"concentrate deeply" is correct and usable in written English.
You can use it to describe someone's intense focus on a particular task. For example: "John was so focused on getting the project done quickly that he concentrated deeply until it was finished."
I huddle over the game and concentrate deeply.
I didn't concentrate deeply on conversation as I thought it would detract from photographing.
That was the first time that, through making an effort to concentrate deeply, he caught a glimpse of the stillness, and the mind's potential.
If you would like to learn to concentrate deeply, to really pay attention un-distractedly, and get more out of this precious life, then I highly recommend Burgs' series of online courses, which will be starting again on Sept. 20.
An older neighbor concentrated deeply, the fingertips of his weathered hands held lightly together.
All of the girls concentrated deeply on their work.
Some of the behaviors outlined above may occur when somebody concentrates deeply on speaking (for example, when the topic is sophisticated or the person is stressed).
We may be engaged in an important discussion with our teenager daughter, trying to concentrate and deeply connect to her, to her world and feelings, but our device notifies us that we should pay attention to something 'a lot more important'.
We concentrate on deeply conserved human enhancers; by restricting to 192/975 cis-regulatory regions that show sequence conservation between mammals and teleost fish (last common ancestor existed 450 million years ago) (Table 1, for detailed list see Additional file 1: Table S1).
As for his own state while shooting, he says he's concentrating so deeply that he gets into what the French call an état second, or "second state" – something like a trance.
Her heart raced, her skin got a prickly feeling, and she was forced to concentrate on breathing deeply.
