Quantum squeezing and correlation of slow-light self- induced transparency solitons

A quantum theory of self induced transparency (SIT) solitons is developed with the quantum effects of ensemble atoms taken into account. For the first time one is able to accurately calculate the detectable squeezing ratio for non-optimum homodyne local oscillators. Suggestions for experimental SIT soliton squeezing detection and intersoliton correlation generation are given. ©2007 Optical Society of America OCIS codes: (270.5530) Pulse propagation and solitons; (270.6570) Squeezed states Self induced transparency (SIT) in two-level atomic systems [1] is one of the most well known coherent pulse propagation phenomena that have been intensively investigated. For possible applications of quantum information processing, different ways of manipulating the quantum states of photons and atoms has attracted extensive research interest both in the fields of quantum optics and quantum information science. As a member of the optical soliton family, the SIT solitons have been suggested to be able to play an important role in pulsed squeezed state generation, quantum non-demolition measurements, and quantum information storage and retrieval. In view of these development trends, a usable quantum theory for SIT solitons is urgently needed in order to provide guidelines for experiments and to help predict new phenomena. A quantum theory of SIT solitons has been developed previously by one of the authors based on the linearization approach within the framework of inverse-scattering method [2], where only the quantum noises for the perturbed soliton parameters (photon number, phase, frequency, and position) were calculated accurately. In the present work a more usable quantum theory of SIT solitons is developed with the quantum effects of ensemble atoms taken into account. For the first time we are able to accurately calculate the detectable squeezing ratio when non-optimum homodyne local oscillator pulse-shapes are used. Since in typical squeezing experiments the output mean field pulse is used as the homodyne local oscillator, which is definitely non-optimum, the obtained theoretical results here should be helpful for future SIT soliton squeezing experiments. We will also investigate the possibility of generating quantum correlations between two SIT solitons through the mediation of the atomic medium. For SIT solitons in a two level medium without inhomogeneous broadening, we use the following normalized quantum Maxwell-Bloch equations as the starting point, where U , ˆ P̂ N̂ , are the normalized optical field, the dipole moment density, and the population inversion density operators respectively. The quantum equations as well as the correct commutation relations for the related quantum operators can be derived rigorously from the standard lightatom interaction Hamiltonian used in quantum optics, , ˆ 2 ) , ( ˆ ) , ( ˆ P z t U r z z t U t + ∂ − = ∂ ∂ ∂ (1) , ˆ ˆ 1 ) , ( ˆ U N z t P 2 t = ∂