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QUANTUM NOISE IN JOSEPHSON JUNCTIONS AND SQUIDS

R. H. Koch

Published Apr 1, 1981• 1 citation
OpenAlex

Abstract

A theory for noise in the resistively shunted Josephson junction in the quantum limit is outlined and extended to the dc SQUID. Experimental results for both the single junction and the SQUID are reported.

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The sensitivity limitations due to thermal, quantum and shot noise are calculated for dc and ac SQUIDs. Two approximations are used for the Josephson junctions: i. RSJ model with the equilibrium source of thermal-and-quantum fluctuations and ii. microscopic theory of the tunnel junctions with small capacitance (the latter theory takes into account the shot noise as well). The ultimate "output" sensitivity ε_{V}=/2L\Deltaf is shown to be substantially less than the Planck's constant h, for the both types of SQUIDs. This result does not contradict to the uncertainty principle, because the "total" sensitivity ε=(ε_{V}ε_{I}-εmin{IV}\max{2})^{1/2} rather than ε_{V} is an adequate figure of merit of SQUID as a linear amplifier. The total sensitivity is shown to be, in fact, limited by the quantum fluctuations, ε>h/2. These fluctuations originate in the shunting resistances of the dc SQUID, while in the ac SQUID they are due to quantum noise of the following stage of amplification. Nevertheless, even the total sensitivity ε can be made less than h/2, if the "degenerate" type of SQUID is used, being sensitive to the only one of the quadrature components of the input signal.
The noise temperature of a dc superconducting quantum interference device (SQUID) coupled to a tuned input circuit is computed using the complete quantum expression for the equilibrium noise in the shunt resistance of each junction. At T = 0, where the noise reduces to zero-point fluctuations, the noise temperature for an optimized system is hn/kB ln2, where n is the signal frequency. The computation is extended to nonzero temperatures, and it is shown that a SQUID operated at 1K can approach the quantum limit.
Relaxation Oscillation SQUIDs (ROSs) based on 4x4 micrometers 2 Nb/AlOx Josephson tunnel junctions have been fabricated and characterized. A ROS consists of a hysteretic dc SQUID shunted by an inductor L and a resistor R in series to induce the relaxation oscillations. The values of L range from 20 nH up to about 300 nH, whereas the time constant L/R are between 8 and 45 ns. Frequency-flux characteristics have been recorded with the help of a spectrum analyzer, directly connected to the ROS. The relaxation frequencies range from 5 to 180 MHz. The experimental characteristics can be explained very well with a simple model describing the oscillation cycle. The effect of the self-induced magnetic field due to a magnetic coupling between the dc SQUID and the shunt circuit has been studied in detail. The sensitivity of ROSs and DROSs (Double Relaxation Oscillation SQUIDs) improves with increasing relaxation frequency. In (D)ROSs based on unshunted, hysteretic tunnel junction dc SQUIDs, the maximum relaxation frequency and the sensitivity are limited by LC resonances due to the SQUID capacitance and the shunt inductance. It is shown that the relaxation frequency can be increased up to frequencies of the order of 1 GHz if an extra resistor is integrated to damp these resonances. The optimum value of the damping resistor can be obtained from the ROS parameters. For stable operation of a (D)ROS, the shunt resistance should not be too large. The optimum value of this resistance can be calculated from the effective McCumber parameter and the bias current. Theoretically, the sensitivity of a ROS with a SQUID capacitance of 1 pF, a SQUID inductance of 20 pH and a relaxation frequency of 1 GHz equals about 5h, where h is Planck's constant. In a DROS with voltage readout based on similar SQUIDs, the theoretical sensitivity at a relaxation frequency of 1 GHz is 17h, with an estimated flux-to-voltage transfer coefficient of 5 mV/(phi) 0.