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arXiv:2007.00255 · Physical Review Applied

Photon-Dressed Bloch-Siegert Shift in an Ultrastrongly Coupled Circuit Quantum Electrodynamical System

Shuai-Peng Wang, Guo-Qiang Zhang, Yimin Wang, Zhen Chen, Tiefu Li, J. S. Tsai, Shi-Yao Zhu, J. Q. You

Published May 26, 2020• 27 citations
arXivHTMLPDF

Abstract

A cavity quantum electrodynamical (QED) system beyond the strong-coupling regime is expected to exhibit intriguing quantum phenomena. Here we report a direct measurement of the photon-dressed qubit transition frequencies up to four photons by harnessing the same type of state transitions in an ultrastrongly coupled circuit QED system realized by inductively coupling a superconducting flux qubit to a coplanar-waveguide resonator. This demonstrates a convincing observation of the photon-dressed Bloch-Siegert shift in the ultrastrongly coupled quantum system. Moreover, our results show that the photon-dressed Bloch-Siegert shift becomes more pronounced as the photon number increases, which is a characteristic of the quantum Rabi model.

DOI
10.1103/physrevapplied.13.054063

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A cavity quantum electrodynamical (QED) system beyond the strong-coupling regime is expected to exhibit intriguing quantum phenomena. Here we report a direct measurement of the photon-dressed qubit transition frequencies up to four photons by harnessing the same type of state transitions in an ultrastrongly coupled circuit QED system realized by inductively coupling a superconducting flux qubit to a coplanar-waveguide resonator. This demonstrates a convincing observation of the photon-dressed Bloch-Siegert shift in the ultrastrongly coupled quantum system. Moreover, our results show that the photon-dressed Bloch-Siegert shift becomes more pronounced as the photon number increases, which is a characteristic of the quantum Rabi model.
In recent years, quantum Rabi model has aroused considerable interest because of its fundamental importance and potential applications in quantum technologies. For a conventional cavity-quantum-electrodynamic (cavity-QED) system involving the interaction between an atom and photons in a cavity, the atom-photon coupling frequency is much smaller than the transition frequency of the atom and the frequency of the cavity mode. This cavity-QED system is usually described by the Jaynes-Cummings model in which the rotating-wave approximation can be adopted by neglecting the counter-rotating coupling terms in the Hamiltonian of the system. However, by designing the unique structure of the superconducting circuit, the ultrastrong-coupling regime can be achieved in a circuit-QED system in which the counter-rotating coupling terms become as important as the rotating terms. Thus, the rotating-wave approximation cannot be used in the ultrastrongly coupled circuit-QED system. Owing to the ultrastrong coupling, this circuit-QED system is described by the standard quantum Rabi model when a superconducting qubit is coupled only to a single resonator mode. In this work, we experimentally study an ultrastrongly coupled circuit-QED system consisting of a four-junction superconducting flux qubit and a muti-mode coplanar-waveguide resonator. The transmission-spectrum measurement and numerical simulations show that the system is in the ultrastrong-coupling regime. By changing the photon number in the resonator, we observe the frequency shift of the flux qubit via the spectroscopic measurement. This frequency shift contains the contributions from not only the rotating-coupling terms but also the counter-rotating terms, which is in good agreement with the theory. The result indicates that this ultrastrongly-coupled quantum system can be used as a good platform to investigate the quantum Rabi model and has potential applications in various aspects of quantum technology, such as quantum simulation, ultrafast quantum gates, entangled-state preparation and protected qubits.
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 report the experimental observation of high-order sideband transitions at the single-photon level in a quantum circuit system of a flux qubit ultrastrongly coupled to a coplanar waveguide resonator. With the coupling strength reaching 10% of the resonator's fundamental frequency, we obtain clear signatures of higher order red-sideband and first-order blue-sideband transitions, which are mainly due to the ultrastrong Rabi coupling. Our observation advances the understanding of ultrastrongly coupled systems and paves the way to study high-order processes in the quantum Rabi model at the single-photon level.
The realization of strong nonlinear coupling between single photons has been a long-standing goal in quantum optics and quantum information science, promising wide impact applications, such as all-optical deterministic quantum logic and single-photon frequency conversion. Here, we report an experimental observation of the strong coupling between a single-photon and a two-photon Fock state in an ultrastrongly-coupled circuit-QED system. This strong nonlinear interaction is realized by introducing a detuned flux qubit working as an effective coupler between two modes of a superconducting coplanar waveguide resonator. The ultrastrong light–matter interaction breaks the excitation number conservation, and an external flux bias breaks the parity conservation. The combined effect of the two enables the strong one–two-photon coupling. Quantum Rabi-like avoided crossing is resolved when tuning the two-photon resonance frequency of the first mode across the single-photon resonance frequency of the second mode. Within this new photonic regime, we observe the thresholdless second harmonic generation for a mean photon number below one. Our results represent a key step towards a new regime of quantum nonlinear optics, where individual photons can deterministically and coherently interact with each other in the absence of any stimulating fields. Systems with strong photon-photon interactions enable advanced quantum optical applications as well as the study of highly correlated light-matter states. Here the authors report strong coupling between single- and two-photon states in a superconducting circuit, enabling a new regime of nonlinear quantum optics.
Cavity quantum electrodynamics (QED) investigates the interaction between resonator-confined radiation and natural atoms. Similar phenomena can be explored using superconducting artificial atoms coupled to microwave resonators. Here, we examine incoherent and coherent spectra in a circuit QED system consisting of a flux qubit coupled to an LC resonator, considering different coupling configurations to the output transmission line. Although such systems can be effectively described by the quantum Rabi model, we demonstrate that the choice of the coupling between the resonator and the input-output channel can significantly affect the emission properties, particularly in the ultrastrong coupling regime. Specifically, we show that when the resonator is capacitively coupled with the input-output transmission line, the spectral features at zero flux offset can be mapped onto those of the cavity QED model. However, this correspondence breaks down for the mutual inductive coupling case. Extending our analysis to the parity-symmetry broken regime of the flux qubit, we further highlight how capacitive and inductive coupling mechanisms lead to distinct spectral features, emphasizing the necessity of a careful input-output treatment for an accurate description of the emission processes.
We show that the counter-rotating terms of the dispersive qubit-cavity Rabi model can produce relatively large and nonmonotonic Bloch-Siegert shifts in the cavity frequency as the system is driven through a quantum-to-classical transition. Using a weak microwave probe tone, we demonstrate experimentally this effect by monitoring the resonance frequency of a microwave cavity coupled to a transmon and driven by a microwave field with varying power. In the weakly driven regime (quantum phase), the Bloch-Siegert shift appears as a small constant frequency shift, while for a strong drive (classical phase) it presents an oscillatory behavior as a function of the number of photons in the cavity. The experimental results are in agreement with numerical simulations based on the quasienergy spectrum.