The traditional low- tech tool here is a broomstick, tapped once as a gentle reminder, _after_ having a polite conversation with your neighbor .
But you've had the police there already; so we can assume that relations with your neighbor may be less than amicable as a result, and answering a noise definitely will produce more noise as a response, and pretty soon you'll have a war on your hands. Okay, on your head.
If the noise is caused by footfalls on a hard floor, offer to help your neighbor pay for carpeting.
If the noise is from the floor squeaking, you could ask the landlord to reinforce it, so it doesn't bend so much.
If those solutions are not appropriate, you could have your ceiling carpeted, or have a false ceiling installed. If supported only at the edges, and not in contact with the real ceiling, a false ceiling could provide considerable attenuation. A common acoustical ceiling, supported by the real ceiling, won't work well; you need something that's structurally independent.
Or you could move to the upper floor and become a nuisance to your new downstairs neighbor.
-Mike-