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

Abstract

We utilize a superconducting stripline resonator containing a dc-SQUID as a strong intermodulation amplifier exhibiting a signal gain of 25 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 a gain of 38 dB in the generated side-band signal. The field of solid-state qubits and quantum information processing has received considerable attention during the past decade [1,2,3,4] and has successfully demonstrated several milestone results to date [5,6,7,8,9,10,11]. 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 [5,6,12,13,14,15]. Hence, this may explain to some extent the renewed interest exhibited recently by the quantum measurement community in the field of phase-sensitive amplifiers [16,17,18,19,20,21]. 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 dc-SQUID [30,31,32]. The paper is mainly devoted to a novel 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 metastability of the dc-SQUID. In addition, at the end of the paper we demonstrate another amplification mechanism, in which the de- * Electronic address: baleegh@tx.technion.ac.il pendence of the dc-SQUID inductance on external magnetic field is exploited to achieve parametric gain [20].The device (see Fig. 1 (a)) is implemented on a highresistivity 34 mm ×30 mm ×0.5 mm Silicon wafer coated with a 100 nm thick layer of SiN. As a preliminary step, thick gold pads (300 nm) are realized at the periphery of the wafer. Subsequently, e-beam lithography is applied in which both the macroscopic resonator and the micro- In general, IM generation is a nonlinear phenomenon which is associated often with the occurrence of nonlinear effects in the res...

Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits

“…These devices also make use of the inductor's flux degree-of-freedom by using a dc-bias current to introduce a controllable oscillator resonant frequency tunable over several GHz. In (Abdo et al, 2009;Castellanos-Beltran and Lehnert, 2007) amplification and quadrature squeezing of an input signal was observed when operated as a degenerate amplifier and driven by a large amplitude pump mode. Additionally, amplification and squeezing of quantum fluctuations were observed by (Castellanos-Beltran et al, 2008) where the use of a coplanar cavity allowed for 10 dB 5 of squeezing.…”

Intermodulation in nonlinear SQUID metamaterials: Experiment and theory

“…The IM between two input frequencies f 1 and f 2 leads to products at frequencies pf 1 ±qf 2 (p and q are integers), forming side bands and additional noise that could diminish the performance of superconducting devices [4,[16][17][18][19][20][21][22][23][24][25][26][27]. On the other hand, IM generation can be used as a diagnostic to determine various types of defects in superconductors [28][29][30][31], to study unconventional superconductors [28,29,[31][32][33][34][35][36][37][38][39][40][41], and to amplify microwave signals [2,27,42,43], even at the quantum limit in Josephson parametric amplifiers [1,3] and Josephson metamaterials [7]. Therefore, IM is of mutual research interest in wireless communication, nonlinear metamaterials, as well as in quantum information processing, and superconducting electronics and materials.…”

Parametric amplification by coupled flux qubits

“…Our amplifier achieves a maximal gain of 20 dB, which is comparable to the gain of similar superconducting parametric amplifiers. 14,16,17 However, the experiments reveal two unknown features, namely two branches of high amplification of the idler signal and in the case of a bias flux of Φ = Φ 0 /2 a periodical pattern of the gain dependent on the flux itself.…”