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Amplitude and frequency sensing of microwave fields with a superconducting transmon qudit

M Donnell Kristen, Andre Schneider, Alexander Stehli, Tim Wolz, Sergey Danilin, H. S. Ku, J. L. Long, Xian Wu, Russell E. Lake, David P. Pappas, Alexey Vladimirovich Ustinov, Martin P. Weides

Published Jan 1, 2020• 26 citations
Publisher

Abstract

Experiments with superconducting circuits require careful calibration of the applied pulses and fields over a large frequency range. This remains an ongoing challenge as commercial semiconductor electronics are not able to probe signals arriving at the chip due to its cryogenic environment. Here, we demonstrate how the on-chip amplitude and frequency of a microwave signal can be inferred from the ac Stark shifts of higher transmon levels. In our time-resolved measurements we employ Ramsey fringes, allowing us to detect the amplitude of the systems transfer function over a range of several hundreds of MHz with an energy sensitivity on the order of 10−4. Combined with similar measurements for the phase of the transfer function, our sensing method can facilitate pulse correction for high fidelity quantum gates in superconducting circuits. Additionally, the potential to characterize arbitrary microwave fields promotes applications in related areas of research, such as quantum optics or hybrid microwave systems including photonic, mechanical or magnonic subsystems.

DOI
10.5445/ir/1000122135

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Experiments with superconducting circuits require careful calibration of the applied pulses and fields over a large frequency range. This remains an ongoing challenge as commercial semiconductor electronics are not able to probe signals arriving at the chip due to its cryogenic environment. Here, we demonstrate how the on-chip amplitude and frequency of a microwave signal can be inferred from the ac Stark shifts of higher transmon levels. In our time-resolved measurements we employ Ramsey fringes, allowing us to detect the amplitude of the systems transfer function over a range of several hundreds of MHz with an energy sensitivity on the order of 10−4. Combined with similar measurements for the phase of the transfer function, our sensing method can facilitate pulse correction for high fidelity quantum gates in superconducting circuits. Additionally, the potential to characterize arbitrary microwave fields promotes applications in related areas of research, such as quantum optics or hybrid microwave systems including photonic, mechanical or magnonic subsystems.
Abstract Experiments with superconducting circuits require careful calibration of the applied pulses and fields over a large frequency range. This remains an ongoing challenge as commercial semiconductor electronics are not able to probe signals arriving at the chip due to its cryogenic environment. Here, we demonstrate how the on-chip amplitude and frequency of a microwave signal can be inferred from the ac Stark shifts of higher transmon levels. In our time-resolved measurements we employ Ramsey fringes, allowing us to detect the amplitude of the systems transfer function over a range of several hundreds of MHz with an energy sensitivity on the order of 10 −4 . Combined with similar measurements for the phase of the transfer function, our sensing method can facilitate pulse correction for high fidelity quantum gates in superconducting circuits. Additionally, the potential to characterize arbitrary microwave fields promotes applications in related areas of research, such as quantum optics or hybrid microwave systems including photonic, mechanical or magnonic subsystems.
Analyzing weak microwave signals in the GHz regime is a challenging task if the signal level is very low and the photon energy widely undefined. A superconducting qubit can detect signals in the low photon regime, but due to its discrete level structure, it is only sensitive to photons of certain energies. With a multilevel quantum system (qudit) in contrast, the unknown signal frequency and amplitude can be deduced from the higher level ac Stark shift. The measurement accuracy is given by the signal amplitude, its detuning from the discrete qudit energy level structure, and the anharmonicity. We demonstrate an energy sensitivity in the order of ${10}^{\ensuremath{-}3}$ with a measurement range of more than 1GHz1\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}1GHz. Here, using a transmon qubit, we experimentally observe shifts in the transition frequencies involving up to three excited levels. These shifts are in good agreement with an analytic circuit model and master equation simulations. For large detunings, we find the shifts to scale linearly with the power of the applied microwave drive. Exploiting the effect, we demonstrated a power meter which makes it possible to characterize the microwave transmission from source to sample.
Quantum systems based on superconducting circuits with qubits with quantized energy levels serve as an efficient physical background for constructing different quantum devices, for instance, quantum sensors. The important class of such engineering devices belongs to the systems with quantum tunneling effects, like Josephson junctions, where the set of energy levels is influenced by the external fields. These fields change the phase properties of the measuring qubits, and, in this way, they can be detected. The weakly anharmonic oscillator is often referred as a transmon qubit. Such qubits are constructed with superconducting capacitor structures connected by Josephson junctions, they can be controlled by microwave pulses of a few nanoseconds. The quantum sensing mechanism studied here is based on coupling the measuring transmon superconducting qubits with magnetic materials. The sensing protocol of Ramsey Fringes interferometry covers several stages and demands high-quality control over the sensor coherence. Although the weakly nonlinear properties of transmons prevent the sensing procedure from the strong influence of external perturbations, nevertheless, the extension of the coherence time interval and minimization of the dephasing effects are still a matter of great importance. Here we discuss the improvement of the quantum sensor performance by the application of feedback control in the form of gradient descent algorithm over the dephasing factor-function.
Interactions between few-photon microwave fields and superconducting artificial atoms provide a method to study photon statistics and manipulate quantum states for photonic quantum information processing. Superconducting transmons couple to microwave fields through an anharmonic ladder of energy levels, producing a response beyond the two-level description. Here, we propose and analyze a detector based on a flux-tunable transmon qudit in circuit quantum electrodynamics. Within a Kerr-type model, we calculate its population response to classical-field excitation and quantized Fock and coherent states. In the four-photon example, a selected detuning produces periodic, nearly complete transfer to the fourth transmon level for a Fock input, while a coherent input of equal mean energy gives a population of approximately 0.2 at the same interaction time. In the linear regime, we derive a target-population bound for classical inputs. From single-tone and two-tone spectroscopy, analyzed using the cosine transmon Hamiltonian, we extract circuit parameters and resolve higher transitions. Ramsey interferometry characterizes dephasing on the fundamental transition. We propose a detection protocol combining flux-selected interaction with dispersive population readout. Our results establish a population-based framework for microwave-state discrimination using a superconducting artificial atom.
The strong requirement for high-performing quantum computing led to intensive research on novel quantum platforms in the last decades. The circuital nature of Josephson-based quantum superconducting systems powerfully supports massive circuital freedom, which allowed for the implementation of a wide range of qubit designs, and an easy interface with the quantum processing unit. However, this unavoidably introduces a coupling with the environment, and thus to extra decoherence sources. Moreover, at the time of writing, control and readout protocols mainly use analogue microwave electronics, which limit the otherwise reasonable scalability in superconducting quantum circuits. Within the future perspective to improve scalability by integrating novel control energy-efficient superconducting electronics at the quantum stage in a multi-chip module, we report on an all-microwave characterization of a planar two-transmon qubits device, which involves state-of-the-art control pulses optimization. We demonstrate that the single-qubit average gate fidelity is mainly limited by the gate pulse duration and the quality of the optimization, and thus does not preclude the integration in novel hybrid quantum-classical superconducting devices.
Having accurate gate generation is essential for precise control of a quantum system. The generated gate usually suffers from linear and nonlinear distortion. Previous works have demonstrated how to use a qubit to correct linear frequency distortions but have not commented on how to handle nonlinear distortions. This is an important issue as we show that nonlinear amplitude distortions from the RF electronics can affect Rabi pulses by as much as 10%. We present work that demonstrates how a transmon qubit can be used as a highly sensitive cryogenic detector to characterize these nonlinear amplitude distortions. We show that a correction can drive these errors down to <1% over a 700 MHz range. This correction technique provides a method to minimize the effects of signal distortions and can be easily applied to broadband control pulses to produce higher fidelity arbitrary quantum gates.