Intermodulation and parametric amplification in a superconducting stripline resonator integrated with a dc-SQUID

We utilize a superconducting stripline resonator containing a dc-SQUID as a strong intermodulation amplifier exhibiting a signal gain of 24 dB and a phase modulation of 30 dB. Studying the system response in the time domain near the intermodulation amplification threshold reveals a unique noise-induced spikes behavior. We account for this response qualitatively via solving numerically the equations of motion for the integrated system. Furthermore, employing this device as a parametric amplifier yields an abrupt rise of 38 dB in the generated side-band signal. Copyright c © EPLA, 2009 The field of solid-state qubits and quantum information processing has received considerable attention during the past decade [1–4] and has successfully demonstrated several milestone results to date [5–11]. However, one of the fundamental challenges hindering this emerging field is noise interference, which either screens the output signal or leads to quantum state decoherence [5,6,12–15]. Hence, this may explain to some extent the renewed interest exhibited recently by the quantum measurement community in the field of parametric amplifiers [16–21]. This interest is driven essentially by two important properties of these amplifiers: 1) their capability to amplify very weak coherent signals; 2) their ability to squeeze noise below the equilibrium level by means of employing a homodyne setup and phase control. These properties are expected to be highly beneficial to the area of quantum communication [22,23] and to the generation of quantum squeezed states [16,17,24,25]. Additional interest in these high-gain parametric amplifiers arises from the large body of theoretical work predicting photon-generation from vacuum via the dynamical Casimir effect [26,27], which can be achieved by employing an appropriate parametric excitation mechanism [28,29]. In this present work we study a superconducting stripline microwave resonator integrated with a dcSQUID [30–32]. The paper is mainly devoted to a novel (a)E-mail: [email protected] amplification mechanism in which the relatively large nonlinear inductance of the dc-SQUID is exploited to achieve large gain in an intermodulation (IM) configuration. We provide theoretical evidence to support our hypothesis that the underlying mechanism responsible for the large observed gain is the metastability of the dc-SQUID. In addition, at the end of the paper we demonstrate another amplification mechanism, in which the dependence of the dc-SQUID inductance on the external magnetic field is exploited to achieve parametric amplification [20]. The device (see fig. 1(a)) is implemented on a highresistivity 34mm× 30mm× 0.5mm silicon wafer coated with a 100 nm thick layer of SiN. As a preliminary step, thick gold pads (300 nm) are evaporated at the periphery of the wafer. Following a stage of e-beam lithography, a two-angle shadow evaporation of aluminium [33] —with an intermediate stage of oxidation— realizes both the resonator and the two Al/AlOx/Al Josephson junctions comprising the dc-SQUID. The total thickness of the aluminium evaporated is 80 nm (40 nm at each angle). In general, IM generation is often associated with the occurrence of nonlinear effects in the resonance curves of a superconducting resonator [34–38]. In fig. 2 we show a transmission measurement of the resonator response, obtained using a vector network analyzer at the resonance while sweeping the frequency upwards. The measured resonance resides at f0 = 8.219GHz which corresponds to