Experiments with one-dimensional arrays of Josephson junctions in the regime of dominating charging energy show that the Coulomb blockade is lifted at the threshold voltage, which is proportional to the array's length and depends strongly on the Josephson energy. We explain this behavior as de-pinning of the Cooper-pair-charge-density by the applied voltage. We assume strong charge disorder and argue that physics around the de-pinning point is governed by a disordered sine-Gordon-like model. This allows us to employ the well-known theory of charge density wave de-pinning. Our model is in good agreement with the experimental data. One-dimensional Josephson arrays show a diverse range of transport regimes. In the regime of dominating Josephson energy, which attracts a continued experimental interest 1-3 , they are highly conducting. In the regime of Josephson energy smaller or comparable to the charging energy, one-dimensional Josephson arrays show insulating (Coulomb blockade) behavior with activated transport 4 . Above a certain threshold value of the bias voltage, finite current appears even at zero temperature in the insulating regime. Initially, this switching was interpreted in terms of propagation onset of charge solitons 5-7 , i.e., the energy one has to pay in order to push one soliton into the array. However, further experiments showed that the threshold voltage is proportional to the array length and depends strongly on the value of the Josephson energy 1,8 . Here we interpret the experimentally found behavior as de-pinning in presence of strong charge disorder 9 . We argue that the system is described by a model similar to a disordered sine-Gordon model. The only difference is the fact that, instead of the usual cosine potential, we have another periodic function, the lowest Bloch band energy, which depends strongly on the Josephson energy. It is this dependence which gives rise to the dependence of the switching voltage on the Josephson energy. Previously, similar models were derived 1,[6][7][8]10 using an additional phenomenological inductance in each cell of the array, which provided the necessary mass term. In Ref. 11 it was shown, that a mass term is generated in the adiabatic regime due to the Bloch inductance 12 and the phenomenological inductance is not needed. We argue that the adiabatic mechanism is sufficient to describe the system prior and at the de-pinning point.For this work, a series of experiments has been performed on a set of three Josephson junction chains. The three arrays have been fabricated in parallel on the The set of samples contains nominally identical arrays (labeled A255, B255, and C255) comprising each 255 SQUIDs. These arrays had very similar resistances. Nevertheless, slight variations in the junction parameters are reflected in the I-V characteristics 13 . The experiments have been performed in a 3 He/ 4 He dilution refrigerator at 20 mK temperature. A scanning electron microscope (SEM) picture of a section of one of the arrays is shown in the left inset of Fig. 1. All...
Quantum physics in one spatial dimension is remarkably rich, yet even with strong interactions and disorder, surprisingly tractable. This is due to the fact that the low-energy physics of nearly all one-dimensional systems can be cast in terms of the Luttinger liquid, a key concept that parallels that of the Fermi liquid in higher dimensions. Although there have been many theoretical proposals to use linear chains and ladders of Josephson junctions to create novel quantum phases and devices, only modest progress has been made experimentally. One major roadblock has been understanding the role of disorder in such systems. We present experimental results that establish the insulating state of linear chains of sub-micron Josephson junctions as Luttinger liquids pinned by random offset charges, providing a one-dimensional implementation of the Bose glass, strongly validating the quantum many-body theory of one-dimensional disordered systems. The ubiquity of such an electronic glass in Josephson-junction chains has important implications for their proposed use as a fundamental current standard, which is based on synchronisation of coherent tunnelling of flux quanta (quantum phase slips).The combined effects of interaction and disorder in superfluid bosonic condensates can have drastic consequences, leading to the Mott insulator [1,2] and BoseAnderson glass [3][4][5]. The latter is thought to describe helium-4 in porous media, cold atoms in disordered optical potentials, disordered magnetic insulators, and thin superconducting films. The prototypical Bose-Hubbard model without disorder predicts a Beresinskii-KosterlitzThouless quantum phase transition between superfluid and Mott insulator. Experimental implementation using arrays of Josephson junctions has been explored [6][7][8], however, the possibility of the insulating glass has not been considered.One-dimensional arrays of Josephson junctions are notable for application as a fundamental current standard [9,10], which is based on synchronisation of a 'dual' Josephson effect, envisioned to arise from coherent quantum tunnelling of flux quanta, or so-called quantum phase slips [11][12][13][14][15]. Unlike the Mott insulator, the insulating glass is compressible, therefore AC synchronisation of charge may not be possible. Although the presence of offset charge disorder is well-established for small superconducting islands, it has not been sufficiently addressed in regards to dual Josephson effects.We have measured critical voltages for a large number of simple chains of sub-micron Josephson junctions with significantly varying energy scales. We observe universal scaling of critical voltage with single-junction Bloch bandwidth. Our measurements reveal a localisation length exponent that steepens with Luttinger parameter, K, arising from precursor fluctuations as one approaches the Bose glass-superfluid quantum phase transition. This contrasts with the fixed exponent found for classical pinning of charge density waves [16], vortex lattices [17] and disordered spin syst...
We present the design of a passive, on-chip microwave circulator based on a ring of superconducting tunnel junctions. We investigate two distinct physical realizations, based on Josephson junctions (JJs) or quantum phase slip elements (QPS), with microwave ports coupled either capacitively (JJ) or inductively (QPS) to the ring structure. A constant bias applied to the center of the ring provides an effective symmetry breaking field, and no microwave or rf bias is required. We show that this design offers high isolation, robustness against fabrication imperfections and bias fluctuations, and a bandwidth in excess of 500 MHz for realistic device parameters.
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