A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.
A theory of resonant Raman scattering spectroscopy of one-dimensional electronic systems is developed on the assumptions that (i) the excitations of the one-dimensional electronic system are described by the Luttinger-liquid model, (ii) Raman processes involve virtual excitations from a filled valence band to an empty state of the one-dimensional electronic system, and (iii) excitonic interactions between the valence and conduction bands may be neglected. Closed form analytic expressions are obtained for the Raman scattering cross sections, and are evaluated analytically and numerically for scattering in the polarized channel, revealing a ``double-peak'' structure with the lower peak involving multispinon excitations with total spin
S=0 and the higher peak being the conventional plasmon. A key feature of our results is a nontrivial power-law dependence, involving the Luttinger-liquid exponents, of the dependence of the Raman cross sections on the difference of the laser frequency from resonance. We find that near resonance the calculated ratio of intensity in the lower energy feature to the intensity in the higher energy feature saturates at a value of the order of unity (times a factor of the ratio of the velocities of the two modes). We explicate the differences between the ``Luttinger-liquid'' and ``Fermi-liquid'' calculations of resonant Raman spectroscopy (RRS) spectra and argue that excitonic effects, neglected in all treatments so far, are essential for explaining the intensity ratios observed in quantum wires. We also discuss other Luttinger-liquid features which may be observed in future RRS experiments.