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Three’s Company, Two’s a Crowd: Meet the Efimov Effect

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The coat of arms of a 15th century Italian noble family by the name of Borromeo featured three interlocking circles. Among the many interpretations, it can be said to represent the inter-marriages that had bound the Borromeos inseparably to two other noble families — a strong, stable alliance that served the family well over many centuries.

In physics, one could say the three rings — or atoms, or particles — are entangled, such that if you pick up any one of them, the other two will follow, and if you cut one, the other two will fall apart. When atoms behave that way, they are said to be an Efimov state. And according to a new paper in Physical Review Letters, that state appears to be scalable, as predicted by the original theory. [UPDATE: Over at Quanta, Natalie Wolchover has even more details about this new result.]

Borromean Rings

It just so happens I blogged about this way back in 2007 (parts of which I adapted for this post), just after  physicists first achieved an Efimov state in the laboratory. Atomically speaking, the Efimov effect is what happens when two atoms that normally repel each other become strongly attracted when a third atom is introduced.

That’s right: three’s company, two’s a crowd, which flies in the face of conventional wisdom. However, the Efimov effect can only be observed in ultracold gases, like cesium, cooled way down to a billionth of a degree above Absolute Zero. That’s colder than the furthest reaches of outer space, which hover around a comfy 3 degrees Kelvin. T

The man behind the Efimov effect is a Russian physicist named Vitaly Efimov. Back in 1969, he had a shiny new PhD in theoretical nuclear physics, along with sufficient youthful optimism to make a strange prediction: even though any two in a group of three atoms will normally repel each other, under just the right kind of conditions, it should be possible to create a state of matter in which they will experience an irresistible attraction, forming an infinite number of “bound states.”

This struck many of his colleagues as a bit preposterous, but the math bore young Vitaly out. Time and again over the years, theorists have tried to disprove the Efimov effect, only to further verify it. But it still hadn’t been seen in a laboratory. The technology to do so didn’t exist. It’s the same reason it took so long to create Bose-Einstein condensates (BECs), a new state of matter first predicted by Albert Einstein and the Indian physicist Satyendra Bose in the 1920s.

Remember that all matter exhibits wave/particle duality. At normal temperatures atoms behave a lot like billiard balls, bouncing off one another and any containing walls. Lowering the temperature reduces their speed. If the temperature gets low enough (billionths of a degree above absolute zero) and the atoms are densely packed enough, their wave nature kicks in. The different matter waves will be able to “sense” one another and coordinate themselves as if they were one big “superatom.” That’s a BEC.

Bose-Einstein Condensate of rubidium atoms. Source: NIST/JILA/CU-Boulder

Eric Cornell and Carl Wieman created the first BEC, using a combination of laser and magnetic cooling equipment. They created a laser trap by cooling about 10 million rubidium gas atoms; the cooled atoms were then held in place by a magnetic field.

But the atoms still weren’t cold enough to form a BEC, so the two men added a second step, evaporative cooling, in which a web of magnetic fields conspire to kick out the hottest atoms so that the cooler atoms can move more closely together. It works in much the same way that evaporative cooling occurs with your morning cup of coffee; the hotter atoms rise to the top of the magnetic trap and “jump out” as steam.

Wieman and Cornell made physics history at 10:54 AM on June 5, 1995, producing a BEC of about 2000 rubidium atoms that lasted 15-20 seconds. Shortly thereafter, an MIT physicist named Wolfgang Ketterle achieved a BEC in his laboratory. Wieman, Cornell and Ketterle shared the 2001 Nobel Prize in Physics.

BECs turned out to be the key to experimentally verifying the Efimov effect, since they spawned a huge new field of research into the properties of ultracold gases. Chris Greene of the the University of Colorado was the first (with a co-author) to predict that ultracold gases were just the ticket for achieving such an odd state in the laboratory. And in 1999, Nobel laureate Steven Chu — a pioneer in laser cooling and trapping of atoms — led a Stanford team that attempted to create an Efimov state. Even at one millionth of a degree above absolute zero, the sample was still too hot.

Modeling the Efimov effect. Source: Rudolf Grimm

Enter Austrian physicist Rudolf Grimm, who met Efimov at a workshop in Seattle in 2005, and was inspired to try his own hand at verifying the Efimov effect. Grimm’s group at the University of Innsbruck took three cesium atoms, placed them in a vacuum chamber, and then used a combination of laser cooling and evaporative cooling to bring the temperature down to -459.6 degrees F.

The technique is almost identical to how a BEC is created, and had BECs not become almost commonplace in physics over the last decade, Efimov’s odd theory might never have been verified.

Within a year of meeting Efimov, Grimm’s team had created the Efimov effect in their lab. The trick is to get the gas to the very edge of condensation, without it ever turning into an actual BEC.

Possibly the most exciting thing about that experimental result was that it should be pretty much universal: we should be able to create this state out of any set of three particles at ultracold temperatures. So naturally it launched an exciting (for physicists) new field devoted to studying the quantum mechanical behavior of just a few interacting particles. That’s because among other things, such states are a great way to study exotic “few-body systems” — those that only have three or four particles, like an atomic nucleus.

In 2010, Grimm’s protege, Cheng Chin, now at the University of Chicago, managed to achieve a mixed Efimov state — that is, one that held ultracold cesium and lithium atoms. But the most elusive goal physicists hoped to achieve was experimental verification of another prediction in Efimov’s original theory: that these so-called “Efimov trimers” should scale upwards. The state achieved by the Innsbruck team was at the smallest possible scale; the next largest should, by Efimov’s calculations, be 22.7 times larger.

Why was this so difficult? Size wasn’t the only thing that scaled. Efimov trimers will break apart immediately after forming if the temperature isn’t the same or smaller than the binding energy that holds the threesome together, which means that you need even colder temperatures — by a factor of 2 — than you need for the smallest such state to scale up the second smallest. Somehow, the Innsbruck team managed to do just that, thanks to a new kind of trap, and found a scaling factor of 21.0 — pretty close to Efimov’s predicted value.

Source: APS/Giovanni Modugno

Assuming you’ve read this far, you might be wondering: “Why should I care?” Condensed matter physicists often complain that their work doesn’t garner the same level of media attention or public enthusiasm as, say, the discovery of the Higgs boson, or quirky neutrino findings.

There’s some truth to that, in large part because it’s tough to convey why this work is so relevant outside of its importance to verifying theory and enabling further ultracold gas experiments to study exotic few-body systems. This in turn could deepen physicists’ knowledge of quantum mechanics.

True, mastering the Efimov effect may make it possible to engineer the most fundamental properties of matter way down at the subatomic level, giving scientists unprecedented control and the ability to create all kinds of new exotic molecules that couldn’t otherwise exist. Nanotechnology tinkers with material properties all the time, but doing so at the quantum level means you can tinker with the atomic interactions as well.

That said, there’s still the small matter of needing ultracold temperatures (near absolute zero) to achieve said state of matter in order to manipulate fundamental properties — which requires cutting-edge technology like magneto-optical traps. So don’t hold your breath for Efimov states finding their way into your iPhone any time soon. The same could be said about BECs, as Chad Orzel pointed out in 2011:

“The primary application of atomic BEC systems is in basic research areas at the moment, and will probably remain so for the foreseeable future. You sometimes hear people talk about BEC as a tool for lithography, or things like that, but that’s not likely to be a real commercial application any time soon, because the throughput is just too low. Nobody has a method for generating BEC at the sort of rate you would need to make interesting devices in a reasonable amount of time. As a result, most BEC applications will be confined to the laboratory.”

Ditto for Efimov states, I fear. So, Jen-Luc Piquant understands why you might not find all this very exciting. But it’s quite an achievement, nonetheless, and sometimes we need to celebrate such unsung heroes, who labor in the shadows with little fanfare, even when they make significant breakthroughs. Now it’s time for them to raise the experimental bar even further and try to produce a third-order Efimov state. At the current rate, they should crack that nut within the decade. Go team!


Chin, C. et al. (2010) “Feshbach Resonances in Ultracold Gases,” Reviews of Modern Physics 82, 1225.

Efimov, V. (1970) “Energy levels arising from resonant two-body forces in a three-body system,” Physics Letters B 33: 563–564.

Efimov, V. (1971) “Weakly-Bound States of Three Resonantly-Interacting Particles,” Soviet Journal of Nuclear Physics 12: 589.

Efimov, V. (2009) “Few-Body Physics: Giant Trimers True to Scale,” Nature Physics 5:533.

Ferlaino, F. and Grimm, R. (2010). “Forty Years of Efimov Physics: How a Bizarre Prediction Turned into a Hot Topic,” Physics 3, 9.

Huang, B. et al. (2014) “Observation of the Second Triatomic Resonance in Efimov’s Scenario,” Physical Review Letters 112: 190401.

Knoop, S. et al. (2009) “Observation of an Efimov-like trimer resonance in ultracold atom–dimer scattering,” Nature Physics 5 (3): 227

Kraemer, T. et al. (2006) “Evidence for Efimov quantum states in an ultracold gas of caesium atoms,” Nature 440 (7082): 315–318.

Zaccanti, M. et al. (2009) “Observation of an Efimov spectrum in an atomic system,” Nature Physics 5 (8): 586.

Jennifer Ouellette About the Author: Jennifer Ouellette is a science writer who loves to indulge her inner geek by finding quirky connections between physics, popular culture, and the world at large. Follow on Twitter @JenLucPiquant.

The views expressed are those of the author and are not necessarily those of Scientific American.

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  1. 1. CharlesRKIss 9:26 am 05/27/2014

    “the Efimov effect can only be observed in ultracold gases,”

    Does this mean it doesn’t happen at higher temps, or simply cannot be observed at higher temps?

    “that state appears to be scalable,”

    Does this mean that state occurs at higher temps, and/or with larger numbers of atoms?

    Just curious because I was discussing polymerization and metal catalysis the other day; any comment on this would be welcome. Thanks.

    Link to this
  2. 2. jtdwyer 11:25 am 05/27/2014

    This is a very interesting finding in respect to low-energy binding of particles, but I object to the use of the term ‘entanglement’ here, as to most readers that refers to the quantum entanglement of particles’ properties such that their property states can only be described as a discrete system. Conversely, Efimov states involve multi-particle bindings (sub-atomic nuclear, atomic and molecular) – not any interdependence of particle property states.
    The preprint copy of the research report is available at – it nowhere uses the term entanglement – neither does or

    Link to this
  3. 3. rossm 8:01 pm 05/27/2014

    If you want your own Borromean rings, here is a good site:

    I am not associated with this business, just a happy customer.

    Link to this
  4. 4. jtdwyer 7:36 am 06/3/2014

    “that state appears to be scalable,”
    “Does this mean that state occurs at higher temps, and/or with larger numbers of atoms?”

    FYI – I was also completely confused about the scaling business, and could not find any straightforward explanation anywhere – until I stumbled upon a perfectly clear illustration on page 11/43 of
    - The scaling refers to the separation distance between the three bound particles! The trimer particle bindings scale in size at discrete intervals!

    Link to this
  5. 5. jtdwyer 7:57 am 06/3/2014

    FYI – In addition to the recent article link provided in the article – – also see

    Link to this
  6. 6. rufusgwarren 11:16 am 06/6/2014

    have any experiments been done with two protons,or two proton and a neutron? It would be interesting if it is shown that the protons never reach BEC but with a neutron it does. In other words, the above only shows what happens with whole molecules that fine a reduced energy configuration. I conjecture not all particles may do so.

    Link to this

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