Message ID: 2349
Entry time: Wed May 22 15:07:09 2019
Reply to this: 2352

Author:

awade

Type:

DailyProgress

Category:

WOPO

Subject:

Demodulation and subtraction for homodyne detector with Zurich box

For the detection of squeezed light the homodyne detector is now configured for digital subtraction in post processing. The measurement scheme is now to take the output of the two TIA amplifiers (see QIL:2324 and QIL:2327), digitize them directly at 210 MSa/s (5 nV/rtHz input ref noise) with the Zurich box and demodulate both detector streams using its internal FPGA at about 1 MHz. The Zurich box allows for direct sampling of the signal out of the FPGA which can then be downloaded either through the web interface or the python API. The signal chain is illustrated below:

WOPO homodyne detection chain (see attachments at bottom for high resolution)

The basic approach is to mix down the shot noise limited light from some higher frequency (somewhere in the range 100kHz - 8 MHz) and then compute the ideal subtraction factor from a short (10 sec) segment of data. The method for optimization is to compute the time domain subtracted signal for a given balancing factor (SF) and compute the goodness of subtraction from the RMS of the signal. An fmin search is done to find the ideal subtraction factor (SF) for shot noise limited light.

It wasn't immediately clear to me what demodulation frequency to choose, the low pass filter and the digitization sampling rate. So I set up a python notebook and did a few sweeps of these parameters to find the best combination of parameters. This book is attached below as 20190514notebook_ZurichDemodeCompairTests.ipynb in a zip. I've pickled data for replotting if needed later.

Sweeping the demodulator 4th order LP corner frequency

At present the detectors are illuminated with 4.5 mA worth of light (as measured from DC voltages / TI gain). This should give about 25 nV/rtHz at the output of the photodetector, as measured by the Zurich box. Fixing the demodulation frequency at 500 kHz and the sampling rate at 30 kHz I found empirically that the when the LP filter (4th order) was kept at 10 kHz and below the minimum subtracted signal converged to about 30 nV/rtHz (about what I expected). With the demodulation frequency set much higher than this, the minimum subtracted signal no longer converged to the predicted SN level. Maybe there is some aliasing thing going on here. The outcome of this experiment is that clearly the demodulation LP filter should be set to at least 1/3 of the sampling rate for the time domain rms minimization to work.

Selection of sampling frequency

I did a similar sweep with the sampling rate while keeping the demodulation frequency fixed at 500 kHz and the demodulation low pass fixed at 10 kHz. The conclusion was basically the same: as long as the demodulator low pass was kept within 1/3 of the sampling frequency then the method of computing the ideal subtraction factor using the total time domain rms as a cost function returned the minimum possible differential noise.

Selection of demodulation frequency

The demodulation frequency choice is a tricker one. Initially I selected 1 MHz but was getting excess noise above what I expected for shot noise. I then looked at a single channel on the Zurich's scope in FFT mode. Data is plotted below

Basically the plot shows that there is a strong peak at about 900 kHz. This is due to the relaxation oscillation of the laser. When the laser's noise eater is turned on this peak is damped with some tradeoff of slightly higher noise at lower frequencies. So when choosing a demodulation frequency it is best to select something well below 1 MHz. I'm not sure if it is best to turn the noise eater off if the demodulation frequency is set well clear of the 900 kHz peak. It seems like there is a noise penalty for the noise eater loop at all other frequencies.

With the noise eater on I then did a sweep of the demodulation frequency while keeping the low pass filter at 10 kHz and the sampling rate at 30 kSa/s. I've plotted the median ASD value in the band between 100 Hz and 1 kHz as an indication of the minimum SN level after digital subtraction verses the demodulation frequency. Plot below. There is a hump at about 1 MHz that should be avoided, and spikes at 87 kHz and just below 300 kHz but anything else in the range of 100 kHz to 700 kHz should be fine.

Current selected configuration

So for now, based on the above sweeps of parameters, I have selected demodulation frequency of 600 kHz that is low passed at 10 kHz with a 4th order filter and sampled at 30 kSa/s. As an example of optimized subtraction I have plotted the two homodyne channels along with the subtracted differential signal (optimized by minimizing subtracted time domain rms) and the dark noise (using the same subtraction value).

Here the clearance from the dark noise floor doesn't seem so great. The input referred noise of the Zuirch box is 5 nV/rtHz per channel. Also the equivalent output noise from the PDs at this point is 2.5 nV/rtHz. As these are uncorrelated noise processes this would place the noise floor at about sqrt(5^2*2+2.5^2*2) = 7.9 nv/rtHz, pretty close to what we are actually seeing.

One option here is to pre-amplify the PDs before going into the zurich box. A standard mini-circuits amplifier like ZFL-500LN+ has an input referred noise of 1.6 nV/rtHz which would bring the dark noise floor down to something closer to 4.2 nV/rtHz. I'll keep going without any pre-pre-amplification for now and see what I can do with 532 nm pumping. There should be enough clearance to see at least something if it is there.