Author:
Ao Ziqiao,Ashhab Sahel,Yoshihara Fumiki,Fuse Tomoko,Kakuyanagi Kosuke,Saito Shiro,Aoki Takao,Semba Kouichi
Abstract
AbstractWe 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 ($$\lambda /4$$
λ
/
4
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 $$\omega _{\textrm{cutoff}}$$
ω
cutoff
for the coupling between the FQ and the modes in the CPWR, where the coupling grows as $$\sqrt{\omega _n}$$
ω
n
for $$\omega _n/\omega _{\textrm{cutoff}}\ll 1$$
ω
n
/
ω
cutoff
≪
1
and decreases as $$1/\sqrt{\omega _n}$$
1
/
ω
n
for $$\omega _n/\omega _{\textrm{cutoff}}\gg 1$$
ω
n
/
ω
cutoff
≫
1
. Here $$\omega _n$$
ω
n
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 $$\omega _{\textrm{cutoff}}$$
ω
cutoff
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.
Publisher
Springer Science and Business Media LLC
Cited by
2 articles.
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