## Atom Interferometers: sensing magnetic and electric fields, motion/acceleration/rotation

Presentation by MIT Professor David E. Pritchard

Atom interferometer: "this would be tremendously sensitive to motion", to "some interaction that the atom had" ,"a magnetic field" or "an electric field" "and that would shift the fringes".

A laser interferometer consists of a laser beam which falls onto on a mirror and is split into two different paths which interfere and produce fringes. "The key point about the fringes is that they're sensitive to what goes on in these two separate paths to a very very high degree. So if I take this mirror here and I move it just a quarter of a wavelength of light - so that's about a tenth of a micron - then the pattern over here will shift: where it was light it will be darker, where it was dark it will be light. And so if you have something that's measuring where the interference fringes are, you can make it a very very accurate measurement of the displacement of this mirror and that's an interferometric measurement."

Can you create something similar with atoms i.e. an atom interferometer? Answer by MIT Professor David E. Pritchard who reports on his work on atom interferometers with applications such as sensing electric fields and sensing acceleration/rotation (the latter in the frame of the military program "Precision Inertial Navigation")

"Before I talk about atom interferometry, I better talk about regular interferometry and that's usually done with light. The essential idea is that although light seems to be just a steady stream of photons or even just some sort of electromagnetic field, in fact light is really a wave, like ocean waves. The key characteristic is that if you have two waves that come along, sometimes the peaks of one add into the peaks of the other and then the waves are much higher, where sometimes the high points on one add into the low points on the other and then you have very little excitation of the water, even though you can see that there are two waves coming in that direction.

And so any any sailor like myself knows that when you're out sailing you go look for the big waves and try to get your boat planing down on the big waves. Whenever you have waves and the waves are differentiated by coming in different directions even in the ocean - just slightly different directions - there are places where there are big waves and where there are small waves and that's basically the interference.

Now in a laser interferometer, you typically have the laser beam come in, it hits a mirror that has only some silver on it so, some of the laser beam bounces off and some of it goes straight through. You put some more laser beams so that these two beams go this way; then they come back together and where they come back together here, they interfere and they make fringes. The key point about the fringes is that they're sensitive to what goes on in these two separate paths to a very very high degree. So if I take this mirror here and I move it just a quarter of a wavelength of light - so that's about a tenth of a micron - then the pattern over here will shift: where it was light it will be darker, where it was dark it will be light. And so if you have something that's measuring where the interference fringes are, you can make it a very very accurate measurement of the displacement of this mirror and that's an interferometric measurement.

If you believe quantum mechanics, then everything's a wave and all atoms are a wave too. And so the question comes: can you make something where the atom comes along, hits the analog of a mirror (of a half-silvered mirror) and goes two different paths and comes together and interferes over here. And you don't have to be that great a physicist to realize that this would be tremendously sensitive to the motion over here of whatever, or to some interaction that the atom had, maybe it went through a magnetic field that was bigger here or there or went through an electric field and that would shift the fringes.

And the atom wavelength, of a typical room-temperature atom, or an atom just out of a sodium oven, you know a little can filled up with sodium and heated so that the sodium comes out the little hole. The wavelength of the atoms coming out there is about 10,000 times less than the wavelength of light. So an instrument made in which atoms interfere could be thousands of times or hundreds of times more sensitive than the kind of sensitive measurements you can already make with photons, with lasers.

Now that's the good news. The bad news is we don't, at least until we had Bose-Einstein condensates, we didn't have any sources of coherent atoms like the coherent photons that come out of a laser. But nevertheless even with just the sodium oven, we persevered and we made an atom interferometer. And so I guess the first thing you'll be curious about is how did you do that? Because if you take a piece of a mirror here, atoms don't go through glass, so you can't use something that's solid. Well, you can use a laser beam, a certain kind of laser beam. We actually used something called a diffraction grating, which we got from some people here at MIT, Hank Smith's group that does nano fabrication. And this was a transmission grating, it really consisted of a series of gold bars like this, that were separated by about a quarter of a light wavelength of light, so it was really really small, you can't see that with a microscope. No optical microscope can see the things because there's so much smaller than a wavelength. But anyway when the atoms go through these, they then split in two going in several different directions. And we took the atom beam and it went through one of these gratings and it split into two directions and then we took a couple more of these gratings and used the ones that came back together and then we had an atom interferometer, where the interference fringes were formed up here and the atoms started down here.

So then the question arose: well what can you do with it. And the answer is you could do all sorts of things. And so in fact this was one of the great times in my scientific career when we had the only instrument in the world, where the atoms were separated enough going through that we could put a metal sheet in between. You're thinking of the atom as being on one side or the other of this sheet. But unless you make a measurement, quantum mechanics says no the atom is represented by a wave and the wave is going both ways and coming back together. And that's the only reason that you can see the interference pattern over here, because of the possibility of the atom going this way or that you didn't look. Okay so now what can we do, (how) can we utilize the sensitivity of the atoms.

Well, one of the things we did was, when we had this metal sheet here, we put an electric field over here on one side but not on the other side. But when the atoms go through the electric field they have a property called polarization. Polarizability is a number characterizing the ability that an electric field can pull the electron away from the center of the atom. The atom in going through the electric field would get accelerated or decelerated a little bit or would have its energy changed so that it would shift the fringes. And that's a very sensitive measure of the interaction with the electric field. And so we were able to measure the polarizability about 20 times better than had been measured before. And of course at that time there were maybe 25 or 30 different theories of how to calculate the polarizability and there we had a definitive measurement, so we were able to determine which calculations work best and which type of calculation work best.

Another thing that we did was to put a gas on one side of the metal plate but not on the other. Now normally you think, well there's a gas there so the atoms is in the interferometer will just come and bounce off the gas molecules they will hit it and that will be the end of them. And yes that does happen. But the gas also acts like a piece of glass for an optical wave and there's a slight interaction that changes the wavelength of the waves going through the gas and so we were able to measure what is for optical glass called the index of refraction. We were able to measure the index of refraction of an atomic gas for an atom wave. And of course there's some theories for that and again we could make some measurements there.

So when you have an atom interferometer the atoms spend some time going through the interferometer. And if the interferometer were to rotate during that time the atoms that were traveling through it wouldn't know that the atom interferometer rotated. And so what you would see is that the fringes would appear for the detector to be in the wrong place. And the faster the atom interferometer rotates the farther the fringes would shift. So you could use atom interferometers as a sensor for rotation. Or you can use them as a sensor for atoms falling, namely you could expect the interference pattern to be here, but because there's gravity the atoms would actually be pulled down and so you'd see the fringes down lower. Now remember you can make these fringes positions very very precise either with this fabricated grating that we used or by using light waves. And so when you work out all the numbers, atom interferometers turn out to be wonderful sensors of inertial motion, of motion in space.

So there was a big program funded by the military called "Precision Inertial Navigation". And the idea was to use atom interferometers both to sense gravity or to sense acceleration and also to sense direction. And the challenge was I will make a box and I will put some atom interferometers in it and I will tell the box that it's parked in a Jeep. And now the Jeep will just drive off and will drive all around for an hour and then the box will tell you where you are because every time the Jeep started it said "oh we're accelerating in that direction" and then when the Jeep turned it said "oh now we're going that way and now we slowed down". But it just adds up the velocity, adds up the rotation and the goal was to know where the Jeep was within 10 meters after an hour, completely independent of you know the global positioning system or what route the Jeep went or whether it went up and down hills or whatever.

So that's just an example of a kind of sensitivity that atom interferometers have and I suppose it's probably a military secret now whether you can really build such a box and make it work. But my suspicion is that it's possible to do that but that it's probably right now a little bit too expensive.

So I see two futures for our atom interferometers that are very intriguing and interesting at the present time. The first one is measuring fundamental constants. Just the fact that the atom interferometer are so sensitive that we can measure things like the recoil velocity of an atom when a photo single photon hits it and this will enable us to determine things like the charge on the electron and other basic parameters, maybe the fine-structure constant, we can determine them better.

And the second thing which is a little bit more interesting to me is probing the nature of quantum mechanics. So we started doing this a little bit by shining light on the atom as it went through. And showing that when two paths the atom could take had diverged sufficiently that we were able to resolve with a microscope which way it went. Then there were no more fringes. But if we didn't look at the photon and then we post selected the atoms that had scattered the photon in one direction, we got the the fringes back. So this is getting at the fundamental question of when do things act like atoms, when do things act like waves, how can we change this, how can we retro actively change the system's mind about which it was and what is reality what is the nature of reality. All these are questions are fundamental questions of quantum mechanics and atom interferometers will certainly play an important role in elucidating them."

## Atom interferometry and phase lags (phase shifts-dephasing) of electromagnetic origin

phase Aharonov-Bohm (AB) 1959 - magnetic field
phase Aharonov-Casher (AC) 1984 - electric field
phase He-McKellar-Wilkens (HMW) 1993-1994 (Maxwell duality)

Notes based on dissertation abstract and also text starting on p.104

The vectorial Aharonov-Bohm effect occurs when an electron or other charged particle propagates in an interferometer whose arms enclose a magnetic flux e.g. a solenoid of infinite length with the magnetic field being strictly confined inside the solenoid.

Although there is no magnetic field on the trajectory of the particles, these will be dephased with the phase being dependent only on the strength of the magnetic field (and not for instance on the velocity of the particle). It is demonstrated that the phase is due to the electromagnetic potential vector.

The Aharonov-Casher effect occurs when a neutral particle which constitutes a magnetic dipole propagates in an interferometer whose arms enclose an electric field.

By applying the Maxwell duality i.e. exchanging magnetic and electric fields, a different phase, the HMW phase is observed when an electric dipole propagates in a magnetic field.

With reference to the HMW phase, a configuration has been proposed for a radial electric field of the interferometer which polarizes the atom (cf. polarizability).

## Ramsey interferometry

Ramsey interferometry, also known as Ramsey–Bordé interferometry "is a form of atom interferometry that uses the phenomenon of magnetic resonance to measure transition frequencies of atoms. It was developed in 1949 by Norman Ramsey [2] who built upon the ideas of his mentor, Isidor Isaac Rabi, who initially developed a technique for measuring atomic transition frequencies. Ramsey's method is used today in atomic clocks and in the S.I. definition of the second. Most precision atomic measurements, such as modern atom interferometers and quantum logic gates, have a Ramsey-type configuration [3]. A modern interferometer using a Ramsey configuration was developed by French physicist Christian Bordé and is known as the Ramsey–Bordé interferometer."

Rabi oscillations

A beam of atoms are sent through an interaction zone of length L where an oscillating magnetic field is applied for time τ. The atoms are characterized by a transition of energy h ω0 (where ω0 is the Larmor frequency which is equal to ω0=γB with B being the magnetic field). They will perform Rabi oscillations with a frequency of Ω=γBv

Ramsey interferometer

Two very short interactions zones are used, each applying a π/2 pulse. Ramsey fringes are obtained.

Ramsey–Bordé interferometer

Measured effects:

Polarizability, Aharonov–Bohm effect, Sagnac effect

Figure: Ramsey fringes (from Wikipedia).

## Atomic clocks

How atomic clocks work (NIST)

https://www.nist.gov/news-events/news/2014/04/nist-launches-new-us-time-standard-nist-f2-atomic-clock