Bounded gaps between product of two primes in imaginary quadratic number fields

We study the gaps between products of two primes in imaginary quadratic number fields using a combination of the methods of Goldston-Graham-Pintz-Yildirim (Proc Lond Math Soc 98:741-774, 2009), and Maynard (Ann Math 181:383-413, 2015). An important consequence of our main theorem is existence of infinitely many pairs alpha(1), alpha(2) which are product of two primes in the imaginary quadratic field K such that |sigma(alpha(1) - alpha(2))| <= 2 for all embeddings sigma of K if the class number of K is one and |sigma(alpha(1) - alpha(2))| <= 8 for all embeddings sigma of K if the class number of K is two.