why federal fund rate vs treasury bond yield generally move in the same direction? My own thought is, if the fed lowred federal fund rate, peoole should look for investment with greater return, like treasury bond. More demand=decline in yields but why do they generally move in the same derection?. Same goes for Mortgage rate during 2001-2005, why would mortgage rate go down if all the fed did was just lowering federal fund rate which has nothhing to do with mortgage?
Federal funds rate is a rate at which banks can borrow extra money at an overnight market. This can be viewed as 'banks' cost' since when people want to lend from certain bank, the bank will often get the money not from some new deposits it itself attracts but from the overnight market.
Consequently if the Fed funds rate drops they can afford to lend money more cheaply. The reason why they also do so instead of pocketing all the difference as a higher profit is the competition amongst the bank.  If you want to completely see the mechanism laid bare you can have look at chapter 3 of Freixas and Rochet, Microeconomics of banking. Hence this is the reason why mortgage rates will fall as well. Banks simply can create those mortgages more cheaply now.
The bond yield is also affected by the above. The current bond yield ($Y$) is given as:
$$Y = \frac{C}{A}$$
where $C$ is the annual coupon payment and $A$ is the asset price. The coupons are already fixed so bond which pays ${\\\$}100$ coupon and trades for ${\\\$}1100$ will have yield of $\approx 9\%$. Now whether that $9\%$ is a lot or not depends on prevailing interest rate. If the interest rate  is $10\%$ then yield of $9\%$ is small and if interest rate is $5\%$ yield of $9\%$ is high.
If the interest rate falls relatively to the yield the bond will get more desirable (like the situation when interest rate would be $5\%$ and yield $9\%$. In such case people will simply demand more bonds and then you will get the standard supply-demand story. People will bid the bond prices until $A$ increases sufficiently enough so people are indifferent between buying bond and putting money in some deposit account bearing that $5\%$ interest (or some other instruments). As you can clearly see from the formula above, higher bond price will imply lower yield. Hence when interest rate falls yield prices fall as well.