Development of a Superconducting Differential Double Contour Interferometer

Abstract

We study operation of a new device, the superconducting differential double contour interferometer (DDCI), in application for the ultra sensitive detection of magnetic flux and for digital read out of the state of the superconducting flux qubit. DDCI consists of two superconducting contours weakly coupled by Josephson Junctions. In such a device a change of the critical current and the voltage happens in a step-like manner when the angular momentum quantum number changes in one of the two contours. The DDCI may outperform traditional Superconducting Quantum Interference Devices when the change of the quantum number occurs in a narrow magnetic field region near the half of the flux quantum due to thermal fluctuations, quantum fluctuations, or the switching a loop segment in the normal state for a while by short pulse of an external current. Higher sensitivity of DDCI compared to the conventional SQUID is provided by strong discreteness of the energy spectrum of the continuous superconducting loop [6]. According to the conventional theory [7] the total energy of the persistent currentin a loop with small cross section s ≪ λ 2 L (T ) is determined mainly by the kinetic energy [8]:L /s)L is the kinetic inductance of the loop of side l; L ≈ µ 0 l is the magnetic inductance; s is the cross section of superconducting wires; n s is the density of the Cooper pairs;is the London penetration depth. Two permitted states n and n + 1 have equal energy at Φ = (n + 0.5)Φ 0 according to (2) and thus equal probability P ∝ exp(−E k /k B T ). The probability of other permitted states is negligible and P (n+1) ≈ 1−P (n) at Φ ≈ (n+0.5)Φ 0 when Φ 2 0 /2L k = I p,A Φ 0 ≫ k B T . The probability of the n state may be described with the relationat the magnetic flux Φ = (n + 0.5)Φ 0 + δΦ, when δΦ ≪ Φ 0 . Here I p,A = Φ 0 /2L k is the persistent current (1) at |n − Φ/Φ 0 | = 1/2 and ǫ = I p,A Φ 0 /k B T . The probability (3) changes from P (n) ≈ 1 to P (n) ≈ 0 in a region of the magnetic flux from δΦ ≈ −Φ 0 /2ǫ to δΦ ≈ Φ 0 /2ǫ. This region may be very narrow due to a big value ǫ = I p,A Φ 0 /k B T ≫ 1 equal, for example ǫ ≈ 1500 at the temperature of measurement T ≈ 1 K and a typical value I p,A = 10 µA measured, for example in [9]. Measurements [10] of flux qubit (superconducting loop with three

Observation of flux qubit states with the help of a superconducting differential double contour interferometer

“…The method proposed in this work is based on a new device, the superconducting differential double contour interferometer (DDCI) studied in [25]. DDCI consists of two superconducting contours.…”

“…The bias current flows into the upper loop, passes through the Josephson junctions J a , J b in the lower loop and flows out the other side of the lower loop, Fig.1. It was shown theoretically [26] that the maximum value of the superconducting bias current [25]. The both superconducting loops of the DDCI used in [25] were not interrupted by the Josephson junctions.…”

“…It was shown theoretically [26] that the maximum value of the superconducting bias current [25]. The both superconducting loops of the DDCI used in [25] were not interrupted by the Josephson junctions. Therefore the quantum number changed when the persistent current I p,i = (n i Φ 0 − Φ)/L k in the loop i reached a critical value I c,i ≈ Φ 0 l/2πξ(T )L k with the magnetic flux Φ variation [29,29] rather than at Φ ≈ (n ′ + 0.5)Φ 0 .…”

“…Here L k is the kinetic inductance; l is the length of the loop; ξ(T ) is the coherence length of the superconductor. The voltage jumps up when the sum n u + n d becomes odd because of the change the quantum number in one of the loops and returns back when the quantum number changes in another loop [25]. The period B 0 = Φ 0 /S between the jumps up or down corresponds the flux quantum Φ 0 inside the loop [25].…”

“…The voltage jumps up when the sum n u + n d becomes odd because of the change the quantum number in one of the loops and returns back when the quantum number changes in another loop [25]. The period B 0 = Φ 0 /S between the jumps up or down corresponds the flux quantum Φ 0 inside the loop [25]. More than 1000 jumps with period B 0 ≈ 0, 053 Oe were observed at low temperatures in the interval 30 Oe < B < 30 Oe at the measurement of the DDCI with the side of the square loops a ≈ 20 µm and the area S = a 2 ≈ 400 µm 2 [25].…”