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arXiv:0901.3110 · Physical Review B

Intermode dephasing in a superconducting stripline resonator

Oren Suchoi, Baleegh Abdo, Eran Segev, Oleg Shtempluck, M. P. Blencowe, Eyal Buks

Published May 24, 2010• 12 citations
arXivHTMLPDF

Abstract

We study a superconducting stripline resonator (SSR) made of niobium, which is integrated with a superconducting interference device (SQUID). The large nonlinear inductance of the SQUID gives rise to a strong Kerr nonlinearity in the response of the SSR, which in turn results in strong coupling between different modes of the SSR. We experimentally demonstrate that such intermode coupling gives rise to dephasing of microwave photons. The dephasing rate depends periodically on the external magnetic flux applied to the SQUID, where the largest rate is obtained at half integer values (in units of the flux quantum). To account for our result we compare our findings with theory and find good agreement.

DOI
10.1103/physrevb.81.174525

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Journal of Physics Conference Series•Jun 1, 2010•4 citations
We study a superconducting stripline resonator (SSR) made of niobium, which is integrated with a superconducting interference device (SQUID). The large nonlinear inductance of the SQUID gives rise to a strong Kerr nonlinearity in the response of the SSR, which in turn results in strong coupling between different modes of the SSR. We experimentally demonstrate that such intermode coupling gives rise to dephasing of microwave photons. The dephasing rate depends periodically on the external magnetic flux applied to the SQUID, where the largest rate is obtained at half integer values (in units of the flux quantum). To account for our result we compare our findings with theory and find good agreement.
We study self-sustained oscillations (SO) in a Nb superconducting stripline resonators (SSR) integrated with a DC superconducting quantum interface devices (SQUID). We find that both the power threshold where these oscillations start and the oscillations frequency are periodic in the applied magnetic flux threading the SQUID loop. A theoretical model which attributes the SO to a thermal instability in the DC-SQUID yields a good agreement with the experimental results. This flux dependant nonlinearity may be used for quantum state reading of a qubit-SSR integrated device.
The nonlinearity exhibited by the kinetic inductance of a superconducting stripline couples stripline resonator modes together in a manner suitable for quantum nondemolition measurement of the number of photons in a given resonator mode. Quantum nondemolition measurement is accomplished by coherently driving another resonator mode, referred to as the detector mode, and measuring its response. We show that the sensitivity of such a detection scheme is directly related to the dephasing rate induced by such an intermode coupling. We show that high sensitivity is expected when the detector mode is driven into the nonlinear regime and operated close to a point where critical slowing down occurs.
We study self-sustained oscillations in a Nb superconducting stripline resonator integrated with a dc superconducting quantum interference device (SQUID). We find that both the power threshold where these oscillations start and the oscillation frequency are periodic in the applied magnetic flux threading the SQUID loop. A theoretical model which attributes the self-sustained oscillations to a thermal instability in the dc-SQUID yields a good agreement with the experimental results. This flux dependant nonlinearity may be used for quantum state reading of a qubit-superconducting resonator integrated device.
Recently the exploration of nonlinear microwave response in superconducting circuits has been extended to Nb nanobridges that can operate at higher magnetic fields, frequencies, and temperatures than their conventional Al counterparts. Nb nanobridge-based Superconducting Quantum Interference Devices (SQUIDs) have shown potential applications in quantum information processing, weak signal detection, and single spin detection. Combining such non-linear elements with circuit Quantum Electrodynamic (QED) elements like coplanar waveguide (CPW) resonators allows the study of the nonlinearity of such systems. In this work we report on the design, fabrication and dispersive microwave readout of a Nb DC nanoSQUID embedded in a superconducting quarter-wavelength resonator. The measured flux-tuneability of the resonance shows a modulation of a few MHz and fits simulations, giving a critical current of 330 μA and a screening parameterβLof 4.07. Following this we present results showing Kerr-type detuning with a pump tone applied to the device.
We investigate nondegenerate parametric oscillations in a superconducting microwave multimode resonator that is terminated by a superconducting quantum interference device (SQUID). The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonant tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.
We evaluate mutual inductance between two horizontally-placed strip lines in niobium integrated chips, by means of both experiments and numerical calculations. In the experiments, one strip line is used as a part of a superconducting quantum interference device (SQUID) loop, and the other is used as a control line for applying external magnetic flux to the SQUID loop. The mutual inductance is obtained from the modulation period of the SQUID. In the numerical calculations, we employ a three-dimensional inductance extraction software (FastHenry). Three types of strip line structures on a lower ground plane (GP) are examined: two horizontally-placed microstrip lines without an upper GP (MSLs), two horizontally-placed strip lines with a floating upper GP (FLSLs), and two strip lines with an upper GP connected to the lower GP (COSLs). We have found that each strip line structure has different dependence of mutual inductance on the line center distance. The mutual inductance between the MSLs exhibits strong dependence on the line center distance, whereas that between FLSLs is almost independent on the distance. Negligible mutual inductance is obtained for the COSLs.