Shuyu, you have to give more details about the interferometers that you want to build. How do you want people to advise you when you don't describe the device you want to build?

Interferometers for particles are not as simple as those for light, because mirrors for particles are not as simple as those for light.

There are experimental works that probably can help you, but first be more clear.

Dear Sofia，

I did some experiments with an atom interferometer on an atom chip with 87Rb（boson）. I had not experences for fermions. But I am interested in the difference between them because I read some paper which claims fermions are good for realizing precision atom interferometry (for example,S.Aubin et. al., Nature Physics 2, 384 - 387 (2006) ). I also learn from some references that the sensitivity of interferometer can be enhanced by using entangled atoms of both bosons and fermions.

If talk about a kind of special interferometer, I would mention guided atomic gyroscope on an atom chip.

Best wish

Shuyu

Dear Remi，

Thank you very much！

Dear Shuyu,

It seems to me that you speak of single-particle interferometry. There is a big difference between this and two-particle interferometry of type Hanbury-Brown and Twiss (what we call 2nd order correlations). So, please make it clear of which one you speak.

About single-particle interferometry let me give you the information that I have. That would help us to hold a clearer conversation, because I have no idea how looks like your interferometer. Does it have metal gratings? Is it Fraunhoffer interferometry? Do you have a 2slit interferometer? What type of interferometer you have?

As far as I know, the problem in building interferometers for matter (atoms), e.g. Mach-Zender interferometers  is to build the reflecting mirrors. So, please have a look at some interferometry experiments that I appreciate. In experiments with 87Rb the mirror is a magnetic field, not a silver plate. (The expert about these experiments and with which I talked in the past was a kind fellow, Michael Kohl.) The beam of 87Rb behaved as behaves a coherent light beam.

Additional experiments of atom interferometry (Argon atoms), and very interesting, are with gratings of light - performed by the Zeilinger group.

About trapped fermion gases I attached here a work of the Esslinger group. The fermions indeed keep distance from one another, and of course this is an advantage in single-particle interferometry because you don't want two particles at once in the interferometer. That would blur the fringes. Bosons, to the contrary, display the phenomenon of bunching, i.e. of appearing two at once, blurring the single-particle fringes. However, I am not aware of interference experiments with beams extracted from Fermi trapped gases. There are such beams, but if they are suitable for interference experiments, I am not sure. But I'll look for references.

I'll tell you also the advantage of working with entangled particles, but it's 1:00 o'clock in the morning. We'll talk tomorrow.

All the best,

Sofia

Dear Sofia,

Thank you very much for your valuable suggestions and references.

Currently, most of atomic interferometers measured the 1st order correlation, as you said. But it dose not mean higher order correlations do not play a role if we use Bose-Einstein condensates or Degenerate Fermi gases even there is no interaction between atoms. For example, when we discuss the origin of the phase in the interference of Bose-Einstein condensates, the many body correlation is a key point[PRL76_161,AJP74_880]. Different quantum statistics of bosons and fermions, as Mr Remi mentioned [PRA58_4904], also make the strategy for enhancement of interferometers different[PRL56_1515]. I think interaction free of spin-polarized Fermi gases at ultra-low temperatures also can be considered as an effect coming from quantum statistics. Is it right?

The key point for building an atomic interferometer is how to split and recombine matter wave packets coherently. Although there are many methods for these purposes, for example, I finished an interference experiment recently with Bose-Einstein condensates in a magnetic lattice near an atom chip surface[arXiv: 1502.01605]. But the most common method is based on photo recoil from a pair of laser beams with Raman [PRL78_2046]or Bragg pulses[PRL110_093602].

Best wish

Shuyu

Dear Shuyu,

You ask,

"I think interaction free of spin-polarized Fermi gases at ultra-low temperatures also can be considered as an effect coming from quantum statistics. Is it right?"

I am not an expert in condensates or trapped gases at low temperatures. But I believe that, since the fermions can't get close to one another because of the anti-bunching, they indeed can't interact. The anti-bunching is of course a quantum effect predicted by the 2nd order correlations.

A lot of thanks for the articles that you sent me, it spares me the effort of browsing in journals and arXives. Now, please see what is written in Yurke's abstract of his article "Input States for Enhancement of Fermion Interferometer Sensitivity":

"A conventional fermion interferometer, in which the fermions enter only one of the two input ports, can achieve a phase sensitivity Δφ = 1 / √n, where n is the total number of fermions which have passed through the interferometer. Here it is shown that by injection of fermions into both input ports the phase sensitivity can approach 1/n provided that the fermions in the two input beams are suitably correlated."

Now, I recall that you asked how the sensitivity of the interferometer can be enhanced. What you mean by this enhancement of sensitivity? Can you be more clear?

Next, how do you plan to do experiments with fermionic atoms? Do you have such sources? Anyway, let me mention an experiment performed by the Aspect group with fermions released from a trapped Fermi gas (see attach). Unfortunately, the beam does not expand as a parallel beam but it has rather a Gaussian profile. I can say nothing about the coherence of this beam, but I don't know if it is relevant in single-particle interference. We currently do interference experiments with thermal light which is not at all coherent.

I also promised you to tell you why experiments with entangled particles are an advantage. Typically, people do such experiments with pairs of down-conversion photons, time-energy entangled. The photons in such a pair appear an extremely short time one after another (100femtoseconds). One of the photons is detected in a separate detector, and its detection tells us that we have a photon (i.e. the other one) in the interferometer. It's very convenient, because in this way we can eliminate events in which two photons entered the interferometer too soon one after another.

My best wishes,

Sofia

Dear Sofia,

Thank you for your answer and reference.

Currently I don't have the setup to investigate interference with fermion. Just because I am writing a section of a review paper which involves a little of fermion on an atom chip. Therefore I have the question about what is the advantage to using fermions for building interferometers. Until now, I am sure due to the different quantum statistics interferometers of fermions should differ from those of boson. But it is still not clear to me that the interferometer with fermion can achieve higher accuracy. Because using boson we also have many ways to improve. Anyway, I will continually think about it.

Best wish

Shuyu

Dear Shuyu,

I believe that you express yourself in a confusing way. You say "using fermions for building interferometers". The interferometers are not built from fermions. I believe that you mean to build interferometers FOR testing fermion interference.

A small suggestion: the issues worth to pay attention are not only whether fermions are easier to do interferometry with, but also, there are interesting phenomena on which fermion interferometry may eventually shed some light.

I just venture an idea: you see, a question that interests many people is the minimal distance between two fermions of the same energy. If one inputs in an interferometer a very diluted beam of fermions of quite sharp energy, it takes some time until the fringes build up. But if the density of the beam increases, in the same time-interval the visibility increases. How much can we increase the density? There is a limit, isn't it? The fringe visibility achieved in the same interval of time would also have a limit. From the density we can infer the minimal distance between two fermions.

However, the electron clouds of atoms also repel one another. Which effect is stronger? Maybe comparison with boson interferometry can answer.

Needless to say, if we could produce entangled pair of fermions it would be excellent because we could measure times with precision from the detection time of the heralding fermion in each pair.

I just ventured some ideas inspired by my own research.

Best wishes,

Sofia