Make the rosemary syrup first: combine the sugar, water, and 2 rosemary sprigs in a small saucepan and simmer over medium heat for 3 minutes, stirring, until the sugar fully dissolves.

Remove the syrup from the heat, let it cool to room temperature, then strain out the rosemary; the syrup keeps in the refrigerator for up to 2 weeks.

Fill a wine glass with ice.

Add the pomegranate juice, lime juice, and 1/2 ounce of the cooled rosemary syrup.

Stir for 5 seconds to combine.

Top slowly with the chilled sparkling water, pouring it down the inside of the glass so the bubbles survive the trip.

Garnish with the remaining rosemary sprig and a spoonful of pomegranate arils.