Erratum: ac Stark Shift and Dephasing of a Superconducting Qubit Strongly Coupled to a Cavity Field [Phys. Rev. Lett.94, 123602 (2005)]

Abstract

Figure 5a in the Letter presents the ac Stark shift of a Cooper pair box inside a coplanar waveguide resonator as a function of microwave probe power driving the resonator. Within lowest order perturbation theory, the corresponding cavity photon number is linear in the drive power. The photon number fit to the data using Eq. (1) in the Letter is shown in Fig. 5a. Lowest order perturbation theory is expected to break down [1] on the scale of the critical photon number n c 2 =4g 2 82. This breakdown is not visible in Fig. 5a which shows the ac Stark shift to be almost perfectly linear in probe power even slightly beyond n c . We pointed out in the Letter that this was a result of the compensation of the two most important nonlinear effects beyond lowest order perturbation theory. Approximate modeling of these nonlinearities [2] shows that the cavity photon number begins to be superlinear in probe power even below n c . The photon number scale in Fig. 5a is thus low by about 50% at the largest power. However, the ac Stark shift per photon is correspondingly sublinear in photon number leading to the accidental cancellation. As a consequence the photon number scale in Fig. 5b at high powers is low by the same amount. A version of this plot taking into account the higher order corrections is presented in Fig. 3 of Ref.[2].

Quantum and classical resonant escapes of a strongly driven Josephson junction

“…[16][17][18][19][20] These authors demonstrated that previously quantum mechanically explained single-or multiphoton resonance, the effective barrier suppression, and the Rabi oscillation can also be understood from the classical point of view. Interpretations on both the classical and quantum bases are also reported [19][20][21][22] for the results involving multiphoton, multilevel Rabi oscillation, and ac Stark shift at high W. [21][22][23][24] It is found that at high W, the predictions of the classical and quantum pictures may converge. 22 These results indicate that the Josephson junction system can have a dual character, classical and quantum mechanical, when a microwave field is applied.…”

Collective modes in the fluxonium qubit

“…To understand how the qubit-collective modes interactions can affect coherence, let us briefly review the so-called photon shot noise (or measurement-induced) dephasing, originating from the interaction between a qubit and the electromagnetic modes of the cavity in which it is placed [28,29]. As a consequence of this coupling, the qubit frequency ω 10 depends on the occupation of the cavity modes ω 10 ({n μ }) = ω 10 + 2 μχ μ n μ , (1) where n μ is the occupation number of mode μ andχ μ denotes the dispersive shift of that mode.…”

Coherence Times of Dressed States of a Superconducting Qubit under Extreme Driving

“…The magnitude of the rate agrees well with the theory, extracting a coupling constant C µ /C Σ ≈ 0.02 which agrees with measured circuit parameters. We include in the fit the effects of inhomogenous broadening of the dressed state resonance, which can be caused by photon number fluctuations in the oscillator [25]. To estimate this effect, we start with the frequency shift per photon g 2 osc /πδω ≈ 26 MHz, where g osc /2π ≈ 15 MHz is the qubit-oscillator coupling and we have used δω = 2πf c /Q.…”