Poor man's entangler

How are entangled qubits generated in the laboratory? Entangled photons can be generated relatively simply, using downconversion and other nonlinear optics methods, as has been previously mentioned in the context of squeezed light. However, entangling states of matter is generally more difficult, although not as difficult as performing unitary quantum gates between matter qubits. This is because a probabilistic method, known as the "poor man's entangler," exists for generating entangled states, as we describe here for two atoms. Recall that a beamsplitter presented with the inputs $|1{\rangle }|1{\rangle }$ outputs $B_{\theta }|11\rangle =(\cos ^{2}\theta -\sin ^{2}\theta )|11\rangle +{\sqrt {2}}\cos \theta \sin \theta (|20{\rangle }-|02\rangle )$.