Monthly Archives: August 2012

The Unbearable Lightness of Quantum Mechanics

Updated below.

Gravity and Quantum Mechanics don’t play nice together. Since Einstein’s time, we have two towering theories that have defied all attempts by some very smart people to be reconciled. The Standard Model, built on the foundations of quantum mechanics, has been spectacularly successful. It allows the treatment of masses acquired from the binding energies, and, if the Higgs boson confirmation pans out, accounts for the elemental rest masses - but it does not capture gravity. (The current mass generation models that involve gravity are all rather speculative at this point.)

Einstein’s General Relativity has been equally successful in explaining gravity as innate geometric attributes of space and time itself. It has survived every conceivable test and made spectacular predictions (such as gravity lenses).

On the surface this dysfunctional non-relationship between the two major generally accepted theoretical frameworks seems very puzzling. But it turns out that the nature of this conundrum can be described without recourse to higher math (or star-trek like animations with a mythical sound-track).

Much has been written about the origin of this schism: The historic struggle for the interpretation of Quantum Mechanics, with Einstein and Bohr being the figureheads of the divided physics community at the time. Mendel Sachs (who, sadly, passed away recently) drew the following distinction between the philosophies of the two fractions:

[The Copenhagen Interpretation views] Schroedinger's matter waves as [complex] waves of probability. The probability was then tied to quantum mechanics as a theory of measurement - made by macro observers on micro-matter. This view was then in line with the positivistic philosophy, whereby the elements of matter are defined subjectively in terms of the measurements of their properties, expressed with a probability calculus. [...] Einstein's idea [was] that the formal expression of the probability calculus that is called quantum mechanics is an incomplete theory of matter that originates in a complete [unified] continuous field theory of matter wherin all of the variables of matter are 'predetermined'.

(From Quantum Mechanics and Gravity)

These days, the Copenhagen Interpretation no longer reigns supreme, but has some serious competition: E.g. one crazy new kid on the block is the Many World Interpretation.  (For an insightful take on MWI I highly recommend this recent blog post from Scott Aaronson).

But the issue goes deeper than that. No matter what interpretation you favor, one fact remains immutable: Probabilities will always be additive, mathematically they behave in a linear fashion. This, despite its interpretative oddities, makes Quantum Mechanics fairly easy to work with.  On the other hand, general relativity is an intrinsically non-linear theory.  It describes a closed system in which the field, generated by gravitating masses, propagates with finite speed and, in a general, non-equilibrium picture, dynamically affects these masses, in turn rearranging the overall field expression.  (Little wonder Einstein's field equations only yield to analytical solutions for drastically simplified scenarios).

There is no obvious way to fit Quantum Mechanics, this linear peg, into this decidedly non-linear hole.

Einstein considered Quantum Mechanics a theory that would prove to be an approximation of a fully unified field theory.  He spent his last years chasing after this goal, but never achieved it. Mendel Sachs claims to have succeeded where he failed, and indeed presents some impressive accomplishments, including a way to derived the quantum mechanics structure from extended General Relativity field equations.  What always struck me as odd is how little resonance this generated, although this clearly seems to be an experience shared by other theoretical physicists who work off the beaten path. For instance, Kingsley Jones approaches this same conundrum from a completely different angle in his original paper on Newtonian Quantum Gravity. Yet the citation statistic shows that there was little up-take.

One could probably dedicate an entire blog speculating on why this kind of research does not break into the mainstream, but I would rather end this with the optimistic notion that in the end, new experimental data will hopefully rectify this situation. Although the experiment on a neutral particle Bose-Einstein condensate proposed in Kingsley Jones' paper has little chance of being performed unless there is some more attention garnered, other experiments to probe the domain where gravity and quantum mechanics intersect get a more lofty treatment: For instance this paper was featured in Nature although its premise is probably incorrect. (Sabine Hossenfelder took Nature and the authors to task on her blog - things get a bit acrimonious in the comment section).

Nevertheless, it is encouraging to see such a high profile interest in these kinds of experiments, chances are we will get it right eventually.


Kingsley Jones (who's 1995 paper paper I referenced above) has a new blog entry that reflects on the historic trajectory and current state of quantum mechanics.  I think it's fair to say that he does not subscribe to the Many World Interpretation.




Diamonds are a Qubit’s Best Friend

A Nitrogen Vacancy in a diamond crystal isolates the nuclear spin yet makes it accessible via the hyperfine coupling.

A while ago, I looked into the chance that there would ever be a quantum computer for the rest of us. The biggest obstacle for this is the ultra-low temperature regime that all current quantum computing realizations require.  Although a long shot, I speculated that high temperature super-conductors may facilitate a D-Wave-like approach at temperature regimes that could be achieved with relatively affordable nitrogen cooling. Hoping for quantum computing at room temperature seemed out of the question. But this is exactly the tantalizing prospect that the recent qubit realization within a diamond's crystal structure is hinting at - no expensive cooling required at all. So, ironically, the future quantum computer for the rest of us may end up being made of diamond.

A qubit requires a near perfectly isolated system i.e. essentially any interaction with the environment destroys the quantum information by randomly transitioning the pure qubit quantum state to a mixed ensemble state (a random superposition mixture of wavefunctions).  The higher the temperature, the more likely are these unwanted interactions via increased Brownian and thermal background radiation, a process know as decoherence.  Solid state qubit realizations are therefore always conducted at temperatures close to absolute zero, and require expensive Helium cooling.  Even under these conditions, qubits realized on superconducting chips don't survive for very long. Their typical coherence time is measured in micro-seconds. On the other hand, ion-based systems can go for several minutes. While this is an obvious advantage, the challenge in using this design for quantum computing is the ability to initialize these systems into a known state, and the read-out detection sensitivity.  But great strides have been made in this regard, and in the same Science issue that the diamond results were presented, this article has been published that demonstrates a suitable system that exhibits quantum information storage for over 180 seconds.

All these coherence times are very sensitive to even the slightest temperature increase i.e. every millikelvin matters.  (This graph illustrates this for the first commercially available quantum computing design).

Key is to not have too many point defect.

It is in this context that the result of a successful qubit storage in a diamond lattice is almost breathtaking. A coherence time of over one second at room temperatureHarvard is not know for cutting edge experimental quantum computing research, so this result is surprising in more than one respect.

The diamond in question is artificially made and needs to contain some designer irregularites (but not too many of them):  These point defects replace a carbon atom in the diamonds crystal grid with a nitrogen one. If there are no other nitrogen vacancies nearby, the nuclear spin of this atom is very well isolated. Rivaling one would otherwise require close to absolute zero temperatures. On the other hand, this atom's extra electron can readily interact with EM fields, and this is eactly what the researchers exploited. But there is more to it.

The really intriguing aspect is that this nuclear spin qubit in turn can be made to interact with the spin states of the excess electron, and the coherence times of both can be individually enhanced by suitably tuned laser exposure. The different coupling mechanisms are illustrated in the I came across this popular science write-up that does an excellent job in explaining this (long time readers know that I am rather critical of what usually passes as popular science, so I am delighted when I find something that I can really recommend).

The original paper concludes that additional coherence enhancing techniques could yield  jaw-dropping qubit storage of up to 36 hours at room temperature.

Of course, when everything else fails, physicists can always fall back on this novel approach, a song designed to scare a qubit to never come out of its coherent state:

Lies, Damned Lies, and Quantum Statistics?

Statistics has a bad reputation, and has had for a long time, as demonstrated by Mark Twain's famous quote[1] that I paraphrased to use as the title of this blog post. Of course physics is supposed to be above the fudging of statistical numbers to make a point.  Well, on second thought, theoretical physics should be above fudging (in the experimental branch, things are not so clear cut).

Statistical physics is strictly about employing all mathematically sound methods to deal with uncertainty. This program turned out to be incredibly powerful, and gave a solid foundation to the thermodynamic laws.  The latter were empirically derived previously, but only really started to make sense once statistical mechanics came into its own, and temperature was understood to be due to the Brownian motion. Incidentally, this was also the field that first attracted a young Einstein's attention. Among all his other accomplishments, his paper on the matter that finally settled the debate if atoms were for real or just a useful model is often overlooked. (It is mindboggling that within a short span 0f just 40 years ('05-'45) science went from completely accepting the reality of atoms, to splitting them and unleashing nuclear destruction).

Having early on cut his teeth on statistical mechanics, it shouldn't come as a surprise that Einstein's last great contribution to physics went back to this field. And it all started with fudging the numbers, in a far remote place, one that Einstein had probably never even heard of.

In the city that is now the capital of Bangladesh, a brilliant but entirely unknown scholar named Satyendra Nath Bose made a mistake when trying to demonstrate to his students that the contemporary theory of radiation was inadequate and contradicted experimental evidence.  It was a trivial mistake, simply a matter of not counting correctly. What added insult to injury, it led to a result that was in accordance with the the correct electromagnetic radiation spectrum. A lesser person may have just erased the blackboard and dismissed the class, but Bose realized that there was some deeper truth lurking beneath the seemingly trivial oversight.

What Bose stumbled upon was a new way of counting quantum particles.  Conventionally, if you have two particles that can only take on two states, you can model them as you would the probabilities for a coin toss. Lets say you toss two coins at the same time; the following table shows the possible outcomes:

    Coin 1
     Head  Tail
 Coin 2  Head  HH  HT
   Tail  TH  TT

It is immediate obvious that if you throw two coins the combination head-head will have a likelihood of one in four.  But if you have the kind of "quantum coins" that Bose stumbled upon then nature behaves rather different.  Nature does not distinguish between the states tails-head and head-tails i.e. the two states marked green in the table.  Rather it just treats these two states as one and the same.

In the quantum domain nature plays the ultimate shell game. If these shells were bosons the universe would not allow you to notice if they switch places.

This means, rather than four possible outcomes in the quantum world, we only have three, and the probability for them is evenly spread, i.e. assigning a one-third chance to our heads-heads quantum coin toss.

Bose found out the hard way that if you try to publish something that completely goes against the  conventional wisdom, and you have to go through a peer review process, your chances of having your paper accepted are almost nil (some things never change).

That's where Einstein came into the picture.  Bose penned a very respectful letter to Einstein, who at the time was already the most famous scientist of all time, and well on his way to becoming a pop icon (think Lady Gaga of Science).  Yet, against all odds, Einstein read his paper and immediately recognized its merits.  The rest is history.

In his subsequent paper on Quantum Theory of Ideal Monoatomic Gases, Einstein clearly delineated these new statistics, and highlighted the contrast to the classical one that produces unphysical results in the form of an ultraviolet catastrophe. He then applied it to the ideal gas model, uncovering a new quantum state of matter that would only become apparent at extremely low temperatures.

His audacious work set the state for the discovery of yet another fundamental quantum statistic that governs fermions, and set experimental physics on the track to achieving ever lower temperature records in order to find the elusive Bose-Einstein condensate.

This in turn gave additional motivation to the development of better particle traps and laser cooling. Key technologies that are still at the heart of the NIST quantum simulator.

All because of one lousy counting mistake ...

[1] Actually the source of the quote is somewhat murky - yet clearly inducted into popular culture thanks to Twain  (h/t to my fact checking commenters).

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