Josephson effects in an alternating current biased transition edge sensor

Abstract

We report the experimental evidence of the ac Josephson effect in a transition edge sensor (TES) operating in a frequency domain multiplexer and biased by ac voltage at MHz frequencies. The effect is observed by measuring the non-linear impedance of the sensor. The TES is treated as a weakly-linked superconducting system and within the resistively shunted junction model framework. We provide a full theoretical explanation of the results by finding the analytic solution of the non-inertial Langevian equation of the system and calculating the non-linear response of the detector to a large ac bias current in the presence of noise.Superconducting transition-edge sensors (TESs) are highly sensitive thermometers widely used as radiation detectors over an energy range from near infrared to gamma rays. In particular we are developing TESbased detectors for the infrared SAFARI/SPICA 1 and the X-ray XIFU/Athena 2 instruments. TESs are in most cases low impedance devices that operate in the voltage bias regime while the current is generally read-out by a SQUID current amplifier. Both a constant or an alternating bias voltage can be used 3,4 . In the latter case changes of the TES resistance induced by the thermal signal modulate the amplitude of the ac bias current. The small signal detector response is modelled in great details both under dc and ac bias 5,6 . Those models however do not fully explain all the physical phenomena recently observed in TESs. It has been recently demonstrated that TES-based devices behave as weak-links due to longitudinally induced superconductivity from the leads via the proximity effect 7 and a detailed experimental investigation of the weak-link effects in dc biased x-ray microcalorimeters has been reported 8 . Evidence of weaklink effects in ac biased TES microcalorimeters has been given 9 , but an adequate experimental and theoretical investigation is still missing. We previously proposed a theoretical framework 10 based on the resistively shunted junction model (RSJ) that can be used to describe the resistive state of a TES under dc bias. In this letter, we extend the model to calculate the stationary non-linear response of a TES to a large ac bias current in the presence of noise and we compare it to the experimental data obtained with a TES-based bolometer. We report a clear signature of the ac-Josephson effect in the TES biased at MHz frequencies.The general equation for the Frequency Domain Multiplexing (FDM) electrical circuit, simplified for a single a) Electronic mail: l.gottardi@sron.nl resonator is 6(1) where V (t) is the total voltage across the TES, L and C are respectively the inductance and the capacitance of the bias circuit, r s is the total stray resistance in the circuit and Z T ES is the TES impedance, which depends on temperature T and current I(t). As previously reported 8,11 , the superconducting leads proximitize the TES bilayer film over a distance defined by the coherence length ξ. As a result, the superconducting order parameter |Ψ| is spatially dependent over the ...

Modelling proximity effects in transition edge sensors to investigate the influence of lateral metal structures

“…Such Fraunhofer-like flux-dependencies have been observed experimentally. 24,38 We also see a periodic dependence of the electrothermal parameters α and β on applied magnetic field, as demonstrated by Figure 13. Again, the relationship is not perfectly symmetric -there is a slight skew in the curve.…”

Josephson Effects in Frequency-Domain Multiplexed TES Microcalorimeters and Bolometers

“…The RSJ model assumes this resistance to be constant and equal to the weak-link normal resistance R N . Despite this simplification of the problem, the RSJ model has been widely used to explain the major effects observed in many types of weak-links and Josephson junctions [12], including the TES-based detectors biased at MHz frequencies [8,9]. In the case of an ac voltage-biased TES, the gauge-invariant phase ϕ oscillates at the bias frequency ω 0 , is π/2-out-phase with the voltage and its peak value is proportional to V 0 /ω 0 .…”

“…The TES detector physics and its interaction with the read-out circuit are not completely understood. The TES behaviour under dc and ac bias is strongly affected by proximity effects caused by the connection to the higher T c superconducting Nb leads and by the normal metal structures introduced to suppress the excess noise [3][4][5][6][7][8]. The TES behaves typically as an SS'S or SNS junction, and the Josephson effects are regularly observed both in the response to the perpendicular magnetic field and, under ac bias, in the changes of the TES reactance across the superconducting transition.…”

Development of the superconducting detectors and read-out for the X-IFU instrument on board of the X-ray observatory Athena

“…In figure 2 the model of the resistive transition for a TiAu TES bolometer developed at SRON [16] is shown. The Josephson current has been directly observed in TES-bolometers operating in a frequency domain multiplexer and biased by ac voltage at MHz frequencies [16]. The recent development in understanding the physics of the TES's is con- The pixels array for X-IFU, based on MoAu TES's and Au-Bismuth absorbers is currently under development at NASA-Goddard [17].…”