I know that AI can be used to design printed circuit boards (PCBs), so it can be used to solve complex tasks.
Is there any programming language designed by deep learning (or any other AI technique)?
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There are certainly things like this.
I'd say a strong example is layered learning approaches, descended from Peter Stone's work.
A programming language is essentially a collection of useful shorthands for assembly-level instructions. Ultimately, everything you do in a programming language eventually gets executed in assembly. So making a programming language amounts to learning how to write short, reusable, assembly language programs that you can then use as building blocks to solve harder problems.
An example of this in action is Kelly & Heywood's approach to constructing 'Tangled Program Graphs' for reinforcement learning (IJCAI 2018). Here an evolutionary algorithm is used to learn short assembly programs, that can be combined into a graph to make more complex programs. This is similar to graphical programming languages like J.