We show that the stationary state of single-qubit laser is a phase-averaged nonlinear coherent state, provide superconvergent iterations method for its finding and investigate characteristic quantum properties of the state.
The stationary state of a single-atom (single-qubit) laser is shown to be a phase-averaged nonlinear coherent state---an eigenstate of a specific deformed annihilation operator. The solution found for the stationary state is unique and valid for all regimes of the single-qubit laser operation. We have found the parametrization of the deformed annihilation operator which provides superconvergence in finding the stationary state by iteration. It is also shown that, contrary to the case of the usual laser with constant Einstein coefficients describing transition probabilities, for the single-atom laser the interaction-induced transition probabilities effectively depend on the field intensity.
We investigate an incoherently pumped single-qubit laser as a system, providing optical nonlinearity for the generation of nonclassical states. We show that, in the general case of arbitrary values of coupling strength and other system parameters, the stationary state of an incoherently pumped single-qubit laser is a nonlinear coherent state, being the phase-averaged eigenstate of the deformed annihilation operator of a specific form. The manifestation of the inherent nonlinearity of the system is found in the form of the stationary state nonclassicality, present for any values of the system parameters. Another important implication of inherent system nonlinearity and nonclassicality is the impossibility of describing the lasing effect by means of field-independent spontaneous and induced transition probabilities, as in the case of a conventional laser.
We consider a class of nonlinear coherent states, which are right-hand eigenstates of the product of the boson annihilation operator and a nonlinear function of the number operator. Such states may appear as stationary states of the center-of-mass motion of a trapped and bichromatically laser-driven ion far from the Lamb-Dicke regime. Besides coherence properties, they exhibit nonclassical features such as amplitude squeezing and self-splitting, which is accompanied by pronounced quantum interference effects. \textcopyright{} 1996 The American Physical Society.
We present a quantum control scheme in which two different feedback methods are combined to produce a stable single mode atom laser. A difficulty of producing an atom laser comes from the nonlinear effect of Bose-Einstein Condensates which is described by Gross-Pitaevskii type of equations. One feedback method is used to eliminate the nonlinear effect of atom-atom interactions. Another difficulty comes from nonlinear interactions with an optical field which is introduced to detect the BEC state for feedback. The other feedback method is used to suppress fluctuations due to this interaction and keep the coherent properties of the atom laser.