We present single-dish and interferometric millimeter line observations of the HH 111 outflow and its driving source . The physical conditions of the protostellar core have been determined from the emission of the millimeter line emission of CO and its isotopomers and CS with the IRAM 30m telescope , and the CO J = 7 \rightarrow 6 line with the Caltech Submm Observatory . The molecular gas emission reveals a small condensation of cold ( T = 20 - 25 \hbox { \kern 2.0 ptK } ) and dense gas ( n ( \hbox { H$ { } _ { 2 } $ } ) = 3 \times 10 ^ { 5 } \hbox { \kern 2.0 ptcm$ { } ^ { -3 } $ } ) . The low-velocity outflowing gas has been mapped with the IRAM Plateau de Bure interferometer . The cold gas is distributed in a hollow cylinder surrounding the optical jet . The formation of this cavity and its kinematics are well accounted for in the frame of outflow gas entrainment by jet bow shocks . Evidence of gas acceleration is found along the cavity walls , correlated with the presence of optical bow shocks . The cavity has been expanding with a mean velocity of 4 \hbox { \kern 2.0 ptkm \kern 2.0 pts$ { } ^ { -1 } $ } on a timescale of 8700 \hbox { \kern 2.0 ptyr } , similar to the dynamical age of the optical jet . The separation of the inner walls reaches 8 \arcsec - 10 \arcsec , which matches the transverse size of the wings in the bow shock . CSO observations of the J = 7 \rightarrow 6 line show evidence of a high-velocity and hot gas component ( T = 300 - 1000 \hbox { \kern 2.0 ptK } ) with a low filling factor . This emission probably arises from shocked molecular gas in the jet . Observations of the ^ { 3 } P _ { 2 } - ^ { 3 } P _ { 1 } [ CI ] line are consistent with C-type non-dissociative shocks . Mapping of the high-velocity molecular bullets B1-B3 , located beyond the optical jet , with the IRAM PdBI reveals small structures of 3 \arcsec \times 7 \arcsec flattened perpendicular to the flow direction . They are made of cold ( T \sim 30 \hbox { \kern 2.0 ptK } ) , moderate density gas ( n ( \hbox { H$ { } _ { 2 } $ } ) = ( 0.5 - 1.0 ) \times 10 ^ { 4 } \hbox { \kern 2.0 ptcm$ { } ^ { -3 } $ } ) . We find evidence that the bullets are expanding into the low-density surrounding medium . Their properties are consistent with their being shocked gas knots resulting from past time-variable ejections in the jet .