  We consider an atom-field coupled system, in which two pairs of four-level
atoms are respectively driven by laser fields and trapped in two distant
cavities that are connected by an optical fiber. First, we show that an
effective squeezing reservoir can be engineered under appropriate conditions.
Then, we show that a two-qubit geometric CPHASE gate between the atoms in the
two cavities can be implemented through adiabatically manipulating the
engineered reservoir along a closed loop. This scheme that combines engineering
environment with decoherence-free space and geometric phase quantum computation
together has the remarkable feature: a CPHASE gate with arbitrary phase shift
is implemented by simply changing the strength and relative phase of the
driving fields.
