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arXiv:cond-mat/0102232 · Physical review. B, Condensed matter

Interference effects in isolated Josephson junction arrays with geometric symmetries

Dmitri A. Ivanov, L. B. Ioffe, V. B. Geshkenbeǐn, G. Blatter

Published Dec 17, 2001• 28 citations

Abstract

Reducing the size of the junctions in a Josephson junction array takes the system from the classical to the quantum regime and turns the condensate phases on the islands into periodic quantum variables. Under suitable conditions such quantum arrays exhibit Aharonov-Bohm-Casher-type interference effects which change the spectrum of this macroscopic object by the addition of one Cooper pair to the array. We discuss the case of an isolated symmetric loop of N identical junctions encircling one half superconducting quantum of magnetic flux. We argue that the ground state is nondegenerate if the total number of Cooper pairs on the array is divisible by N, and doubly degenerate otherwise (after the stray charges are compensated by the gate voltages). This result is first established in the two opposite limits of dominating Josephson and charging energies, and is further explained using symmetry arguments. As long as the ground-state symmetry is preserved, its degeneracy remains unchanged in the entire range of charging-to-Josephson energy ratio. Such interference effects may be relevant in applications of superconducting junction arrays for quantum computing.

DOI: 10.1103/physrevb.65.024509

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A neutral quantum particle with magnetic moment encircling a static electric charge acquires a quantum-mechanical phase (Aharonov-Casher effect). In superconducting electronics, the neutral particle becomes a fluxon that moves around superconducting islands connected by Josephson junctions. The full understanding of this effect in systems of many junctions is crucial for the design of novel quantum circuits. Here, we present measurements and quantitative analysis of fluxon interference patterns in a six Josephson junction chain. In this multijunction circuit, the fluxon can encircle any combination of charges on five superconducting islands, resulting in a complex pattern. We compare the experimental results with predictions of a simplified model that treats fluxons as independent excitations and with the results of the full diagonalization of the quantum problem. Our results demonstrate the accuracy of the fluxon interference description and the quantum coherence of these arrays.

We observe the effect of the Aharonov-Casher (AC) interference on the spectrum of a superconducting system containing a symmetric Cooper pair box (CPB) and a large inductance. By varying the charge n_{g} induced on the CPB island, we observe oscillations of the device spectrum with the period Δn_{g}=2e. These oscillations are attributed to the charge-controlled AC interference between the fluxon tunneling processes in the CPB Josephson junctions. The measured phase and charge dependences of the frequencies of the |0⟩→|1⟩ and |0⟩→|2⟩ transitions are in good agreement with our numerical simulations. Almost complete suppression of the single fluxon tunneling due to destructive interference is observed for the charge n_{g}=e(2n+1). The CPB in this regime enables fluxon pairing, which can be used for the development of parity-protected superconducting qubits.

By exploiting the Aharonov–Casher effect, we demonstrate a significant suppression of magnetic flux tunneling in a hybrid charge quantum interference device. The main part of this device is two Josephson junctions with a small superconducting island between them. To minimize phase fluctuations across Josephson junctions, this structure is embedded in a compact superinductive NbN loop. The interference between the flux tunneling paths is determined by the island-induced charge, which is controlled by an external voltage. The charge sensitive operation of the device is subjected to poisoning by the quasiparticles generated in the NbN film.

By exploiting the Aharonov-Casher effect we demonstrate a suppression of magnetic flux tunneling in a Hybrid Charge Quantum Interference Device. The main part of this device is two Josephson junctions with a small superconducting island between them. To minimize phase fluctuations across Josephson junctions, this structure is embedded in a compact super-inductive NbN loop. The Interference between the flux tunneling paths is determined by the island-induced charge, which is controlled by an external voltage. The charge sensitive operation of the device is subjected to poisoning by the quasiparticles generated in the NbN film.

We suggest a system in which the amplitude of macroscopic flux tunneling can be modulated via the Aharonov-Casher effect. The system is an rf SQUID with the Josephson junction replaced by a Bloch transistor--two junctions separated by a small superconducting island on which the charge can be induced by an external gate voltage. When the Josephson coupling energies of the junctions are equal and the induced charge is q = e, destructive interference between tunneling paths brings the flux tunneling rate to zero. The device may also be useful as a qubit for quantum computation.

We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers.The individual interferometers realize effective cos 2φ elements that exchange "pairs of Cooper pairs" between the superconducting islands when gate tuned into balance and frustrated by a half-flux quantum.If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset-charge and magnetic field fluctuations for a sizable window around zero offset charge and half-flux quantum.This protection window broadens upon increasing the number of interferometers if the individual elements are balanced.We use an effective spin model to describe the system and show that a quantum phase transition sets the critical flux value at which protection is destroyed.