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arXiv:quant-ph/0511033 · Physical Review A

Dephasing due to intermode coupling in superconducting stripline resonators

Eyal Buks, Bernard Yurke

Published Feb 17, 2006• 20 citations
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Abstract

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.

DOI
10.1103/physreva.73.023815

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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 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.
The technique of cavity quantum electrodynamics was proposed for coupling solid-state qubits. We study the prospects of employing superconducting stripline resonators as cavities for this purpose. The strong nonlinearity in these resonators originated by the effect of kinetic inductance may provide new tools for manipulating the state of the system and for measuring the outcome. Based on theoretical analysis and experimental results we show that such nonlinearity can be exploited for achieving strong intermodulation gain as well as quantum squeezing. Moreover, we demonstrate the ability to tune the mode frequencies of the resonator, which is needed for implementing these effects for coupling qubits.
We study a configuration for displacement detection consisting of a nanomechanical resonator coupled to both a radio frequency superconducting interference device and to a superconducting stripline resonator. We employ an adiabatic approximation and rotating wave approximation and calculate the displacement sensitivity. We study the performance of such a displacement detector when the stripline resonator is driven into a region of nonlinear oscillations. In this region the system exhibits noise squeezing in the output signal when homodyne detection is employed for readout. We show that displacement sensitivity of the device in this region may exceed the upper bound imposed upon the sensitivity when operating in the linear region. On the other hand, we find that the high displacement sensitivity is accompanied by a slowing down of the response of the system, resulting in a limited bandwidth.
We propose a scheme for dispersive readout of stored energy in one mode of a nonlinear-superconducting microwave ring resonator by detection of the frequency shift of a second mode coupled to the first via a Kerr nonlinearity. Symmetry is used to enhance the device responsivity while minimizing self-nonlinearity of each mode. Assessment of the signal to noise ratio indicates that the scheme will function at the single-photon level, allowing quantum nondemolition measurement of the photon-number state of one mode. Experimental data from a simplified version of the device demonstrating the principle of operation are presented.
The addition of nonlinearity to an harmonic resonator provides a route to complex dynamical behaviour of resonant modes, including coupling between them. We present a superconducting device that makes use of the nonlinearity of Josephson junctions to introduce a controlled, tunable, nonlinear inductance to a thin film coplanar waveguide resonator. Considering the device as a potential quantum optical component in the microwave regime, we create a sensitive bifurcation amplifier and then demonstrate spectroscopy of other resonant modes via the intermode coupling. We find that the sensitivity of the device approaches within a factor two quantitative agreement with a quantum model by Dykman but is limited by a noise that has its source(s) on-chip.
We study the backaction of a driven nonlinear resonator on a multilevel superconducting qubit. Using unitary transformations on the multilevel Jaynes-Cummings Hamiltonian and quantum optics master equation, we derive an analytical model that goes beyond linear response theory. Within the limits of validity of the model, we obtain quantitative agreement with experimental and numerical data, both in the bifurcation and in the parametric amplification regimes of the nonlinear resonator. We show in particular that the measurement-induced dephasing rate of the qubit can be rather small at high drive power. This is in contrast to measurement with a linear resonator where this rate increases with the drive power. Finally, we show that, for typical parameters of circuit quantum electrodynamics, correctly describing measurement-induced dephasing requires a model going beyond linear response theory, such as the one presented here.