Measurement of quantum phase-slips in a Josephson junction chain

vendredi 21 mai 2010

Josephson junction chains attract currently a lot of interest due to their possible applications in metrology or quantum information. For example, under microwave irradiation of frequency f, such chains could exhibit current quantization I=2nef where 2e is the charge of a Cooper pair and n is an integer number. They could be used for the definition of a new quantum current standard. In view of the potential applications, we have measured the ground state of a Josephson junction chain. Here we have analysed our results in terms of “quantum phase-slips”, the central phenomenon governing these superconducting networks.

A Josephson junction is constituted of two superconducting electrodes separated by an insulating layer. A phase difference between the two electrodes φ yields a supercurrent through the junction I(f)=Ic sin(φ). Ic maximum value of this supercurrent is fixed by the junction Josephson energy EJ which depends on the superconducting gap of the electrodes and on the junction normal state resistance. The junction charging energy EC=q2/2C (C is its capacitance) induces quantum fluctuation on the phase difference φ across the junction.These quantum phase fluctuations induce so-called “quantum phase-slips” where the phase across the junction changes by 2π. If a phase-slip occur ocross a junction embedded in a chain with many other junctions, new phenomena appear. Here, a quantum phase-slip on one junction leads to a collective response of all the others.

Fig. 1 : SEM image of the sample. a) 6 SQUID chain shunted by the read-out junction. b) One SQUID. c) One SQUID junction. d) The read-out junction.
This collective behaviour implies the formation of new energy levels εn(δ).Here δ is the overall phase difference over the chain given by the sum of all junctions’ phase differences φi. For a large phase-slip rate υ, i.e. the number of quantum phase-slips per second, the current-phase relation of a Josephson junction chain, Ichain(δ)=Icchain sin(δ) has the same form as for a single junction but with an effective critical current Icchain. This critical current is determined by the number of junctions in the chain and the quantum phase-slip rate. In the measurements, the ground state of a Josephson junction chain containing 6 SQUIDs is determined by measuring the critical current of the chain shunted by a read-out junction (Fig.1). As each junction is a SQUID, the EJ/EC ratio can be tuned in situ by changing the magnetic flux ΦS through the SQUIDs. Fig. 2 shows the chain’s critical current as a function of ΦS. With increasing flux, the critical current is suppressed due to the increase of quantum fluctuations. From our measurements, the quantum phase-slip rate υ is deduced. Quantum phase-slips in Josephson junction networks offer interesting prospects in the realisation of topologically protected qubits and for current standards.
Fig. 2 : Measured critical current (black points) as a function of flux ΦS0 through the SQUID. The red curve is the theoretical fit. Inset : Quantum phase-slip rate u as a function of flux.

Further reading :

  • Measurement of the effect of quantum phase-slips in a Josephson junction chain, I. Pop, . I. Protopopov, F. Lecocq, Z. Peng, B. Pannetier, O. Buisson, W. Guichard, arXiv:0912.2417 accepted for publication in Nature Physics
  • Measurement of the current-phase relation in Josepshon junction rhombi chains, I. Pop, K. Hasselbach, 0. Buisson, W. Guichard, I. Protopov, B. Pannetier, Phys. Rev. B, Phys. Rev. B 78, 104504 (2008)

Cet article est repris du site C’NANO Rhône-Alpes

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