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arXiv:2005.01975 · Physical Review A

Tunable and weakly invasive probing of a superconducting resonator based on electromagnetically induced transparency

Byoung-moo Ann, Gary Alexander Steele

Published Nov 24, 2020• 12 citations
arXivHTMLPDF

Abstract

Superconducting cavities with high quality factors play an essential role in circuit quantum electrodynamics and quantum computing. In measurements of the intrinsic loss rates of high frequency modes, it can be challenging to design an appropriate coupling to the measurement circuit in such a way that the resulting signal is sufficiently strong but also that this coupling does not lead to an unwanted loading circuit, obscuring the intrinsic internal loss rates. Here, we propose and demonstrate a spectroscopic probe of high-Q resonators based on the phenomena of electromagnetically induced transparency (EIT) between the resonator and qubit in the weak dispersive coupling regime. Applying a sideband drive signal to the qubit, we observe an interference dip originated from EIT in the qubit spectroscopy, originating from the quantum interference between the qubit probe signal and sideband transition. From the width and the depth of the dip, we are able to extract the single-photon linewidth of the resonator from an analytical model. Working in a previously unexplored regime in which the qubit has a larger linewidth than the resonator reduces the technical challenge of making a high-coherence qubit and is advantageous for remaining in the weakly invasive limit of coupling to the resonator. Furthermore, the sideband and the dispersive coupling between the resonator and the qubit can be tuned $in\phantom{\rule{3.33333pt}{0ex}}situ$ controlling the strength of the sideband drive power. This in situ tuneability allows the technique to be applied for efficient measurement of the resonator loss rate for any quality factor below a fixed upper bound, on the order of ${10}^{8}$ for our device, allowing a wide range of quality factors to be probed using a single design.

DOI
10.1103/physreva.102.053721

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Superconducting cavities with high quality factors play an essential role in circuit quantum electrodynamics and quantum computing. In measurements of the intrinsic loss rates of high frequency modes, it can be challenging to design an appropriate coupling to the measurement circuit in such a way that the resulting signal is sufficiently strong but also that this coupling does not lead to an unwanted loading circuit, obscuring the intrinsic internal loss rates. Here, we propose and demonstrate a spectroscopic probe of high-Q resonators based on the phenomena of electromagnetically induced transparency (EIT) between the resonator and qubit in the weak dispersive coupling regime. Applying a sideband drive signal to the qubit, we observe an interference dip originated from EIT in the qubit spectroscopy, originating from the quantum interference between the qubit probe signal and sideband transition. From the width and the depth of the dip, we are able to extract the single-photon linewidth of the resonator from an analytical model. Working in a previously unexplored regime in which the qubit has a larger linewidth than the resonator reduces the technical challenge of making a high-coherence qubit and is advantageous for remaining in the weakly invasive limit of coupling to the resonator. Furthermore, the sideband and the dispersive coupling between the resonator and the qubit can be tuned insituin\phantom{\rule{3.33333pt}{0ex}}situinsitu controlling the strength of the sideband drive power. This in situ tuneability allows the technique to be applied for efficient measurement of the resonator loss rate for any quality factor below a fixed upper bound, on the order of 108{10}^{8}108 for our device, allowing a wide range of quality factors to be probed using a single design.
We discuss level splitting and sideband transitions induced by a modulated coupling between a superconducting quantum circuit and a nanomechanical resonator. First, we show how to achieve an unconventional time-dependent longitudinal coupling between a flux (transmon) qubit and the resonator. Considering a sinusoidal modulation of the coupling strength, we find that a first-order sideband transition can be split into two. Moreover, under the driving of a red-detuned field, we discuss the optical response of the qubit for a resonant probe field. We show that level splitting induced by modulating this longitudinal coupling can enable two-color electromagnetically induced transparency (EIT), in addition to single-color EIT. In contrast to standard predictions of two-color EIT in atomic systems, we apply here only a single drive (control) field. The monochromatic modulation of the coupling strength is equivalent to employing two eigenfrequency-tunable mechanical resonators. Both drive-probe detuning for single-color EIT and the distance between transparent windows for two-color EIT can be adjusted by tuning the modulation frequency of the coupling.
Electromagnetically induced transparency (EIT) has usually been demonstrated by using three-level atomic systems. In this paper, we theoretically proposed an efficient method to realize EIT in microwave regime through a coupled system consisting of a flux qubit and a superconducting LC resonator with relatively high quality factor. In the present composed system, the working levels are the dressed states of a two-level flux qubit and the resonators with a probe pump field. There exits a second order coherent transfer between the dressed states. By comparing the results with those in the conventional atomic system we have revealed the physical origin of the EIT phenomenon in this composed system. Since the whole system is artificial and tunable, our scheme may have potential applications in various domains.
Superconducting resonators with high quality factors are extremely sensitive detectors of the complex impedance of materials and devices coupled to them. This capability has been used to measure losses in multiple different materials and, in the case of circuit quantum electrodynamics (circuit QED), has been used to measure the coherent evolution of multiple different types of qubits. Here, we report on the implementation of a scanning resonator for probing quantum coherent devices. Our scanning setup enables tunable coherent coupling to systems of interest without the need for fabricating on-chip superconducting resonators. We measure the internal quality factor of our resonator sensor in the single-photon regime to be >104 and demonstrate capacitive imaging using our sensor with zeptoFarad sensitivity and micron spatial resolution at milliKelvin temperatures. We then use our setup to characterize the energy spectrum and coherence times of multiple transmon qubits with no on-chip readout circuitry. Our experiments introduce a new tool for using circuit QED to measure existing and proposed qubit platforms.
Characterizing noise in superconducting qubits is essential for improving coherence and gate performance. Conventional noise-sensing methods typically use the qubit itself as the sensor, which limits both accessible bandwidth and applicability during driven operation. Here, we measure qubit frequency noise by detecting the photon loss it induces in a coupled high-Q superconducting cavity. We use repeated mid-circuit qubit measurements with post-selection to separate this induced loss from intrinsic cavity decay. We validate the protocol using injected noise and show that the extracted loss scales as expected with the applied noise strength. We place an upper bound of 0.70×103 rad2/s0.70\times10^3\,\mathrm{rad}^2/\mathrm{s}0.70×103rad2/s on the intrinsic qubit frequency-noise power spectral density at the cavity-qubit detuning of 508 MHz. The protocol opens access to a higher-frequency spectral window than standard qubit-based spectroscopy and may enable noise characterization during strong driving.
In this work, I investigate how to implement and quantify \\emph{in-situ} tunable quantum interface between superconducting qubits and resonators using external transverse driving fields beyond the rotating wave approximation (RWA). When studying the system under the time-periodic driving field, we typically rely on RWA, a useful technique that significantly reduces the analytical difficulties in solving the dynamics with time-dependent Hamiltonian. Nonetheless, it does not correctly describe the systems' dynamics when the drive fields are excessively strong and far off-resonant. Especially in circuit QED platform, the RWA often breakdowns. Many studies before, however, mainly focus on the transition frequency shifts. How the RWA distorts the interaction rates between two systems has been rarely explored. I have performed quantitative studies over two different systems. One is the quantum Rabi model (QRM) where a two-level atom is dispersively coupled to a resonator mode. The other is dispersively coupled a transmon and resonator system, which is the same as the QRM except that the transmon replaces the two-level atom in QRM. In both cases, I have revealed that the RWA significantly mislead the sideband transition rates between two elements. In the latter case, I have performed the experiments, and the results nicely agree with the analytical and numerical calculations. In addition to these, I also have introduced a study where the tunable coupling between a transmon and resonator is used for non-invasive resonator probing.
Sideband transitions are spectroscopically probed in a system consisting of a Cooper pair box strongly but nonresonantly coupled to a superconducting transmission line resonator. When the Cooper pair box is operated at the optimal charge bias point, the symmetry of the Hamiltonian requires a two-photon process to access sidebands. The observed large dispersive ac-Stark shifts in the sideband transitions induced by the strong nonresonant drives agree well with our theoretical predictions. Sideband transitions are important in realizing qubit-photon and qubit-qubit entanglement in the circuit quantum electrodynamics architecture for quantum information processing.