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 \cite{GGPY}, and Maynard \cite{MAY}. 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 $\mathrm{\mid }\sigma ({\alpha }_1-{\alpha }_2)\mathrm{\mid }\le 2$ for all embedding $\sigma$ of $K$ if the class number of $K$ is one and $\mathrm{\mid }\sigma ({\alpha }_1-{\alpha }_2)\mathrm{\mid }\le 8$ for all embedding $\sigma$ of $K$ if the class number of $K$ is two.