Can we reach deep meditative states without teachers?
A teacher is generally required but difficult to find. The Pali suttas say:


  Tathāgatappaveditassa dhammavinayassa desetā puggalo dullabho lokasmiṃ
  
  Rare in the word is a person who teaches the teaching and training
  proclaimed by a Realized One.
  
  AN 6.96


For an individual with a keen intellect, this 'teacher' could simply be the Pali suttas. However, even in this case, the discernment of what the Path is must be acutely discerned. Generally, even an intelligent person needs a 'rare teacher' to verbally guide through the true meaning of the Pali suttas.