Two slit interferometry – the fully quantum edition

 

Today, I want to write about something a bit different – a unique 2-slit interferometer (aka the double-slit experiment).  In the standard 2-slit interferometer, a beam of photons, electrons, ions or whatever spreads out and passes through two slits.  The beams passing through the two slits recombine, producing an interference pattern.  You might have seen this demonstrated in high school or college, but the basic idea is pretty straightforward.

Some standard elements of this are that the source is a single beam, and then that the beams recombine after passing through the two slits.  Today, I want to discuss a unique version of this experiment that lacks both of these elements.    

This interferometer consists of two relativistic heavy ions that encounter each other at a collider.   One ion can emit a photon, which can then scatter off of the other ion, and emerge as a particle – this can be a rho⁰, phi , J/psi or other vector meson –particles with the same quantum numbers as the photon.   At low transverse momentum), we cannot tell which nucleus emitted the photon, and which is the target.  Quantum mechanics (QM) tells us that these two possibilities can interfere with each other.  Because vector mesons have negative parity, this interference is destructive, and the production rate goes to zero as the transverse momentum approaches zero.  This suppression was experimentally observed by the STAR Collaboration back in 2009.

One important point is that the two ions come from completely different directions and share no common history, so there is no single source!  Instead, the two sources are synchronized in-phase by the symmetry of the problem. 

Another unique feature is that vector mesons are very short-lived, with the rho⁰ lifetime about  10^-23 seconds, so that, even moving at the speed of light, a rho⁰ travels about 1 fermi (1 fermi = 10^-15 m) before decaying.  This is far less than the minimum ion-ion separation, which is about 15 fermi.   When the rho⁰ decays, it produces two charged pions (pi⁺pi^-).   Because of the near-immediate decays, the two ions are essentially sources of pion pairs.

So, any interference pattern can only appear much later, when the pi⁺pi^- amplitudes overlap.  However, the p⁺ and p^- go in nearly opposite directions, and are well separated by the time pions from the two sources can overlap.  In short, the only way for this interference to happen is if the amplitudes summing and interference appear long after the rho⁰  decays, and the system has spread out.   Strange as this sounds, this well explained by quantum mechanics where the wave function collapse occurs when the interference is observed.   The question of when this observation actually occurs is the subject of debate, but one can think of it happening when the pions interact in the detector.  The figure below nicely illustrates these points of the interference.  

 Why am I writing this now?  Four colleagues and I have written a long review paper discussing this interference, which has just been published in Progress inNuclear and Particle Physics (with open access); it is also available here onthe arXiv.  The article also recaps the data that supports the existence of this interference - both the suppression above, and some interesting angular effects.  

Many aspects of this interference may be somewhat counterintuitive.  However,  they are in accord with the ideas of quantum mechanics, and, more importantly, are well supported by data.  So, they are useful descriptions of the way that Nature works.

Enjoy.  

Neutrinos are lighter

 One of the biggest questions in neutrino physics is: how heavy are they?  We know that there are three types of neutrinos, associated with the electron, muon and tau leptons.  By observing their oscillations, we can observe the mass differences (actually, the square of the mass differences, so we're not sure which is heaviest) between these three types.  However, their actual masses are still unknown.  

Over the past few decades, we have worked to measure their absolute masses, but so far have only determined a succession of ever-more-stringent upper limits.  Most attention is focused on the electron neutrino, because it allows for the most stringent limits.  The technology of choice is the beta decay of tritium - an isotope of hydrogen consisting of one proton and two neutrons.  Tritium decays into helium three, plus an electron and an electron-neutrino, with a half life of 12.3 years.  This is a low-energy decay, releasing about 18,590 electron volts of energy.  For comparison, other, more typical beta decay reactions release ten to thirty times as much energy.  Another point of comparison is an old-fashioned cathode-ray tube in a television receiver, which uses electrons accelerated to up to 25,000 volts - more than from tritium beta decay.

In these beta decay reactions, some of the energy is carried off by the neutrino, with most of the rest going into the electron; the recoiling helium-3 also carries off a bit of energy.   Because beta decay is well understood, we can very accurately predict the distribution of energies carried off by the electron; this predicted spectrum has a small dependence on the neutrino mass;.  The number of events where the electron carries off almost all of the energy decreases as the neutrino mass increases.  We can fit the electron energy spectrum in this endpoint region to determine the neutrino mass. 

The KATRIN collaboration has done this, and just released a new upper limit on the electron-neutrino mass; it is less than 0.45 electron volts, at a 90% confidence level.  For comparison, this is less than one one-millionth of the mass of the electron.  It is about a factor of 2 below previous measurements.  The result is an enormous tour-de-force, since the change in the energy spectrum is tiny.  The collaboration used an enormous spectrometer (pictured above) and studied 36 million electrons, which were already selected for being of particularly high energy.  

Although KATRIN will release results with more data, and, likely, a tighter upper limit, this is near the end of the line for the spectrometric approach that we have used for the past few decades.  A better spectrometer would also have to be a bigger spectrometer, and it is just not possible (economically, and probably technically) to build a much larger instrument.  Instead, we are starting to investigate new approaches that involve trapping electrons in a uniform magnetic field, and observing the synchrotron radiation that they produce, using very sophisticated radio detectors.

 

The new neutrino heavyweight champion - part 2

 In October (2024), I wrote about the very high energy neutrino event found by the KM3NeT Collaboration, which is building a neutrino telescope in the Mediterranean Sea, of the coast of France.  Details of that event have finally been published in Nature, with enough new info to be worth a second look.   The event seems well reconstructed as a through-going muon, with a muon energy in the detector of about 120_{-60}^+100 PeV.  Assuming that the muon comes from a neutrino (alternatives have been discussed in the literature, but they all involved speculative beyond-standard-model physics), then the neutrino energy will depend on how far from the KM3NeT detector the muon was produced (they lose about half their energy in 1400 m of water), and what fraction of the neutrino energy was transferred to the muon.   This becomes a fairly complex probability calculation, where the most likely energy depends on the assumed neutrino energy spectrum, but the most likely neutrino energy is about 220 PeV, with a 68% confidence level of 110-790 PeV and a 90% range of 72 PeV to 2.6 EeV (see the KM3NeT paper for details).  These are very high energies; 220 PeV is 30,000 times the maximum energy of a proton in CERN's Large Hadron Collider.

The paper also addresses the question of where the neutrino came from; the sky map below shows the best-fit direction along with the uncertainty contours, along with some possible source candidates. To make a long story short, there are some plausible candidates from near (within the error circles), but nothing stands out as a likely candidate.

 

 

The paper also addresses the tension between IceCube's non-observation of any similarly energetic neutrino and the KM3NeT event.   The KM3NeT paper refers to 287 days of live time, whereas the complete/almost complete IceCube has been taking data for about 16 years.  And, KM3NeT is only partially complete, so it currently has much less sensitivity than IceCube.  The degree of tension depends on many details of the calculation, but it is somewhere between one and two orders of magnitude, or between 2 and 3 sigma.  This is not that likely, but it is also not that unlikely.   And, given that the event looks solid, we will probably have to live with it.

The plot at the top of this post shows the flux calculated by KM3NeT (in blue) along with a 2018 limit from IceCube and another limit, from the Auger surface air-shower array in Argentina.  The points at lower energies are IceCube data, but at energies above 10 PeV, there are only limits.  It is worth pointing out that IceCube has a new limit - available on the arXiv, not mentioned in the KM3NeT paper, that is a factor of 3-4 lower than our 2018 limit, further increasing the tension between the two experiments.