Bring the water and sugar to the boil, stirring until the sugar has dissolved.
Squeeze the limes and add the juice along with the cachaca. Allow to cool and freeze in the ice cream or sorbet machine or a metal bowl in the freezer. Stir the contents of the bowl every 30 minutes and freeze for a good 2 hours.
Peel and quarter the pineapple, remove the stalk and cut into beautiful cubes.
Arrange the pineapple in the glass, pour ice over it and decorate with mint or pineapple leaves and physalis.