Serializing Map<Date, String> with Jackson

I want to serialize a Map with Jackson. The Date should be serialized as a timestamp, like all my other dates.

The following code renders the keys in the form "Tue Mar 11 00:00:00 CET 1952" (which is Date.toString()) instead of the timestamp.

Map<Date, String> myMap = new HashMap<Date, String>();
...
ObjectMapper.writeValue(myMap)

I assume this is because of type erasure and jackson doesn't know at runtime that the key is a Date. But I didn't find a way to pass a TypeReference to any writeValue method.

Is there a simple way to achieve my desired behaviour or are all keys always rendered as Strings by jackson?

Thanks for any hint.