Not sure if they actually buy the ES and SPY outright. The Fed creates an 'easy money' policy by purchasing US Treasuries which floods the banks with liquidity. This money ends up funneling into the stock market, since rates are so low.
There is always chatter of a PPT (plunge protection team) but the Fed will never admit it, so it's labeled as conspiracy theory.
However, the term "quantitative easing" or "QE" used by the Fed is simply a defacto way of pumping up the market.
Check out this link for more info: