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Yeah, no. That'll make some nice fiber flambé. You had the right idea going free space. But you can actually still make it work with a fiber EOM. Sure you can. You basically already said it. Split a milliwatt or two off your main beam and send it into a fiber EOM (or free space EOM, whichever...

I haven't used one myself, but all of my coworkers who have ended up switching to fiber EOMs just due to the sheer hassle (getting the requisite voltage, and alignment issues resulting in residual amplitude modulation). I think the only good reason to use a free space EOM is if you absolutely...

Your Hamiltonian has a constant Rabi rate and a time-dependent detuning. What would you expect in the limit where ##B \rightarrow 0##? Well, A is your Rabi rate and you'd expect Rabi flopping at a timescale ##\frac{1}{A}## (up to factors of ##2\pi##, which I always mess up). Based on your...

One final update on this thread. After taking a truly painful amount of data, we found that the magnitude of non-reproducible changes in the elasticity of the sapphire plate are linearly related to the coefficient of static friction between the sapphire plate and the ball bearings. In other...

Take the average of ##f_i## to get the center frequency. Some of your measurements will be red-detuned and some will be blue-detuned, but they should (to first order) occur with equal probabilities. This is exactly right. You're not ignoring the uncertainty in ##df_i##. Hopefully, ##df_i## is...

I would surprised if anyone's done this analysis, and if someone had, it still might not get published because there's little motivation for it. However, here's how I would start your literature search, if I were you: The closest thing I know of that people actually study in molecules is the...

Yes, this is a decent method. This is the second-best way to estimate the error on the mean (based only on the assumption that your measurements are normally distributed). Is ##df_i## is a measured or fitted uncertainty? By "fitted uncertainty" I mean you do your experiment once and get a...

Hello, I am trying and failing to derive that the shear modulus ##G## is equal to the Lame parameter ##\mu##. I start with the linear, symmetric, isotropic stress-strain formula: $$\sigma = \lambda \mathrm{tr}(\epsilon) \mathrm{I} + 2\mu \epsilon$$ I then substitute a simple (symmetric) shear...

I don't have the text you are following, but I think I can follow. You have a charge density distribution that is symmetric under a charge-flip + reflection about the xy plane, as you have said. First, you need to consider the intrinsic symmetries of the electric field. Intrinsically, no...

Quick update: Tl;dr: Grease works, dry powders don't. I measured coefficients of friction for different ball bearing materials, and recorded them. Some of the notable points are: PTFE ball on sapphire (dry): ##\mu_s=0.129\pm0.009## PTFE ball on sapphire (greased): ##\mu_s=0.028\pm0.001##...

Why indeed. :oldlaugh: The original argument for this design choice is that you can't control where the point of contact will be on a flat surface, so point contact will be easier to model and will allow us to achieve a higher level of symmetry in the constraining forces. That idea is being...

Ok this idea of relaxing stresses in the contact area is really interesting to me, because the effect we're trying to mitigate is a non-reproducible change in the elasticity of the sapphire plate. By non-reproducible, I mean the effect changes every time we pick up the sapphire plate off the...

Will that affect the static case? The sapphire part isn't supposed to move at all. Sorry if that wasn't made clear in the original post. I know it's a little weird that we need low friction for a part that doesn't move, but regardless our experimental data says low friction = better performance...

It wouldn't be possible because of our vacuum requirements. Helium is really hard to pump out and I feel like the amount of flow needed to levitate the sapphire part (is that what you meant?) would be impossible to pump out continuously. Nominally, the PTFE balls and sapphire part are as clean...

I have a flat planar part made of crystalline sapphire (about ~2k weight, and polished to a mirror finish) that rests on three ball bearings, and I want to minimize the static friction at these 3 interfaces. The ball bearings are fixed so they cannot roll, and the sapphire part can only slip...

Your analysis looks right to me, in the limit of ##\Omega << E_2 - E_1##.

Sorry for the really slow reply! Check out this paper: https://arxiv.org/abs/0708.2925 Specifically, the paragraph near the bottom of the left column on page 2 that starts "We calculate C...". In short, there is some mixture of quantum numbers in either parity state that allows a weak...

Something sounds very wrong, and I doubt it's related to the off-axis parabolic mirror or the spatial filter. If your beam was that asymmetric before the 4f collimator, you'd be able to tell just by looking at the beam profile on a piece of paper (since it's probably huge after the spatial...

Sorry for the slow reply. I had started working it out, and I spilled tea on my papers o:) I don't think there is a direct formula. The way I was working it out was getting the spin-up and spin-down populations as a function of time from 2nd order TDPT, then taking the expectation value over...

I don't, sorry. Sounds hard, from an experimental point of view.

It seems different by a few 10's of MHz. Let's say 20 MHz, to be generous. 20 MHz / 6550MHz = 0.3%, consistent with the terms you omitted. I think you nailed it?

Gotcha. Thanks for the clarification I have a suggestion, it just might not be accurate. I've never used it personally. Try equation A.16 of this appendix. Again, this ignores any other structure in your system (like the DC tail of a microwave resonance), which would add as a background to the...

Looks pretty good to me? Am I missing something? The only differences I can see are at the 1% level or so. This is consistent with ##\gamma/B \approx 0.013##. Also, can you say which unperturbed state is which plot line?

If your rotation frequency is comparable to the level splitting, then you have a resonant process and you can use the rotating wave approximation. This isn't really a limit on the adiabatic theorem. If the system has a large transition dipole moment (##d## in your post), then you can transform...

It's probably just noise. I wouldn't read too much into it.

Probably fluctuations either in the laser frequency or in your cavity's optical path length. It's impossible to discriminate between the two of them with the tools at your disposal. There are tricks you could try if you had two lasers (or equivalently, a fiber EOM phase modulator for...

When you scan the laser with a scan rate of 10Hz, what is the range of the scan? What I really need is the frequency-per-second scan rate. For example, in post #50, it was ##300\mathrm{kHz}## in ##20\mathrm{\mu s}##, or ##15\mathrm{kHz / \mu s}##. What was this rate in the data in post #52?

Sorry for the confusion. I'm saying at 964nm, the linewidth of the cavity will be bigger than 30kHz. Since you have finesse of 10,000 at 1064nm, that means your reflectivity must be at least 99.99%, and probably much better. It depends what kind of mirror coating you use, but the reflectivity...

Your linewidth won't be as narrow when you're at, say, 964nm. See if you can't get a reflectivity vs wavelength curve for your mirrors and you can estimate the new linewidth.

Well, your laser *does* have frequency (and/or power) variations when closed-loop based on your noisy error signal. If anything, your power noise might be larger in closed loop, because it could be driven by the servo compensating for frequency noise. You said earlier that your power was stable...

I believe the concern is about power fluctuations when the servo is closed-loop, not in the open-loop configuration (you measured it in the open-loop configuration, since you had no cavity signal). The response from the laser company suggests that your laser is a DBR or DFB. If that's true, then...

What they're suggesting is that your servo is trying to control the laser frequency but ends up getting confused by fluctuations in the laser output power. For example, if your servo locks when the transmission photodiode reads 1V, but then your laser power drops to 80%, then your transmission...

Just to clarify, you engaged the differentiator, and the result was that the error still remained just as noisy and the transmitted power did not increase? That's really bizarre. Did you try the lowpass filter on the photodiode? I know the feeling. I'm sorry it's been such a slog. You've really...

You're right about the reflection being at an angle. I forgot about that quirk of bowtie cavities. Looking back at post #11 again, I noticed the timescale of your noise events is really fast (roughly 10 microseconds), so I think you're right. This is way too fast to be environmental...

Yep, sorry. I just suck at math apparently :oldbiggrin: Yep, that's what I meant. That's exactly what I meant by frequency noise: side-to-side motion of the transmission peak when you scan the laser. That's quite a lot. Sorry if you mentioned this before now. This thread's gotten a little...

This is very suspicious. If I were you, I would spend some time to confirm your linewidth measurement before anything else. A broader-than-expected linewidth could very likely mean that you have dirt on your cavity mirrors. Dirt scatters light from the cavity mode into random, uncoupled modes...

I work on optical cavities a lot, and I can say that me and my coworkers all agree that cavities are just hard and troubleshooting them can feel like you're going in circles. It's not a reflection on your abilities. Cavities are just scheming little gremlins. It's a little hard to understand...

I'll write a longer reply when I have more time, but I want to second the suggestion to try a different servo other than the Vescent. Do you happen to have another stabilized 1064 laser? I know it's unlikely, but if you do I would beat the two lasers on a photodiode so you can see the spectrum...

I'm sure the state population is entangled with whether or not the bureaucrats had their coffee :oldbiggrin: Ah, this is trickier because the spontaneous emission will also cause decoherence in addition to siphoning ions away from the ionized population. It's not as simple as a binomial process...

1. Yes, the ionization test will project the ion (assuming there is only 1 ion) back to the 100% positive parity state. The probability of ionization after 20ms will be still 10%, like you said. 2. That's a really good question. I think we can work it out from first principles. For simplicity...

So when you turn the 2nd integrator off, you're not setting the corner to 0, you're removing that feature from the gain plot entirely. So if you turn off the 2nd integrator and the differentiator, what you have is a typical PI gain curve: Edit: Whoops, I forgot to respond to your second...

Ok, that sounds like parasitic oscillation (overall gain too high) in some form or another. Totally reasonable. For what you're doing, you probably won't need it ever. Fair enough, I couldn't find a good summary online either. The second integrator is to give the user the ability to suppress...

Oh! Ok then that makes sense. In post #11 you called it the error signal and I got confused. Sorry about that. Does the noise on the error signal get bigger or smaller when you increase the P gain (using the coarse gain knob)? It bugs me that your servo doesn't even try to keep up with the...

Sorry for the slow reply. This week hit me like a freight train. Ok, you are most certainly locked. There is definitely something wrong, as your transmission signal seems to fluctuate all the way to 0 while you are locked. I am confused about the error signal trace (blue, in pic #2 of post...

What laser servo are you using? Is it commercial or homebrew?

Oh! Are you trying to side-lock to the transmission peak? (Sorry, I'm used to PDH locking.)

Can you record what your error signal looks like unlocked when you manually tune the laser on resonance? Also, can you lock the laser and show side-by-side the error signal and the control signal (output of the servo)? I suggest that on the scope settings you set triggering to the 60Hz AC...

First, a jargon thing: by error signal you mean the input to your locking servo, correct? Some people I know call the output of servo the error signal, and it gets confusing. (For the sake of clarity, I always call the output of the servo the "control signal." Also, what's the vertical scale on...

Raman transitions are just one way to implement a spin flip on an ion qubit. Spin flips are a coherent process and do not break entanglement. As others have already said, it's measurement that breaks entanglement. In a typical ion quantum computer, measurement is performed by fluorescence: you...

I believe (very strongly) that when you see a single spot you are best aligned. If you want to be absolutely sure, try measuring the peak brightness in each of your images by loading them in matlab/python/whatever. You'll have to do this by eye because there are always a few random "hot...