I ordered 5 of AD734 and thinking about how to make a circuit for squaring the signal.

    The "chopping" signal readout technique requires that we square the signals.  Basically we need to (as rana suggested):

(1) square the signal from PD, (after 10-100Hz bandpass) to convert it to power, and band pass it again.

(2) square the driving signal (might be varied from 0.1- 1Hz.) This is illustrated in the diagram as doubling the frequency ("2 x freq" box.)  The driving signal for PZT is offset. So the signal is  V drive = A + B xsin (2pi fdrive t) with A > B. This ensures that the voltage on one end of the PZT is always higher than another end. We might need to high pass this signal first, to get a signal with only 2 fdrive frequency after we square it.      

(3) multiply signal from (1) and (2) to demodulate the signal.

Basically, 3 multipliers are needed.

The first one is for (1), so the input frequency is ~ 10 -100Hz, and the output is 20-200 Hz.

The second multiplier is for (2), the signal is ~ 0.1 - 1 Hz, but this one might have large DC term after we square it.

The third one is for (3), this one has to multiply 2 low f signals together which is quite similar to (2), so the design can be the same.

I'll consult Frank and/or Koji again before finalize the multiplier circuit.