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Condensed-matter physics

Repulsive polarons found

Nature volume 485, pages 588589 (31 May 2012) | Download Citation

Quasiparticles known as repulsive polarons are predicted to occur when 'impurity' fermionic particles interact repulsively with a fermionic environment. They have now been detected in two widely differing systems. See Letters p.615 & p.619

Polarons are well known in the solid state. For example, when a charge carrier, such as an electron, is placed in a crystal lattice, the surrounding lattice ions are displaced. The electron, together with the surrounding lattice distortion, forms a quasiparticle — a polaron — that has an energy and effective mass quite different from that of a bare electron. Polarons have an important role in a wide range of exotic many-body phenomena in condensed-matter physics, including high-temperature superconductivity in copper oxide compounds and colossal magnetoresistance in rare-earth manganites1. In two papers published on Nature's website today, Kohstall et al.2 and Koschorreck et al.3 describe how they have detected an elusive form of these quasiparticles — the repulsive polaron.

In the case of attractive Fermi polarons, 'impurity' fermionic particles (particles that have half-integer spin, such as electrons) interact attractively with a Fermi 'sea', an environment of other fermionic particles. Such polarons were observed4,5 in 2009 for ultracold fermionic lithium (6Li) impurity atoms of spin-down orientation in a Fermi sea of spin-up 6Li atoms. During the past year, theoretical work6 has suggested that a novel metastable quasiparticle associated with repulsive interactions, the repulsive polaron, may also exist. The experimental realization of such a polaron was expected to be challenging, because the strong repulsive interaction between atoms trapped in a potential well also results in a weakly bound molecular state, into which the repulsively interacting atoms may rapidly decay.

In their experiments, Kohstall et al.2 and Koschorreck et al.3 produced well-defined repulsive polarons. Kohstall and colleagues created the repulsive polaron by immersing heavy fermionic potassium (40K) impurity atoms in a Fermi sea of light 6Li atoms (Fig. 1). The authors2 detected the polaron by measuring the energy excitation spectrum of the 40K impurity atoms as they interacted with the surrounding 6Li atoms, using radio-frequency spectroscopy, which involves flipping the orientation of the 40K atoms' spins from an initial non-interacting state to a state in which the 40K atoms interact with the surrounding 6Li atoms. The authors varied the magnitude and sign (attractive or repulsive) of the interaction between the 40K and 6Li atoms by tuning an external magnetic field across a Feshbach resonance, which occurs at a particular magnetic-field strength at which the two interacting atomic species pass through an intermediate (molecular) state in which they are weakly bound.

Figure 1: When fermionic potassium meets fermionic lithium.
Figure 1

a, Kohstall et al.2 demonstrate a repulsive polaron by immersing a fermionic potassium 40K atom (red) in an ultracold Fermi 'sea' of lithium 6Li atoms (blue). b, Turning on a repulsive interaction between the two atomic species leads to the formation of the repulsive polaron, which consists of the 40K atom and the surrounding 6Li atoms.

Meanwhile, Koschorreck et al.3 produced the repulsive polaron by immersing spin-down 40K impurity atoms in a two-dimensional Fermi sea of spin-up 40K atoms. The lower-dimensional Fermi sea was used to help stabilize the repulsive polaron. These authors also used radio-frequency spectroscopy, but in addition to determining the energy of the spin-flipped atoms, they resolved the atoms' momentum. This allowed them to obtain an energy–momentum excitation spectrum of the system, which can be calculated from theory and can be used to study the dynamics of the polaron as it evolves.

Kohstall et al.2 find that the 40K–6Li repulsive polaron is remarkably stable against decay into an attractive polaron or into molecular states. The observed repulsive polaron has lifetimes ranging from about 0.4 milliseconds at large interaction strengths (close to the centre of the Feshbach resonance) up to about 20 milliseconds at smaller interaction strengths. The authors' theoretical analysis2 shows that the long lifetimes originate predominantly from a relatively large effective range over which the 40K and 6Li atoms strongly interact, which in turn arises because the Feshbach resonance for the 40K–6Li system is relatively narrow (0.88 gauss). The lifetimes of the 40K repulsive polaron detected by Koschorreck and colleagues3 are about tenfold shorter than those of the polaron observed in the 40K–6Li system.

The evidence for the existence of metastable repulsive polarons in two such widely differing fermionic systems is compelling. When the systems' interactions were tuned to the repulsive regime, the authors2,3 detected a well-defined narrow spectral peak, which is associated with the polaron, superimposed on a broad, incoherent background arising mainly from excitation of 'continuum' states in the Fermi sea (see, for example, Fig. 1 of the Supplementary Information to Kohstall and colleagues' paper2). For the 40K–6Li system, measurements of the polaron's energy, lifetime, effective mass and quasiparticle residue — which quantifies how much of the non-interacting state is contained in the polaron's wavefunction — as a function of the strength of the repulsive interaction are in excellent agreement with theory2, which takes account of the finite effective range over which the strong interaction occurs.

Now that the repulsive polaron has been observed, it will allow repulsive many-body fermionic states to be exploited in regimes that have so far been unexplored. In particular, it will be interesting to investigate the phase diagram of systems in the regime of repulsive interactions as a function of the relative concentrations of the impurity and Fermi-sea atoms, and as a function of the interaction strength and temperature. Such investigations would allow a search to be made for a predicted phase transition to itinerant ferromagnetism, which involves a phase separation of the atoms into spatially separated magnetic domains in which the spins of the atoms in each domain are oriented in the same direction. Itinerant ferromagnetism, which is responsible for the magnetic properties of metals such as iron, cobalt and nickel, was first proposed7 almost 80 years ago, but the transition towards itinerant ferromagnetism is still not well understood and has not yet been demonstrated experimentally8.

It will also be interesting to study other impurity many-body phenomena, such as the Kondo effect9, in which magnetic impurity atoms interact with a surrounding Fermi sea to give an anomalous enhancement of the low-temperature electrical resistance seen in a metal, and Anderson's orthogonality catastrophe10, which predicts how abruptly an impurity many-body state in a Fermi sea responds to a sudden change in the interaction.


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  1. Peter Hannaford is at the Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122, Australia.

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Correspondence to Peter Hannaford.

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