Generation of atomic dipole squeezing in the thermal two-photon Jaynes-Cummings model

Historically the Heisenberg lower limit is used as the reference level for the definition of squeezing in observables. However, in the measurement of observables corresponding to noncanonical operators, it may not work [Puri, Phys. Rev. A49, 2178 (1994)]. Then, one should employ the Schrodinger uncertainty relation for further studies, where the Schrodinger lower limit sets a higher bound on quantum fluctuations than the Heisenberg one does. In this paper, using Heisenberg's and Schrodinger's uncertainty relations, we have made a comparative study on the squeezing properties of quantum fluctuations in atomic dipole variables in the thermal two-photon Jaynes-Cummings model, including the discussion of the difference between both cases, the influence of initial atomic coherence or thermal photons on the atomic dipole squeezing, and the possibility of realization of atomic dipole squeezing in two-photon micromaser experiments with Rydberg atoms in a high-Q cavity.