• Attachement #1 shows the input (ch4-green) modulation frequency and the photodiode output (ch1-yellow) when the modulation frequency is about 100 Hz
• Attachement #2 shows the input (ch4-green) modulation frequency and the photodiode output (ch1-yellow) when the modulation frequency is about 30 Hz
• The output frequency is varying in accordance with variation in modulation frequency. It is observed that, for a given modulation frequency also, the output frequency is fluctuating. There could be multiple reasons for this behaviour. One of the main reasons is the frequency noise of the laser itself. Also, there could be acoustic noise coupled to the system (eg, by change in length of the fiber).
• The experimental setup is then modified as shown in attachment #3. The thick beam spliiter is replaced with a thinner one. The mount is also changed such that the transmitted beam can be now coupled to an other photodiode (earlier  the transmitted light was blocked by the mount). One more photodiode (PDA55) is introduced .So now the two photodiodes in the setup are PDA520 and PDA 55. 
• We then applied frequency modulation on the input laser and observed the output of the two photodiodes. But we didn't get the results as we expected and observed earlier (shown in attachment #1 &2). Looks like, the problem is poor mode matching between the two beams. 

The alignement was disturbed after the replcement of the beam splitter. We tried to get the alignment back . But we are not succeeded yet in getting good interfernce pattern. This is mainly because of poor mode matching of two beams. We will also try with the spooled fiber.

[anjali, gautam]

just main points, anajli is going to fill out the details.

To rule out mode-matching as the reason for non-ideal output from the MZ, I suggested using the setup I have on the NW side of the PSL enclosure for the measurement. This uses two identical fiber collimators, and the distance between collimator and recombination BS is approximately the same, so the spatial modes should be pretty well matched. 

The spooled fiber we found was not suitable for use as it had a wide key connector and I couldn't find any wide-key FC/PC to narrow-key FC/APC adaptors. So we decided to give the fiber going to the Y end and back (~90m estimated length) a shot. We connected the two fibers at the EY table using a fiber mating sleeve (so the fiber usually bringing the IR pickoff from EY to the PSL table was disconnected from its collimator). 

In summary, we cannot explain why the contrast of the MZ is <5%. Spatial mode-overlap is definitely not to blame. Power asymmetry in the two arms of the MZ is one possible explanation, could also be unstable polarization, even though we think the entire fiber chain is PM. Anjali is investigating.

We saw today that the Thorlabs PM beam splitters (borrowed from Andrew until our AFW components arrive) do not treat the two special axes (fast and slow) of the fiber on equal footing. When we coupled light into the fast axis, we saw huge asymmetry between the two split arms of the beamsplitter (3:1 ratio in power instead of the expected 1:1 for a 50/50 BS). Looking at the patch cord with an IR viewer, we also saw light leaking through the core along it. Turns out this part is meant to be used with light coupled to the slow axis only.

1. Delay fiber was replaced with 5m (~30 nsec delay)
   • The fringing of the MZ was way too large even with the free running NPRO (~3 fringes / sec)
   • Since the V/Hz is proportional to the delay, I borrowed a 5m patch cable from Andrew/ATF lab, wrapped it around a spool, and hooked it up to the setup
   • Much more satisfactory fringing rate (~1 wrap every 20 sec) was observed with no control to the NPRO
2. MZ readout PDs hooked up to ALS channels
   • To facilitate further quantitative study, I hooked up the two PDs monitoring the two ports of the MZ to the channels normally used for ALS X.
   • ZHL3-A amps inputs were disconnected and were turned off. Then cables to their outputs were highjacked to pipe the DC PD signals to the 1Y3 rack
   • Unfortunately there isn't a DQ-ed fast version of this data (would require a model restart of c1lsc which can be tricky), but we can already infer the low freq fringing rate from overnight EPICS data and also use short segments of 16k data downloaded "live" for the frequency noise measurement.
   • Channels are C1:ALS-BEATX_FINE_I_IN1 and C1:ALS-BEATX_FINE_Q_IN1 for 16k data, and C1:ALS-BEATX_FINE_I_INMON and C1:ALS-BEATX_FINE_I_INMON for 16 Hz.

At some point I'd like to reclaim this setup for ALS, but meantime, Anjali can work on characterization/noise budgeting. Since we have some CDS signals, we can even think of temperature control of the NPRO using pythonPID to keep the fringe in the linear regime for an extended period of time.

• Attachment #1 shows the time domain output from this measurement. The contrast between the maximum and minimum is better in this case compared to the previous trials.
• We also tried to extract the frequency noise of the laser from this measurement. Attachment #2 shows the frequency noise spectrum. The experimental result is compared with the theoretical value of frequency noise. Above 10 Hz, the trend is comparable to the expected 1/f characteristics, but there are other peak also appearing. Similarly, below 10 Hz, the experimentally observed value is higher compared to the theory.
• One of the uncertainties in this result is because of the length fluctuation of the fiber. The phase fluctuation in the system could be either because of the frequency noise of the laser or because of the length fluctuation of the fiber.  So,one of the reasons for the discrepancy between the experimental result and theory could be because of  fiber length fluctuation. Also, there were no locking method been applied to operate the MZI in the linear range.
• The next step would be to do a heterodyne measurement. Attachment #3 shows the schematic for the heterodyne measurement. A free space AOM can be inserted in one of the arms to do the frequency shift. At the output of photodiode, a RF heterodyne method as shown in attachment #3 can be applied to separate the inphase and quadrature component. These components need to be saved with a deep memory system. Then the phase and thus the frequency noise can be extracted.
• Attachment #4 shows the noise budget prepared for the heterodyne setup. The length of the fiber considered is 60 m and the photodiode is PDA255. I also have to add the frequency noise of the RF driver and the intensity noise of the laser in the noise budget.

If I understand correctly, the Mach-Zehnder readout port power is only a function of the differential phase accumulated between the two interfering light beams. In the homodyne setup, this phase difference can come about because of either fiber length change OR laser frequency change. We cannot directly separate the two effects. Can you help me understand what advantage, if any, the heterodyne setup offers in this regard? Or is the point of going to heterodyne mainly for the feedback control, as there is presumably some easy way to combine the I and Q outputs of the heterodyne measurement to always produce an error signal that is a linear function of the differential phase, as opposed to the sin^2 in the free-running homodyne setup? What is the scheme for doing this operation in a high bandwidth way (i.e. what is supposed to happen to the demodulated outputs in Attachment #3 of your elog)? What is the advantage of the heterodyne scheme over applying temperature feedback to the NPRO with 0.5 Hz tracking bandwidth so that we always stay in the linear regime of the homodyne readout?

Also, what is the functional form of the curve labelled "Theory" in Attachment #2? How did you convert from voltage units in Attachment #1 to frequency units in Attachment #2? Does it make sense that you're apparently measuring laser frequency noise above 10 Hz? i.e. where do the "Dark Current Noise" and "Shot Noise" traces for the experiment lie relative to the blue curve in Attachment #2? Can you point to where the data is stored, and also add a photo of the setup?

My understanding is that the main advantage in going to the heterodyne scheme is that we can extract the frequecy noise information without worrying about locking to the linear region of MZI. Arctan of the ratio of the inphase and quadrature component will give us phase as a function of time, with a frequency offset. We need to to correct for this frequency offset. Then the frequency noise can be deduced. But still the frequency noise value extracted would have the contribution from both the frequency noise of the laser as well as from fiber length fluctuation. I have not understood the method of giving temperature feedback to the NPRO.I would like to discuss the same.

The functional form used for the curve labeled as theory is 5x10⁴/f. The power spectral density (V²/Hz) of the the data in attachment #1 is found using the pwelch function in Matlab and square root of the same gives y axis in V/rtHz. From the experimental data, we get the value of V_max and V_min. To ride from V_max to V_min , the corrsponding phase change is pi. From this information, V/rad can be calculated. This value is then multiplied with 2*pi*time dealy to get the quantity in V/Hz. Dividing V/rtHz value with V/Hz value gives  y axis in Hz/rtHz. The calculated value of shot noise and dark current noise are way below (of the order of 10^-4 Hz/rtHz) in this frequency range. 

I forgor to take the picture of the setup at that time. Now Andrew has taken the fiber beam splitter back for his experiment. Attachment #1 shows the current view of the setup. The data from the previous trial is saved in /users/anjali/MZ/MZdata_20190417.hdf5

From the earlier results with homodyne measurement,the V_max and V_min values observed were comparable with the expected results . So in the time interval between these two points, the MZI is assumed to be in the linear region and I tried to find the frequency noise based  on data available in this region.This results is not significantly different from that we got before when we took the complete time series to calculate the frequency noise. Attachment #1 shows the time domain data considered and attachment #2 shows the frequecy noise extracted from that. 

As discussed, we will be trying the heterodyne method next. Initialy, we will be trying to save the data with two channel ADC with 16 kHz sampling rate. With this setup, we can get the information only upto 8 kHz. 

We repeated the homodyne measurement to check whether we are measuring the actual frequency noise of the laser. The idea was to repeat the experiment when the laser is not locked and when the laser is locked to IMC.The frequency noise of the laser is expected to be reduced at higher frequency  (the expected value is about 0.1 Hz/rtHz at 100 Hz ) when it is locked to IMC . In this measurement, the fiber beam splitter used is Non PM. Following are the observations

1. Time domain output_laser unlocked.pdf : Time domain output when the laser is not locked. The frequency noise is estimated from data corresponds to the linear regime. Following time intervals are considered to calculate the frequency noise (a) 104-116 s (b) 164-167 s (c) 285-289 s

2. Frequency_noise_laser_unlocked.pdf: Frequency noise when the laser is not locked. The model used has the functional form of 5x10⁴/f as we did before. Compared to our previous results, the closeness of the experimental results to the model is less from this measurement. In both the cases, we have the uncertainty because of the fiber length fluctuation. Moreover, this measurement could have effect of polarisation fluctuation as well.

3.Time domain output_laser locked.pdf :Time domain output when the laser is locked. Following time intervals are considered to calculate the frequency noise (a) 70-73 s (b) 142-145 s (c) 266-269 s. 

4. Frequency_noise_laser_locked.pdf : Frequency noise when the laser is locked

5. Frequency noise_comparison.pdf : Comparison of frequency noise in two cases. The two values are not significantly different above 10 Hz. We would expect reduction in frequency noise at higher frequency once the laser is locked to IMC. But this result may indicate that we are not really measuring the actual frequency noise of the laser.