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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Toward coupling solid-state qubits using superconducting stripline resonator

Eyal Buks

Published Aug 24, 2004• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.541847

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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.
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We theoretically investigate selective coupling of superconducting charge qubits mediated by a superconducting stripline cavity with a tunable resonance frequency. The frequency control is provided by a flux-biased dc superconducting quantum interference device attached to the cavity. Selective entanglement of the qubit states is achieved by sweeping the cavity frequency through the qubit-cavity resonances. The circuit is able to accommodate several qubits and allows one to keep the qubits at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-qubit-cavity system, and analyze appropriate circuit parameters. We present a protocol for performing Bell inequality measurements, and discuss a composite pulse sequence generating a universal control-phase gate.
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 report on ultrastrong coupling between a superconducting flux qubit and a resonant mode of a system comprised of two superconducting coplanar stripline resonators coupled galvanically to the qubit. With a coupling strength as high as 17.517.5%17.5 of the mode frequency, exceeding that of previous circuit quantum electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The spectroscopic response of our multimode system reveals a clear breakdown of the Jaynes-Cummings approximation. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction.
We study a system consisting of a superconducting flux qubit strongly coupled to a microwave cavity. The fundamental cavity mode is externally driven and the response is investigated in the weak nonlinear regime. We find that near the crossing point, at which the resonance frequencies of the cavity mode and qubit coincide, the sign of the Kerr coefficient changes, and consequently the type of nonlinear response changes from softening to hardening. Furthermore, the cavity response exhibits superharmonic resonances (SHR) when the ratio between the qubit frequency and the cavity fundamental mode frequency is tuned close to an integer value. The nonlinear response is characterized by the method of intermodulation and both signal and idler gains are measured. The experimental results are compared with theoretical predictions and good qualitative agreement is obtained. The SHRs have potential for applications in quantum amplification and generation of entangled states of light.
One of the most studied model systems in quantum optics is a two-level atom strongly coupled to a single mode of the electromagnetic field stored in a cavity, a research field named cavity quantum electrodynamics or CQED. CQED has recently received renewed attention due to its implementation with superconducting artificial atoms and coplanar resonators in the so-called circuit quantum electrodynamics (cQED) architecture. In cQED, the couplings can be much stronger than in CQED due to the design flexibility of superconducting circuits and to the enhanced field confinement in one-dimensional cavities. This enabled the realization of fundamental quantum physics and quantum information processing experiments with a degree of control comparable to that obtained in CQED. The purpose of this chapter is to investigate the situation where the resonator to which the atom is coupled is made nonlinear with a Kerr-type nonlinearity, causing its energy levels to be nonequidistant. The system is then described by a nonlinear Jaynes-Cummings Hamiltonian. This considerably enriches the physics since a pumped nonlinear resonator displays bistability, parametric amplification, and squeezing. The interplay of strong coupling and these nonlinear effects constitutes a novel model system for quantum optics that can be implemented experimentally with superconducting circuits. This chapter is organized as follows. In a first section we present the system consisting of a superconducting Kerr nonlinear resonator strongly coupled to a transmon qubit. In the second section, we describe the response of the sole nonlinear resonator to an external drive. In the third section, we show how the resonator bistability can be used to perform a high-fidelity readout of the transmon qubit. In the last section, we investigate the quantum backaction exerted by the intracavity field on the qubit.