ArticleScientific reports2023
Extremely large lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator.
Article in Scientific reports, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed, 13 citations in OpenAlex.
- Spectral properties of two superconducting artificial atoms coupled to a resonator in the ultrastrong coupling regime.Nature communications · 2025Article
- Multiple interacting photonic modes in strongly coupled organic microcavities.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2024Article
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8 authors at 4 institutions in 1 country.
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Abstract
We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator ([Formula: see text] CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency [Formula: see text] for the coupling between the FQ and the modes in the CPWR, where the coupling grows as [Formula: see text] for [Formula: see text] and decreases as [Formula: see text] for [Formula: see text]. Here [Formula: see text] is the frequency of the nth mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above [Formula: see text] at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3% and the total Lamb shift from all the modes is 96.5%. This result illustrates that the coupling to the large number of modes in a CPWR yields an extremely large Lamb shift but does not suppress the qubit energy to zero, which would happen in the absence of a high-frequency cut-off.
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