Adopted dog that seems to have separation anxiety

I adopted a 6 year chihuahua/dachshund mix from my local animal shelter this week and he has been the most laid back dog I have ever encountered when I am around him. He doesn't ever bark or get flustered. The issue is whenever I am not in the same room with him he starts to whine and bark extremely loudly, which is a problem because I live in an apartment so I do not want to bother my neighbors around me.

Growing up my family always had dogs, however this is the first dog that I have had by myself as an adult. Over the last couple of days he has laid in his bed while I am watching TV and hanging out at home, however when it is time to go to sleep and I crawl into bed he will start barking and whining. I know I have only had him a couple of days so I am sure he is still adjusting to his new life, but I would love to hear if anybody has any suggestions or tips to help him adjust to being by himself.