My photos actually on searches from black holes to the basement. As you'll see, the basement includes basements here in Oxford. And there are a lot of Oxford connections for the research I'm to tell you about. Yeah. So this topic is how to discover fundamental so not in the current condensed matter context that just told us about fundamental axioms. Axioms. Why should you own or actually own some string theory or axiom like particles?
And there are a huge range of possibilities for searches, for axioms. This is actually an immensely growing field. In fact, over the last ten years there have been literally hundreds of new experiments and observations suggested. And so this is one of most exciting fields of experimental physics, experimental astrophysics and cosmology. So here is the axiom math I'm always going to call the actual mass you saw by here in TV.
And this a very wide range of masses. And actually this is only a subset of all the possible mass is the axiom could have you say many of magnitude and every one of these things is a different experiment or observation or test you can do. So it's really quite incredible the range of things. And I'm going to tell you about two particular bits of this diagram and two particular things. So I want to tell you, just remind you just a little bit of actions. The things can be important for us.
So as Joe explained to us, actually expected to often be very light with mass is much, much below the electron mass, let's say. And as you showed on this diagram for I was looking at a lot of axioms, what may be one of your ten to the minus ten TV or even lighter axioms. Right. And also expected and constrained to be very feebly interacting. So that's the two things. They're very light, they're very feebly interacting. They also have a whole variety of types of interactions with normal matter.
And I'm going to discuss those types later on. Okay. Now the key see the axial has this formula for its mass which were like this scale fe sometimes called the axis on the constant or something like this to the axial mass. So there's a definite relation. So for instance, I took for you to be ten to the 17 gives a large scale that's close to the unification scale. Then the kicking axial mass will be this tiny number.
And if and later on you'll see it's useful to express this in terms of distances. So the in terms of distances, this constant wavelength is three kilometres, three kilometres inversely, right? So the constant wavelength would be three kilometres. Right. And that's going to be interesting for us. And this formula was first really written down by Weinberg and we'll check in the very famous papers in the late seventies.
So this scale, if I use large scale, also suppresses all interactions the action by one over five factors. So correspondingly because the scale is very large constrain to be very large for fundamental actions, this is a very feebly interacting particle. Okay, now this is the relation for the Q, see the XY on axial like particles of generalised.
You see the action like curve very often in string theory share many features of the action, except they don't have this tight relationship between mass and this this scale, this strength of the couplings. Right. That's violated or broken. Right. So Axion, mass and Axion interaction, strength for this scale and our independent parameters. And that's the thing I want you to remember about. So back to the huge range of possibilities.
They come in broad categories. We could do collider experiments with new particles and fact. How this is the original. Weinberg We'll check axioms look for in fact the original proposal. Weinberg would check what they thought the mass of the actual might be was rolled out very quickly by precision. Experiments are colliders. There's also either astro or cosmological observations. Well, we can either look for new particles, new forces, or it could be the dark matter, as you'll see.
That's a very interesting possibility. We can also do lab experiments looking for new forces. Or again, it could be that this axial natural light particles of the dark matter and we see that's a very exciting possible the in fact, there's a whole range of other things here. All the categories even I'm not even go into. So I'm going to focus in this talk on two things. I'm going to focus on what is a very interesting astrophysics constraint on new particles.
It doesn't have to be the dark matter. All right. And I'm also going to go in the second half of my talk lab experiment, searching for Axion dark matter. So I'm going to tell you two different things and those are particularly interesting. One, well, they are strong also connections with both of these things. That's nice. But also on this diagram, the astro thing involves black holes and you see this a very strong constraint. This goes down to even very, very tiny couplings.
And actually, if this thing was to extend off further to the left in mass, it would go down way lighter ranges. So it's a very stringent and very good constraint over a lot of parameter space. And the other thing the lab experiments impacts on dark matter also are very sensitive. So you see most of these things are up here, but these are some of the things that go down towards this action of the action line.
So this strong relationship between mass and coupling strength is this line here for the case of Axion outs can live anywhere in this diagram general out of 50 actually is here and these experiments are some of the few that get down to sufficient sensitivity. So I'm going to tell you about these two classes of things and the very interesting new physics and thoughts. What's going on here, both theoretical and experimental. So first, the astro constraints.
So it is a very remarkable statement. I'm one of the people who came up with this. I'm with my friends on the West Coast in the States. Remarkably, astrophysical black holes provide a way to search for light actions, and this search only depends upon their absolutely mandated gravitational interactions. So this, in fact, doesn't use any of the weak couplings. Right. The only thing it cares about is the fact that you interact with gravity and everything interacts with gravity.
We're going to use that. This is very powerful. In fact, you can be used to search for any light particles. With one caveat I'll tell you about. So we're going to use what we now know exists. And I'm doing this, which is black holes. I'm going to tell you about black hole, super radiance or an acciones or black holes as nature's detectors. Right. So we know now remarkably, of course, that as fiscal black holes exist, we see advanced like I have seen gravity wave signals from merging black holes.
We have a whole family of mergers of different black holes, masses. We know actually that there are lots of different black holes and binary black holes existing in our universe. And we know that the short idea the size of these black holes varies from a few kilometres for solar mass black holes up to 10 to 10 kilometres for the biggest galactic centre black holes. So some of these things can be unbelievably huge this few kilometres.
Remember I gave you this for three kilometres? What the quantum wavelength for the Axion might be. In certain case, that's going to be an important, quote unquote coincidence. All right. So moreover, the black hole has filled. Black holes are rotating. They're always cur black holes. They always have some angular momentum. And how much the rotating is quantified by this finger's spin parameter. A star I'm always going to call the axis on this the I right.
A star is a different thing. It's the spin parameter for black holes. And this is the angular momentum of the black hole divided by G. Newton and the mass of the black hole square. And this is a useful variable because I start being zero means they're not rotating at all. An ice star equals one. Is maximum rotation the maximum you can ever rotate? This is where effectively the black hole horizon velocity is is the speed of light right going around.
And we know from measurements this is for galactic sort of mass, this is for ten to the six up to ten to the nine. So low mass black hole so so galactic centre black holes. People have done measurements, this band parameter and you see that a very often very high above 0.9. Right. Some of them up to a point. 6.8. Right. And so we know, in fact, there many black holes are in fact relativistic, like rotating, which is a quite incredible thing.
So black holes contain a huge amount rotational kinetic energy. It's a wonderful, remarkable fact with this angular momentum they have and this rotational kinetic energy can be extracted.
From a black hole. In fact, of our very good friend Roger Penrose show that there is this classical Penrose process and its close relatives and it can extract energy that he was proposing back in, I think, late 1960s when I wrote this paper that maybe advanced civilisations would power their civilisation by doing this process, sending in stuff, gathering things, split, extracting the energy, setting angular momentum.
And maybe this our balance of power relations ultimately would power themselves. However, I'm not interested in this process. I'm interested in a remarkable quantum process that occurs. So if you have a non-zero mass, it's very important that it's not exactly zeroth, a non-zero mass feebly interacting. That's also important. It can't be too strongly self interacting.
Right. Bose on. So Bose wants let me remind you of spin zeros and ones with two in each of our equals one units and most historians and I'm going to say H by two one and C equals one just to drive, you know, many of you crazy as the units in which I think and I'll put some balances back right at the very end, then there's a process called quantum super radiance. In fact, super radiance, the thing that occurs in many, many different domains and has many different guises.
But I'm going to talk about a particular thing. So what does this quantum super radiance in words do for you in a black hole environment? Well, what it does it say is a cloud of both zones. In a nonzero angular momentum, bound states around the black hole grows exponentially, actually, due to a form of lasing instability of this curve. Black holes. You start off with this curve, black hole. Let me show you in pictures.
All right. Here it is. Here's my black hole. It's got some large angular momentum. It's highly spinning. Spin parameter is near one. All right. And what happens is there's a quantum instability of this where a cloud in a bound state of like feebly interacting particles. Ross actions is formed outside the black hole. And this thing extracts most of the angular momentum of this initial object, not all of it, and extract some percentage of the mass.
So the initial mass energy of this black hole and puts it in this region exterior. And so the end situation is some part of the original mass has gone into the cloud and a lot of the angular momentum has gone into the cloud, this axial cloud. Okay, this is quantum super radians for spinning black holes. Now why does it occur? So I can say this a little bit more mathematically.
And the reason is this. If you study the the quantum mechanics of a massive Bose field right in a black hole background, you find that it has bound states with with where they don't have purely real energy eigenvalues. All right. Remember, if I take you back also to trigger warning, second quantum mechanics, hamiltonians emission or the eigenvalues of the emission operator are real subtly because of the weird boundary conditions that black holes have. They're absorbing boundary conditions.
This Hamiltonian of the system is not emission, and correspondingly you can have imaginary parts to its eigenvalues. And in fact it has an imaginary part of the energy eigenvalues which is positive, right is gamma is and the decay rate is negative, KMP is negative.
And this leads when you write down mode squared or the Y function to exponential growth in time of this this cloud because we're solving this weird non commission quantum mechanics problem, this, this behaviour was first realised by these people. Press them to tell it to Koski and to more and zeros Erdely and Detweiler and various other people. They thought this was just an interesting, formal, you know, statement quantum mechanics in this background.
An important part of this thing is these states here, the spatial wave function here. So this is exponentially growing. But this spatial other state is very similar to the. L greater than zero orbitals in the hydrogen atom. Looks like these you know these beautiful diagrams I'm sure you see when you do quantum mechanics, the hydrogen atom or chemistry. Quantum chemistry, they look like atomic orbitals, right of non-zero l. Now. Why does this occur? All right.
Why does this feature occur? So here is a particular coordinate system called the tortoise core, and that which is very useful describing because it's right outside a black hole horizon. So the black horizon is way, way off into the left here. And here is the potential a massive particle sees in this in this background, when you translate it to an equivalent quantum mechanics problem.
Right. So what happens is this region here, the ergo region, which Roger Penrose used to do, is classical energy extraction. And Anglo American extraction is a barrier region. This barrier is due to states having nonzero angular momentum and also L.Z. All right. So, you know, the Z component, the Angela mentum operator as well, and this this cool Coulomb like rise of the potential here is due to the mass of the particle. So so if a mass was zero, this wouldn't be this rise wouldn't be there.
So what you see is because of the combination, this barrier and this rise, there's a little well here. All right. Which is interesting. And when you compute the quantum mechanics, this problem, what you find is you find quantum fluctuations of the of the Axion or whatever feeble interacting light particle you have here called sort of anti tunnel or tunnel through this barrier region and lead to this exponential growth of bound states,
which have a tiny, tiny little tile here in this region here. But in fact, the dominantly located in this potential well region. So this is if you're thinking about short SR radii, this is sort of like one and a half to two short, short radio away from the black horizon. So a black hole that size, this size, this cloud is sitting a little bit outside, right in a region displaced from this. And you find this is exponentially growing. Right.
This this this wave function. So you can calculate the analytically, numerically the growth rate for all the various atomic bound states, a function of the black hole speed parameter. And what you find is you always find the fastest growth rates for high speed. The growth rate goes down a lot as you lower the spin. So I'll show you that in a second. It also is a function of the the mass of your light particle times, the gravitational radius of of your black hole.
Remember it spinning. It's not quite the short of radius, but something like it, basically. It's this, though. That's the thing. This is a dimensionless number, this thing of a mass times a distance. So you can think of this also as a ratio of the short, short radius of the black hole to the Compton wavelength of your particle. And what you find here. So here is log scale of this growth rate normalised to the mass, right?
And so you see this thing is varying as you vary. Various things are here on this scale. Here is increasing axial mass linear scale. So here is 0.1.5. Here is point two, here is 1.8 varying the axial mass varying this ratio of gravitational radius of of the black hole to the same wavelength. And you see you quick, very quickly grow and then you fall off. That's a so optimal region you get. This is four different bound states.
The leading state, the one where you super radiantly produce most is the l equals one. M equals one state, the simplest of the hydrogen like orbital.
And then as you increase the black hole spin. So these colours here, this is the really high speed black holes like 0.99, you know, and it's like go down in spin then the growth rates decrease with I said so the dominant thing is I, I dominantly produce acciones will be when the mass is is about 0.4 right of inverse gravitational radius of my CO and I dominantly produce the things when the black hole is my spinning and I slow down a lot as I move away from my spin.
Okay so this the bottom line of this is this is only a fast process for a massive field with Compton wavelength close to the black hole size. Right. That's the answer. In fact, you can look at the two previous timescales, how how for astrophysical black holes, how quickly does this process occur? Let me look at the high spinning highs we saw. We know that black and centre, black holes of high speed and things like this.
So let's look at this high speed case and you find an optimal match between inverse Compton wavelength and the gravitational right, as when this thing is about point four for the leading atomic so bound state, and this timescale turns out to be this. I've written this and C equals one unit so length so the same as times here. So it's about it's almost 10 million times the light crossing time of the black hole.
So in terms of the natural timescale of the black hole, light crossing time of the black hole, this takes a million times or 10 million times longer. So it's slow. But compared to astrophysical and cosmological timescales, in fact, this is very show. This is as short as 100 seconds. Right. Compared to the age of the universe, which is ten to the 17, you know, ten to the 18 seconds. Right. Or or accretion, which takes the place of a black hole ten to the 15 seconds.
So this is a very fast process compared to the universe or anything. Astrophysical, right. And it happened, but it's a slow process as far as kind of minimal timescale it could be, which is like crossing time for the black hole. And as you go away from this optimal coincidence here, you either get exponentially suppressed or polynomials suppressed. All right. And that's what you were doing. These are the analytic formulas you can derive according to the graphs previously.
So bottom line for this is you get fast, black hole spin down. If there exists a boson of the right mass and right mass means, you know, close to this and you can go refactor a few less and a few greater and still have a fast enough spin down. But once you go say a factor of 100 either away from this, then the spin down rates become so low they don't occur in the age of a galaxy.
All right. Now, Astro black holes have have radii between a few kilometres and 10 to 13 kilometres so they can thus act as both produces via this quantum super irradiance instability and detectors. And you'll see how you might do that in a second of light both zones. And if you match these radii up with these with the masses to get this coincidence in Compton wavelength and radii, you find between ten to the -20 V and ten to the -21 Eevee.
So it's 11 orders of magnitude in mass where any light particle which is weakly interacting as long as it's strictly massive, you can produce and try to detect by this process. That's very remarkable. But let's step back. Let's ask what this is. This thing is done for us. So what we've ended up with, if you think about this, is we've ended up with a quite extraordinary statement that there should or can exist gravitational atoms in the sky.
Right. But rather than having, as you would have for a normal atom with electrons, we would only have. So you can see to spin up and spin down electrons in each possible orbital because these are both states. Now you can have arbitrary large occupation numbers. In fact, they're favoured right by Bose in usual Bose statistics argument. In fact, the occupation numbers of this leading state can be as high as ten to the 77. All right. Truly vast occupation numbers. All right.
In this in this leading state carrying possibly four galactic black holes, ten to the eight solar masses worth of mass energy and true and truly vast amounts of angular momentum to. Now, as I said, it's rather important. I didn't mention this caveat.
It's rather important that actually just particles of people interacting, if you turn on self interactions of these bosons or interactions, these photons with other things, in fact, this this exponential growth of this bounced light outside the black hole could be quenched, right? And so you can limit the cloud to small occupancy and you don't get any interesting signals. So you only get this maximal process going up through these kinds of occupation numbers for feebly interacting bosons.
And of course axioms are a they are probably a leading example of something that we think is should be very light but but not exactly massless and also feebly interacting. Right. That's why this is an incredible possibility for action. Such as. So I've argued to you. The Astro Blanco should can have clouds around them. Containing lots angular momentum and a fair amount of mass. All made up of these actions in this cloud like configuration. Well, okay. So what does this cause for you? Right.
How do you see this? What do you do with the test? Well, one test is if you now look at the spin of the black hole itself, there should be regions as you as you look at black holes with different masses. Right. If a black hole happened to be in the region, has this nice fluorescence effect with an axis on the Compton wavelength that all those micro should be spun down. You shouldn't see any high spin guys. For certain regions of black hole mass.
There should be always gaps in the black hole mass. Spin plot. Right. Another thing is this. Well, zoned cloud now modifies the metric around the black hole. It's a black hole in an environment where I've put a lot of mass and angular momentum out there in a quantum state out there outside of my call. And of course, we are seeing black hole mergers through advanced lingo. And so if I have, you know, one of these two black holes has this cloud around it and the second black hole spirals in.
In fact, you would change the spiral signal in delicate, interesting ways. That's another thing you can see. Another thing you could say is just like Joe spoke about in his talk, you could get actions if there's magnetic fields around and there's many fields all over the place in in astrophysics. Right. Then you can get Axion photon conversions. Now, these photons turn out to be of a sort of annoying frequency, very often hard for us to see on earth.
But do we ever have good radio telescopes on the surface of the moon, dark side of the moon, which be a wonderful thing. Maybe that's a good reason to have a moon base. I mean, other things. Just talk to Elon Musk and get him to fund this. We have a radio telescope. We have that possible for us to see such things. That's another possibility. But one of the one of the really, really striking things you could see is you could say monochromatic.
So not a broad spectrum of gravity waves is what we now see in advance logo but monochromatic gravity waves from stellar mass black holes. Right. And the idea here and this was mentioned in our original paper and then studied in a very beautiful follow up paper by Mina and Serguei. In this paper here, you can have these actions, a member or an l equals one orbitals, right?
So one unit of each bar of an aluminium each. You can have two axioms meeting this means the so background metric background gravitational field of the black hole and you can have a process with two actions in this background. Gravitational field can produce a graviton. This graviton carries off two units of angular momentum to a bar that agrees with the two.
What I get from these two axioms, each in the open line commitment states and the graviton energy is at essentially twice times of the mass of the Axion. And you get this monochromatic line, right, which is this sort of frequency, ten kilohertz going down and going down to lower frequencies as you make the axial mass less and less and less. So this and in fact, you could possibly see these lines even in quite distant black holes.
And this is an incredible possibility for the next generation of gravity waves, detectors, that humanity is building different frequency ranges. So the signal enhanced, well, one, you might think, oh, god, how could how could this ever be a fast process? You know isn't there you know factors of one over implying Koji Newton here that's making is really slow.
Well yes but that's true but the the occupation number of these initial states a huge ten to the 77 and these ten to the 70 sevens in fact enhance this signal by square of this state occupation number. So even though this is a this is a almost a quantum this is a quantum gravity process. You're producing a quantum of gravity gravitation here. In fact, it's enhanced by the incredibly large occupation numbers.
Right. So that would be another amazing thing. So you could see like vast numbers of that. You'd be seeing actions, you'd be see you can some aspects of quantum gravity, you'd be doing other tests, you know, you'd be doing something once you saw monochromatic. Let me remind you that we get an immense amount of information about our universe, our world. One of the reasons is from observations of spectra. One of the great things is that Spectra is discrete. All right.
The fact that we saw Obama theories and other things all over, you know, in the universe, we saw it in our sun and we saw it in distant stars, and we can match things together. We could get a tremendous amount of information from the redshift, bit of hints and other things. This discrete. This is another extraordinary thing. Well, there's many, many other signatures of of axioms in astro cosmological environments being an activity by groups all across the world.
It's really quite extraordinary. Rich Field And Joe has already told you about some of the things you can do. But I now want to turn from the sky to the basement, including our basement here in in Clarendon and in the Beecroft. So this is going from this is the black hole spins thing. I've just told you this constraint which carries on down here, and then there's this region here. Right. So I want to tell you about that. So how do we search for feebly interacting actions in labs?
Well, the interactions of the leading interactions of actions with ordinary matter come in three basic forms. There's a thing that both Joe and Sid told us about, which is the action a dot be interaction with electronic and be filled. There's also an interaction of the grade into the Axion with Fermi on spin, whether these could be any fermions electron, proton, neutron. Notice the gradients. This is about some sort of Axion variation. All right. Sometimes it's called the second wind coupling.
And then finally, there's this thing which is special for the quick action, which you can give a thing which is dependent on the electric field. This is an electric field that the nucleons spin. And this can give what will be a varying or time varying electric dipole moment of some objects. Right? So these are three basic things. All of these couplings G, Gamma, Gamma, GIF and GBM, all of these couplings go like one over this far, this large scale.
They're all very tiny couplings. All right. But this is the sort of form that they have. Now, the most commonly used coupling is this action in dot B, electric field, dot magnetic field term. And I'm going to talk about this to both Sid and Joe mentioned this, so I'm going to talk about the use of this. So I want to give you some little bit more intuition for this term. So there are various ways of thinking about this, this term.
So if if both I, the Axion and the and B fields are well described as classical fields, of course, we always usually think of EMG as classical fields. But of course, you know, this photons, we could in principle have discrete packets of of of electromagnetism as well as the continuous classical fields. But if there is the world's most classical fields, then this new term here, this term modifies a Sid.
Explain two of Maxwell's equations and you get Axion electronics, which I believe was first written down by C Kivi and then we'll check over a series of papers and study and here it is. Here the there's two Maxwell equations that stay exactly the same and then you get these two mode of modified Maxwell equations. So this is Dave of the electric field is the normal charge density. So Rho and J here just the normal charge density and current of normal matter.
And you get these extra affective terms. Here we go. Like, gee, I'm a I'm at times derivative of the Axion rather the action dot B or this thing here time to reflect sometimes B and then this thing, which is a curl. All right. Okay.
So what does this mean? Well, if you think about this, I could define as an experimental is I could define everything that occurs on the right hand side of this equation is an effective charge density and everything occurs on the right hand side of this equation is an effective current density. So what it says when I think about this in the presence of any field, the action is a new kind of charge density which is this and a new kind of current density, which is that.
And you could try to look for these new types of charge density and current density. On the other hand, that was for classical things. If one or more of Axion or the field of the B field is the quantum limit, so Axion control and or photons, then it's useful to think in terms of Feynman diagrams. And here's a FINEMAN diagram game. Joe, use this. So here's the incoming action of Quantum of Energy Omega. Here's a background classical B field. All right.
The reason why I'm going to focus on the B field cases that large B fields are very easy to produce in the laboratory. Large E fields are hard to produce in the laboratory, at least macroscopic ones. So here's a large B field, and then this, then this new terminal constant. I b gives you a new Feynman diagram, which is Axion quanta comes in and produces an outgoing photon of energy omega. Okay. So you get axial photon conversion, as Joe described.
So we can try to use this coupling to try to detect actions. So these are very. So one possibility is we detect these very tiny new charges in current cells by the actual field of presence of A and B side by detecting anomalous heating of a cold, shielded cavity, I give you a cold shoulder cavity and I say that some sort of axial is coming in and it should be dumping because it generates currents and electric charges.
It should be dumping electromagnetic energy inside this cold cavity. That's one thing. There's there's also the quantum version of that. Or almost equivalently, you try to detect these very rare photons that are being produced. So by Axion Quanta in the presence of the B here you detect anomalous photon counts in a cold shielded cavity. Okay, so this is the idea. But there's one major thing I haven't told you yet, which is where do these actions come from?
Where do these initial axioms come from? In a black hole case, the black hole itself producing axioms. Right. But I'm assuming I don't have a spare black hole just hanging around the lab that we great piece of equipment to have. But sadly, you know. So one very important possibility is the axioms could occur naturally be produced in the early universe. And this was studying two very beautiful papers by press, quoting wires and evidence giving back in the early eighties.
In fact, the QC, the Axion and also Axion like particles are probably now a leading candidate for dark matter. They could be the dark matter. And I'm not going to tell you about all of these dark matter production mechanisms. That would be an entire other talk. All right. Actually, many talks, but I'm just gonna say it does exist. There's a beautiful set of mechanisms. It would use axioms. Does that not matter?
And it could be. That's what they are. Ex-cons are excellent automatic candidates as they're very feebly interacting. So that dark. Right. And that's what we mean by dark. They're very long lived. They're still around today. I don't care why that would be bad if we had lots of decaying dark matter. You'd already gone. And they have nice production mechanisms that leave them cold.
That's important. That means cold means non relativistic, the moving non relativistic clean out around in our galaxy and in our universe. And that's necessary for successful galaxy formation. So axioms are great dark matter candidates. However, there's one thing I should say that's important to bear in mind. The Axion dark matter is better described not as individual, usually think of dark matter as being lots of particles moving around.
Occasionally it hits you or one of your nuclei and you get some signal. But in fact, because these actions are so light as you just create the mass of dark matter, since we know it has a different given mass density as you decrease the mass of these particles, given the fact you had a fixed mass density to be the dark matter, the number density has to go up and more of these particles.
And moreover, as you decrease that mass their Compton wavelength and also the de broglie wavelengths get longer and longer. So as you just create this mass of the particles, what happens is they're the broad wavelengths very strongly overlap with each other. And this limit when you have a very, very large occupancy per quantum state, the way of saying this is best described as a field.
So in fact, here is the sort of a plot of the of bosonic dark matter landscape wearing with mass is normal wimps. These are now slightly disfavoured and here all the way down from one ivy down to ten to the -22. B If you have bosonic dark matter in this range, then it's best described as the classical field. Right. And it's because the number density which is given by this is much, much bigger than one over the wavelength.
Right. And this is when the mass of the particles is about roughly less than one anything. Right. So this should be described. You should think of dark matter as a classical field that everyone. Now. What is it? Friends, it's everywhere. Prisons is a classical field where these actions are known relativistic, so dominantly oscillates at a frequency set by just the mass. For the first time this talk I put back the C and H, right.
I've turned it on. So here is the frequency term of the Axion field just generate mass. That's because it's basically almost stationary. It's not quite stationary though, because there is some known velocity dispersion of of matter in our galaxy. Right. And so this thing actually means that this field is not perfectly temporally and spatially coherent. It's a it's a quasi coherent Axion field.
And moreover, this frequency that it's normally oscillating at again is this frequency by the axial masses. Amplitude. How about the amplitude of this field? It's set by square root of the dark matter density and the and the axial mass. We know reasonably well up to about a factor of two or three what the dark matter density is and all galaxy. Right. So here's a picture that I drew for some lectures I gave her. He is asked, moving through a random Gaussian field of of actions.
And here is us on the earth, on some experimental lab, and we're moving through the galaxy. Our speed through the galaxy is roughly ten to the minus three at the speed of light. So we are moving slowly through this, slowly moving and varying quasi coherent action fields. This blue and the orange is supposed to do difference coherence patches of the axial. And here is a translation time between the mass. The action is frequency and experiment.
We looking for the the coherence time experiment earth would have and here is the coherence length for these patches. So for instance, if I'm shooting an actions with ten to the -40 V, I get a coherence length which is sort of like maybe ten or a few metres. I get a coherence time, which is something like ten to the minus 4 seconds. Right. And I get a frequency which is sitting up at ten to the ten hertz. Okay. So ten gigahertz. That's the end of the dark matter.
Almost done. So now we know where the Mexicans are coming from. They're coming from the dark matter. And they're not relativistic. They're slowly moving. So how exactly do you search for dark matter axioms when you search for dark matter? Well, it depends, actually. Which dark matter Axion, Mass you're looking at. Technologies vary a lot as you go from one frequency range to others. This comes from a very nice report that was done by the DOE a few years ago. Think about these technologies.
So here gigahertz microwave cat is here a megahertz circuits magnetic resonance atom in parameters right here is on the it varies. In fact there's a very wide range of quantum technologies can be used to actually on detection. I'm going to focus on, well, two things. Oxygen's involved in microwave cavities and almond promises. And in fact, these are two of the leading technologies. I might tell you five times just one other thing.
So here is the basic idea that comes from a basic initial proposal, security back in 83. But finally it's actually being realised and getting to the sensitivity you need to search for actions over a wide range. Here is a cavity you put on. A strong magnetic field is a classical, classical magnetic field. You keep this cavity extremely cold. All right. An axion comes in from the dark matter.
You can think of it because it's a quasi coherent process. In fact, if you leave the experiment waiting for a while, you can build up the signal. Also, because this is a this thing is a quasi coherent field, almost oscillating at a single frequency. You can do high CU resonance enhancement of the signal. So we're going to use the fact is a high queue cavity as well. So you produce really a photon or another way of seeing that is you choose excess power.
So what you do is you then using actually hopefully better than quantum noise, limited amplifiers, squeezed state things. You mix this thing down to a frequency and fast for your transform this and you see the power spectrum of this thing and you hope to see a little excess power somewhere. Right in this corresponding to the action, dumping, anomalous heating inside your cavity. Now. How can you tell if you saw a signal? It's not just some mess up, you know that some suspect.
Well, this thing has. If you turn the field off, this signal should go away. That's one thing you can do. Another thing you can do is you focus. Once you start seeing some excess power, you do even higher IQ cavities. And now you can scan the line shape. And this line shape here actually is predicted to have a definite shape, not absolutely known, but this line shape depends upon this thing, which is the way that the galactic galactic velocity dispersion is.
We know some things about this, not everything about this. So we have some idea about the line shape. In fact, there's a number of other tests you can do which could test that this was truly an action dark matter signal and not some sort of other systematic. Right. I want to emphasise this is resonant conversion of the axioms, which is why it's raining. So this is just like you exit excess v dependent power of a particular furniture.
Now, how much power are we looking for? We're looking for extremely small access power. In fact, of accused. Here is the formula for the expected power. And one of these cavities. He's a 30 metre cavity. Quality factor of the cavity of ten to the five. I should say the sort of line of natural line width is expected to be about ten to the minus ten to the six to the minus six. So this is we are doing slightly broader than the actual line of ten Tesla magnetic fields, which you can now achieve.
Here is the of the power expressed in terms of what the Axion frequency is. Let's say that one gigahertz is a particular choice that gives you the actual mass and you see, but this number is ten to the -23 or few times to the -23 watts. So this is incredibly small deposition or or if you want to take the vote on term, incredibly rarely do you see an excess photon sitting in your cavity.
So it's obviously essential to maximise B field strength cavity parameters and very much minimising thermal and quantum noise. You have to go beyond really standard quantum limit to do this. But finally, over the last couple of years, the experiments worldwide are now reaching the sensitivity. The one fly in the ointment is that they're resonance searches. And that means you do one frequency band, which is pretty narrow. But we don't know where the axial mass is. So you have to step through.
And at the moment with with it's just a flame consuming thing at the moment. The rate of scanning at the moment, we're going to take maybe tens of years to cover, you know, the full range. We would like to speed it up. So a lot of the ideas we're currently working on is how to do the scanning better. Right. And I'll show you one issue with the scanning right at the very end. Right. But we're getting there and. Now. Very nice final statements.
Fortunately, the UK for a long time wasn't really seriously involved in this, this particular kind of actual search, to my great sadness. But in fact, we're now involved in a major project in the area called Quantum Sensors for the Hidden Sector, which I'm one of the theorists. I'm just a parasite on them. Clearly, the real people doing the work are people like Peter League and Boon ten, an experiment at Oxford and other experimentalists. In fact, this is our collaboration.
This is a collaboration between Sheffield, Cambridge, Oxford Royal Holloway, Lankester, UCL National Physics Laboratory, Liverpool. Using incredible expertise we share as this combined group, we are hoping we've got a memorandum of understanding with IBEX, which is the current world leading experiment in this area, and we're going to build an even better facility. In fact, we've got government funding for this actually partially due to Ian, where Ian is.
Thank you Ian. For, for pushing the government to actually provide. We course we went through a competitive review. It wasn't fixed or anything like that. We went through it. But the government actually provided £40 million for quantum technologies for fundamental physics.
Right. And then we're using some about £7 million of this to do this, what we think is going to be a world leading to the actual out search, maybe also another type of hidden photon, a possible in a certain mass range, which is sort of complementary to the idea mixed mass range. So that's this here, this is actually a picture of the AB Max experiment when I mentioned the problem is is scanning how do they change the resonant frequency of the cavity?
The way they do at the moment is you have these incredibly precisely machine bars that you physically move around in the cavity and this changes everything slightly the rest of the modes of the cavity and their resonant frequency. But this is a mechanical way of tuning, so you can imagine that you have to do these incredibly fine scans. This this is the real time, but this is the best thing that was known how to do this five years ago.
We're now thinking about new ways of doing it, which are using quantum electronics to do the scanning. Okay. So that's a new progress. So this is my conclusions. As you've seen from all three of our talks, I hope, in fact, there is a vast number of new experiments and new theory ideas and axiom physics worldwide.
In fact, I think this is one of the most exciting and active areas of all of combined theoretical experimental physics, and I wouldn't be at all surprised if there was some very interesting things happening in future years. I mean, big surprises. So please stay tuned. Thank you.