Quantum physics

Single electrons pop out of the Fermi sea

The ability to control individual electrons in an electronic conductor would pave the way for novel quantum technologies. Single electrons emerging from a sea of their fellows in a nanoscale electrode can now be generated. See Letter p.659

Splashing water in the bath usually leads to small waves, splashes and droplets. Similarly, applying a voltage pulse to the sea of electrons in a nanoscale electrode produces a complex quantum state involving several electrons that have been kicked out of the sea, as well as holes — or missing electrons — left behind. On page 659 of this issue, Dubois et al.1 report the first experimental voltage-pulse generation of just a single electron, not several, emerging on top of an electronic seaFootnote 1.

A nanoscale electrode is a reservoir of electrons, often referred to as a Fermi sea. Applying a voltage to the electrode amounts to changing the sea level by either pouring more electrons into the electrode (thus increasing the sea level) or emptying out electrons (thereby decreasing the sea level). A voltage that varies with time typically stirs up the Fermi sea and causes waves and splashes of electrons. This effect led Levitov and colleagues2,3,4 to investigate theoretically how a time-dependent voltage affects a Fermi sea. Surprisingly, and quite remarkably, they found that a particular shape of voltage pulses should excite just a single electron onto the surface of the Fermi sea, leaving no traces behind. This job would be done by a voltage pulse that changes in time according to the mathematical function called a Lorentzian.

In their experiment, Dubois et al. realize the proposal by Levitov and colleagues, and they name the resulting single-electron wavepacket a leviton, because it resembles a soliton in certain ways. Solitons were first observed in the nineteenth century by the Scottish engineer John Scott Russell who noticed that a boat brought to a sudden stop in the Union Canal running into Edinburgh generated a single, localized wave of water that travelled several kilometres without changing its shape or slowing down (Fig. 1). Such self-sustained waves are now known as solitons, and they occur in a variety of systems described by non-linear wave equations.

Figure 1: Spotting solitons and levitons.

a, Dubois et al.1 have experimentally realized Levitov and colleagues' proposal2,3,4 that a carefully engineered voltage pulse would bring just a single electron to the top of the Fermi sea of electrons in a nanoelectrode; they have named the resulting single-electron wavepacket a leviton. b, Levitons resemble solitons, waves that keep their shape while travelling at constant speed and which were first observed in Edinburgh's Union Canal by John Scott Russell while on horseback.

Just like solitons, levitons of different heights, widths and creation times can be superimposed in a controllable manner and travel unhindered on top of a Fermi sea. To produce levitons, Dubois et al. used a nanoscale circuit consisting of two electrodes connected by a small conductor. They applied Lorentzian-shaped voltage pulses on one electrode to generate levitons that travel through the conductor to the other electrode.

Whereas Russell observed solitons in the Union Canal from the back of his horse, the observation of levitons requires sophisticated experimental techniques. To observe them, the temperature must be as low as it can get to make the Fermi sea as quiet as possible. Dubois and colleagues managed to cool their sample down to 35 millikelvin, close to absolute zero. A sequence of Lorentzian-shaped pulses should yield a noiseless flow of levitons without electrical fluctuations2,3,4. The authors measured the electrical noise5 and found only the background noise caused by tiny thermal fluctuations. Next, they used a narrow constriction in the conductor — a quantum point contact — to filter out a fraction of the levitons. By measuring the increased noise due to the filtering, they could infer the number of emitted levitons and demonstrate that each pulse produces exactly one leviton, with no additional disturbances.

To corroborate their findings, the research team performed a Hong-Ou-Mandel experiment known from optics6. Here, a semi-transparent mirror randomly reflects or transmits photons into two different output arms. However, if two identical photons simultaneously hit each side of the mirror, they always exit into the same output arm. The photons are said to 'bunch', as is typical for the class of particles called bosons. Levitons, by contrast, are fermions, which 'anti-bunch' by exiting into different output arms7. Dubois et al. generated levitons in both electrodes and caused them to interfere at the quantum point contact, which acts as a semi-transparent mirror. Levitons arriving simultaneously at the quantum point contact were found to anti-bunch, confirming their fermionic nature.

Dubois and colleagues' work demonstrates unprecedented control of single electrons in the Fermi sea of a nanoelectrode, and it opens up a plethora of applications and directions for fundamental research. One can envisage future quantum electronics with levitons — levitonics — in which single levitons are emitted into a circuit architecture with edge states (formed in a strong magnetic field) that function as rails for the levitons by guiding them to beam splitters and interferometers for further processing, borrowing ideas and concepts from quantum optics.

Additional experiments might investigate the statistical properties of levitons, including the fluctuations in the number of levitons (full counting statistics8) and the distribution of waiting times between levitons9. A leviton can contain more than one electron and may even carry just a fraction of the electron charge if implemented in a one-dimensional system of interacting electrons known as a Luttinger liquid. Atomic levitons may also be realized in Fermi gases of cold atoms. Further down the road, one can imagine solid-state qua ntum computers with levitons acting as the fundamental carriers of quantum information. The realization of on-demand levitons is a major step forward in the attempts to realize quantum electronics with timed emissions of single electrons into a nanoscale quantum circuit. There are plenty of promising prospects ahead.


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    *This article and the paper under discussion1 were published online on 23 October 2013.


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Correspondence to Christian Flindt.

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Flindt, C. Single electrons pop out of the Fermi sea. Nature 502, 630–631 (2013). https://doi.org/10.1038/nature12699

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