Lake et al ordered phase that is 54% of the value expected in a fully aligned Néel state [1] and its magnetic excitations form a two-spinon continuum rather than well defined spin-waves [2]. Field theory techniques have been used [3], and these account well for the excitation continuum. Another type of low-dimensional antiferromagnet is a dimerized, spin-1/2 system, such as CuGeO 3 in its spin-Peierls phase. In this phase CuGeO 3 consists of weakly coupled, alternating chains. At low temperature it does not order magnetically [4], but rather has a spin-singlet ground state.The low-lying magnetic excitations in CuGeO 3 form a well defined, triply degenerate mode which is characterized by an energy gap at the zone-centre [5]. This energy gap exists only in the spin-Peierls phase and rapidly tends to zero above the transition temperature [6] implying that it arises as a direct consequence of the dimerization. Recent measurements on CuGeO 3 also show evidence of a continuum [7], which lies above the mode and is separated from it by another energy gap. This feature has been predicted to exist in the uncoupled, alternating-chain system [8]. Spin-wave theory can reproduce the well defined excitations in CuGeO 3 but cannot account for the energy gap (without artificially introducing anisotropy), triplet degeneracy of the mode or the continuum. The inadequacy of spin-wave theory is exposed by its inability to explain the excitations of an isolated dimer...