John Diehm 1850's Middlefield, CT

I'm looking for any information available on John Diehm and his ancestors. The information that I have is from the 1860 census: John
Diehm age 50, his wife Clara, 4 children. The birthplace for all except one child is Baden, Germany. The one child is 3 years old. Since the next youngest child is 11 I have concluded that they emigrated from Germany between 1849 and 1857.

At the time of the census they lived in Middlefield, CT and remained there for the rest of their lives. I'm trying to determine the exact year of emigration, the ship the arrived on and the specific town that they lived in in Germany. The children's names are Christine, Andrew, Catherine and Lenore.