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Jonas Neergaard-Nielsen
Works at Technical University of Denmark
Attended University of Copenhagen Faculty of Science
Lives in Copenhagen, Denmark
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Jonas Neergaard-Nielsen

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Can a single electron be in an entangled state?
Today we have a new paper out, on entanglement with single electrons.

As you perhaps know, or recall from previous posts of mine, entanglement is a phenomenon which is at the heart of quantum physics and distinguishes it from our everyday world. Objects that are entangled behave, in a sense, as if they are a single entity even when separated and manipulated independently. Entanglement can improve measurement precision, e.g. the precision of atomic clocks, and it enables quantum computing.

Usually we talk about entanglement between two particles, considering some property that each particle has. For example, the energy state of an atom here might be correlated with the energy of an atom in another location, such that the two atoms are entangled. But there doesn't actually have to be two particles to create entanglement. One is enough.

If we shine light on a half-transparent mirror, half of it will go through, and half of it will be reflected. So we get two beams of light, going off in different directions. If we send a single photon (a particle of light) towards the mirror it can also get transmitted or reflected. So if we put some cameras in the path of the transmitted or reflected light, which measure whether the photon arrives, we will find a correlation: When a photon is detected in one camera, nothing is detected in the other, and vice versa. If we repeat the experiment, sometimes the photon arrives in one camera, sometimes in the other. We don't know in advance which one it is going to be, but always exactly one camera clicks. This looks like a simple correlation, but quantum mechanics tells us that it is actually something more intricate. When the photon hits the mirror, it doesn't simply either go through or get reflected. Instead, we get a so-called superposition of these two possibilities. Nature doesn't decide which possibility is realised until we make a measurement (for example with the cameras), even though this may happen much later than the photon hitting the mirror.

So, considering the two paths after the mirror, we have a superposition of two possibilities: There is a photon in the path on the right of the mirror and none on the left (say), or vice versa. This looks very similar to entanglement. Entanglement between two atoms happens, for example, when we have a superposition where the first atom has a high energy and the second a low one or vice versa. However, now there is just one particle, and it is not a property of the particle that changes (such as the energy), but instead whether the particle is there at all or not, in a given path. Is this entanglement?

This question was debated for quite a while in the past. By now, it is well established that in the case of photons (light), the answer is 'yes', and in fact this entanglement is useful for applications, for example ultra secure cryptography. We call this kind of entanglement 'mode entanglement'. In the example above, each path is a 'mode' which can contain different numbers of photons, and the two separate paths are the objects which are entangled. These are not two particles - instead the number of particles provides the degree of freedom in which the paths are entangled.

So the question is settled for light. What about other particles? What about electrons?

It turns out that for electrons, the question is more subtle and the debate is still ongoing. The thing is that to reveal the entanglement, it is not enough just to measure whether the particle is there or not in each path. One needs to also do 'in between' measurements, which require the creation of superpositions of zero or one particle locally in the path which is measured. This is ok for photons - it's not easy, but there is nothing in principle forbidding such superpositions, and we can do measurements which are not quite optimal but good enough. But for particles with electrical charge - such as electrons - the situation is different. As far as we know, superpositions of states with different total charge cannot exist (this is known as the superselection rule for charge). So in particular, superpositions of zero or one electrons are ruled out, and it is unclear if it is possible to do measurements which will reveal mode entanglement for charged particles.

In this paper, we argue that the answer for electrons is also 'yes'. We propose an experimental setup, which uses single electrons split on a kind of electronic mirror, in an analogue way to how a photon would be split on a mirror for light. In our setup, the entanglement created by the splitting is revealed without breaking any fundamental principles. We need to use two single photons at the same time, split on two separate mirrors. However, while two electrons are involved, we show that the result we obtain would be impossible unless each split single electron creates an entangled state. So, we conclude that single-electron entanglement indeed exists and is observable.

It will be interesting to see the reactions to this paper. Whether our colleagues will be convinced or not. And if they are, whether someone is up for doing the experiment :).
Abstract: Motivated by recent progress in electron quantum optics, we revisit the question of single-electron entanglement, specifically whether the state of a single electron in a superposition of two separate spatial modes should be considered entangled. We first discuss a gedanken experiment ...
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Loophole-free Bell tests

So I learned today while watching the +Q+ hangout with Bas Hensen from Delft (great talk, btw!) that we already now have 3 different loophole-free Bell violating experiments! While the brilliant Delft experiment used photons entangled with diamonds, the two new ones from just a couple days ago employed the tried-and-tested method of creating entangled photons through spontaneous parametric down-conversion (SPDC).

These experiments, at NIST, Colorado and in Vienna, used SPDC sources of entangled photons and TES superconducting detectors to reach detection loophole-beating detection efficiencies.

The papers seem to be very interesting reads, but while I haven't yet assessed their scientific qualities, here's my extremely superficial review of their level of presentation:

The introductions are great (particularly Vienna's), clearly laying out the deal with nonlocality, Bell tests and loopholes.

The papers are both trying hard to increase their cool factor: The Vienna experiment was performed in the Hofburg castle (probably the first time that night shift security officers are acknowledged in a quant-ph paper!) while the NIST experiment used Back to the Future, Monty Python and the Quest for the Holy Grail and other movies and TV shows to create pseudo-random numbers (making it even more unlikely that the random settings were predetermined)! 

Both papers also have some nice space-time diagrams but the NIST one even has a geographical contour plot!

While the Vienna supplement is rather dull, the NIST supplement contains some awesome timing diagrams. Taking this and their very detailed listing of pop-culture references into account, the NIST paper hands down wins on X-factor.

Finally, the NIST guys are totally nonchalant in their conclusion, stating that their Bell test machine is actually just meant to be a source of certified randomness in their public randomness beacon....
Abstract: We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number generators and high-speed polarization measurements.
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I'm with you on that one!
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"Your quantum future is now" - a vision of how various not-so-distant future technologies could be secured using quantum cryptography (QKD - Quantum Key Distribution).

This video was presented at the recent UQCC 2015 event in Tokyo, held in connection with the annual QCrypt conference.
I don't believe QKD will be as omnipresent as speculated here, but some of the use cases may certainly become reality.


QCrypt/UQCC site:
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Very impressive heart simulation!
Our sister project UT-Heart, a detailed heart simulation, has won "Best Visualization or Simulation award" at SIGGraph 2015 for this movie presenting their results. It's a cool movie.
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If your fridge is quantum and you want your beer cold, be sure to optimize your timing!
Today, with Nicolas Brunner, we have a new paper out on the arXiv: . This one studies the behaviour of a small quantum refrigerator.

Thermal machines - such as the refrigerator which keeps your beer cold and makes ice for your caipirinha, or a steam turbine generating electricity from heat in a power plant - have been studied for a long time. The desire to improve early steam engines led to the development of thermodynamics which is now a very broad physical theory dealing with any process where heat is exchanged or converted into other forms of energy. Thermodynamics now allows us to understand well what goes on in thermal machines.

Quantum mechanics is another very successful theory, which gives us a good description of things on very small scales - the interaction of a few atoms with each other, or of an atom with light and so on. As you may know, on these scales the physics is different from everyday experience, and weird things start to happen. Quantum systems can be in superpositions - the famous Schrödinger's cat which is neither dead nor alive - and can show correlations that are stronger than in any classical system (as I have written about before, for example here:

Usually, when we think about thermal processes, such as cooling a beer, large systems with many particles are involved (the beer and the refrigerator consist of zillions of atoms). It is natural to ask though, what happens when we make things so small that quantum effects begin to matter? Can we understand thermodynamics at the quantum level? Can we still define quantities such as heat and work? What happens to important concepts in thermodynamics such as the Carnot efficiency or the second law?

There is a lot of work going on at present trying to answer these questions. One approach is to go back to the beginnings of thermodynamics - steam engines and other thermal machines - and make the machines as small as possible. Such quantum thermal machines are a good testing ground where ideas from thermodynamics and quantum mechanics can be combined. Our work follows this approach. We look at a small absorption refrigerator consisting of just three two-level systems (think of three atoms) coupled to thermal baths at different temperatures.

This quantum fridge has already been used to find several interesting results, for example that quantum entanglement can improve cooling, and that quantum machines can reach Carnot efficiency. These results were obtained by looking at the fridge in the 'steady state' - i.e. after a long time, when the 'beer' in the fridge is already cold. In this paper, we take a look at the 'transient regime' of the fridge - i.e. what happens in the time between putting a warm beer in the fridge and taking out a cold one. Our contribution is a bit technical. We map out some details of this process and find the time scales for the 'beer' to loose it's quantum character or approach the steady state. Among other things, we find that the 'beer' can sometimes get colder at an intermediate time than in the steady state - i.e. if you want the beer cold you shouldn't leave in the fridge too long. This is a purely quantum effect and that happens to single-atom beers but definitely not to that tasty IPA you were saving for later!
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This is such a fabulous idea to hopefully make kids and their friends more comfortable with a disability.

Also: I so want to mod myself with LEGO right now!
Prosthetic arm for children that lets you swap out the normal gripper for a lego attachment. Brilliant.
Hoping to build the confidence of children living with a missing limb, Carlos Arturo Torres Tovar, of Umeå University in Sweden, has designed a prosthetic arm that’s compatible with Lego so kids can swap its gripping attachment for their own custom creations.
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that is so cool :)
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My dear girl, the day you see I'm getting old, I ask you to please be patient, but most of all, try to understand what I'm going through. If when we talk, I repeat the same thing a thousand times, don't interrupt to say: "You said the same thing a minute ago"... Just listen, please. Try to remember the times when you were little and I would read the same story night after night until you would fall asleep.

When I don't want to take a bath, don't be mad and don't embarrass me. Remember when I had to run after you making excuses and trying to get you to take a shower when you were just a girl?

When you see how ignorant I am when it comes to new technology, give me the time to learn and don't look at me that way ... remember, honey, I patiently taught you how to do many things like eating appropriately, getting dressed, combing your hair and dealing with life's issues every day... the day you see I'm getting old, I ask you to please be patient, but most of all, try to understand what I'm going through.

If I occasionally lose track of what we're talking about, give me the time to remember, and if I can't, don't be nervous, impatient or arrogant. Just know in your heart that the most important thing for me is to be with you.

And when my old, tired legs don't let me move as quickly as before, give me your hand the same way that I offered mine to you when you first walked. When those days come, don't feel sad... just be with me, and understand me while I get to the end of my life with love. I'll cherish and thank you for the gift of time and joy we shared. With a big smile and the huge love I've always had for you, I just want to say, I love you ... my darling daughter.

Original text in Spanish and photo by Guillermo Peña.
Translation to English by Sergio Cadena
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This realistic optics rendering demonstration is really good stuff!
See the Light

When we look at wonderfully rendered modern 3D graphics in movies and games we see the result of light scattering off of the various surfaces in the scene, from one or more light sources. But, as is the usual case in the real world, the complex computed light transport is invisible. Benedikt Bitterli wanted to show us interactively on our 2D screens how light travels, splits and combines through different scenes including lenses, a prism, and rough mirror surfaces using geometric optics. In the resultant demonstration the user can change the start point and direction of the light as appropriate in various forms including laser light, beam and cone.  The number of light bounces computed, the number of photon paths, and the emission spectra are also under user control.

But how on earth can all this be computed without a rendering farm in a reasonable amount of time on our individual computers?

A more useful approach is to slightly modify the rendering problem and visualize a quantity known as the fluence instead. We will introduce a more rigorous definition later, but the fluence is essentially the average amount of light passing through a point, and is defined almost everywhere in space (not just surfaces), allowing us to "see" the light between surfaces. Unfortunately, rendering this quantity in 3D is fairly computationally expensive, and still doesn't solve all of our problems: Because the rendered image is only 2D, visualizing a 3D fluence essentially blends everything together along one dimension, and the final rendered image may become very difficult to understand.

To fit the fluence onto a 2D image, I ultimately decided to throw away one dimension of the fluence and solve a 2D rendering problem instead. This 2D fluence is a lot easier to visualize and understand.

More here:

Interactive demonstration here:


Image from article.
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The inimitable Gabor Fekete continues his harassment of physicists worldwide by spamming us with his crackpot theories.

A few months ago he threatened to turn us all over to the FBI for fraud since we didn't give up studying or researching physics as he had previously demanded (see e.g.

This time he's pretending to be various members of the Swedish Academy of Science (the mail appears to come from their actual addresses), claiming that he will receive the Nobel prize this year. Read on for your entertainment:

+ + +
Welcome dear Colleague,
In the last 100 years we donated many Nobel Prizes for worthless and speculative theories and models.
Also was a big mistake to donate Nobel Prize to Francois Englert and Peter Higgs for their ridiculous boson theory.
Joseph Incandela and his team issued a speculative explanation. They said that they detected 133 proton mass Higgs boson. It proved to be a lie, because they detected only 4 muons and 2 photons. The mass of these is altogether 0.4 proton mass.
We are considering to withdraw the undeservedly received Nobel Prizes and we put a proposal because of removal of Joseph Incandela and his team from the management of CERN.
In the future we don't want to donate more Nobel Prizes for ridiculous, worthless and speculative theories and models.
Why did so the Nobel Committe? In this year we received two papers in an email from Gabor Fekete, who is a hungarian reformer physicist.
He demonstrated that the modern physics is a pseudo-science in hundred percent and he described with eight digits accuracy the electromagnetic physics of photons, X-ray-photons, gamma-photons, muons, electrons and all atoms, thus solving all the problems in particle and nuclear physics. At the same time he uncovered the fraud of Joseph Incandela and his team. The papers of Gabor Fekete you can read below.
We think so that in this year the Nobel Winner should be Gabor Fekete. Please let us know if you are in agreement or opposition with our decision. You can contact me in any way as are below. Thank you in advance.

Best regards,
Professor Olga Botner
The Royal Swedish Academy of Sciences
+ + +

...followed by a couple of his "papers".
Jan Moren's profile photoHeikki Arponen's profile photoStipe Galić's profile photoJonas Neergaard-Nielsen's profile photo
+Stipe Galić You're right, of course - I have mixed sentiments about this. On one hand it's crackpot entertainment at a high level, on the other it is indeed disturbing how far he's willing to go and how much effort he spends on it. Must be a serious obsession. 
I believe he lives in Hungary - I wonder if anyone actually contacted authorities there to have him either prosecuted or examined for mental disorder.
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Dimensions by +David C. Roy - a kinetic wooden sculpture that runs for 40 hours straight and is nothing but gorgeous. 

Watch more of its action at and go to David's site to enjoy the rest of his creations:

This sculpture is for sale in a limited edition at 2500$. How I wish I could afford to let it grace my living room wall.

via +Colossal
Manmeet Singh Vasir's profile photoJoe Corneli's profile photoKarsten Uredat's profile photoanthony coles's profile photo
+Kevin Clift
Yes I saw it. David's designs are awesome.
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Students from Aalborg University built a small satellite for shipping lane monitoring with support from ESA. Launching very soon, it will be transported to ISS from where it will be sent into orbit.

Pøj-pøj +Rasmus Gundorff Sæderup!
In 1 HOUR (at 13:50 CET), the HTV-5 spacecraft will launch with #aausat5  onboard, heading for the International Space Station.
You can follow the launch live via NASA TV:

More info about AAUSAT5 can be found in this article:
Via +European Space Agency, ESA  #space  
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Nej, du skal desværre betale for at se TV2 online, men du kan se et lille indslag fra TV2-Nord her:
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From the days when Fourier analysis was not just one of many added functionalities of midrange oscilloscopes.
Harmonic Analysis

When I was interviewed for a position by Hewlett-Packard in the late 1970s they were still a major scientific instruments company with a tagline of if it produces a signal, we can measure it! They had manufacturing facilities in Scotland, or "just down the road" according to Kim, my American interlocutor, a couple of field offices and they were hiring for an R&D facility they were planning in Pinewood, Wokingham.

They had very view dedicated conference rooms in the Winnersh, Wokingham field office and so I was interviewed in their Fourier Analyzer room. I sat alongside a six foot tall, imposing rack machine that included a real-time computer, a Digital to Analog convertor, an Analog to Digital convertor and a lovely HP Oscilloscope. This was an HP digital Fourier Analyzer and it was the first one I had seen.

The purpose of the digital Fourier Analyzer was to take in a complicated continuous signal from the real world, something that was hard to work with like a vibration signal, and break it down into a finite number of manageable sine and cosine functions with their magnitude and phase relationships. This work was based on the development by Jean-Baptiste Fourier, more than a hundred years ago, of his eponymous infinite series. The amazing feat performed by this machine was, however, made possible even with a fast computer in a reasonable amount of time, only by the development of the cunning Cooley-Tukey FFT Algorithm in 1965.

The interactive codepen below gives us an idea of the way that a simple periodic function, like a square wave, or a sawtooth curve, can actually be simulated to a reasonable degree of accuracy with only a limited number of terms.

Interactive Codepen:

Before digital computers, there were analog devices for Fourier Analysis. If you have a bit more time and you haven't seen them yet, you might enjoy these videos (and the e/book) by +Bill Hammack.  He and team restored one such machine. This analog computer was originally developed by Albert Michelson (of Michelson-Morley fame).  It uses gears, springs and levers to add sines and cosines.

(1/4) Intro/History: Introducing a 100-year-old mechanical computer:

(2/4) Synthesis: A machine that uses gears, springs and levers to add sines and cosines:

(3/4) Analysis: Explaining Fourier analysis with a machine:

(4/4) Operation: The details of setting up the Harmonic Analyzer:

Book (free pdf or buy printed):

Further reading:

HP Journal 1970/06:
30 Years of FFT:

Fourier Series (Wikip):
Fourier Transform (Wikip):
Fast Fourier Transform:
Fourier Analysis (Wikip):
Harmonic Analysis: (Wikip):

Image courtesy of Computer History Museum:
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birger monsen's profile photoChris Powell's profile photoDaniel Carollo's profile photoJonas Neergaard-Nielsen's profile photo
It does indeed sound like an entirely different age. We still have a bit of rack-mounted equipment around in our labs, but it's not much. Surely not scopes.

I guess I should be happy enough with what we have now - 20-30 years from now I'll probably look back at it with the same nostalgia :)
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Quantum optician
  • Technical University of Denmark
    Post doc, 2011 - present
  • National Institute of Information and Communications Technology, Tokyo
    Post doc, 2008 - 2011
  • Niels Bohr Institute, University of Copenhagen
    PhD student, 2005 - 2008
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Copenhagen, Denmark
Tokyo, Japan - Hundested, Denmark
Turning mirrors, for a more efficient life
Science, photography, LEGO, making, design, technology, Denmark, Japan and more - my G+ may be as messy as my brain...
  • University of Copenhagen Faculty of Science
    Physics, 1999 - 2005
  • Frederiksværk Gymnasium
    1996 - 1999
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Jonas Schou Neergaard-Nielsen
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