Telegraph flux noise induced beating Ramsey fringe in transmon qubits

TL;DR

The paper addresses nonmonotonic Ramsey fringes observed in frequency-tunable transmon qubits and proposes flux-noise, rather than solely charge-noise, as a key decoherence mechanism. It combines a transmon decoherence model with a random telegraph noise (RTN) framework to simulate Ramsey oscillations under $1/f$ flux noise and strong RTN sources. The main findings show that strong flux-RTN can produce beating Ramsey envelopes in agreement with experimental observations, and that instrument-related flux noise can be a plausible source for these patterns; relocating the instrument mitigates beating. This work provides a concrete mechanism for flux-noise-induced Ramsey beating, offering a practical path to noise mitigation and a basis for extending Ramsey-based analyses to microscopic flux-noise channels. Overall, the study advances understanding of flux-noise decoherence in superconducting qubits and demonstrates the utility of RTN modeling for interpreting complex Ramsey dynamics.

Abstract

Ramsey oscillations typically exhibit an exponential decay envelope due to environmental noise. However, recent experiments have observed nonmonotonic Ramsey fringes characterized by beating patterns, which deviate from the standard behavior. These beating patterns have primarily been attributed to charge-noise fluctuations. In this paper, we investigate the flux-noise origin of these nonmonotonic Ramsey fringes in frequency-tunable transmon qubits. We develop a random telegraph noise (RTN) model to simulate the impact of telegraph-like flux-noise sources on Ramsey oscillations. Our simulations demonstrate that strong flux-RTN sources can induce beating patterns in the Ramsey fringes, showing excellent agreement with experimental observations in transmon qubits influenced by electronic environment-induced flux-noise. Our findings provide valuable insights into the role of flux-noise in qubit decoherence and underscore the importance of considering flux-noise RTN when analyzing nonmonotonic Ramsey fringes.

Figures (6)

• Figure 1: Flux noise in frequency-tunable transmon qubits. (a) Schematic illustration of a transmon qubit coupled to flux noise sources. A single strongly-coupled flux-RTN can induce a doublet-structure in the qubit transition frequency, leading to decoherence. (b) $1/f$ noise power spectrum density. The blue line represents the PSD obtained from the discrete Fourier transform of all generated $1/f$ noise sample functions. The orange line shows the theoretical PSD derived by summing the Lorentzian-type PSD contributions from each RTN source. The green line indicates the ideal PSD for $1/f$ noise. All three PSDs are normalized at $f_{01}=8\times 10^{-4}\ {\rm GHz}$.
• Figure 2: Ramsey fringe of a transmon qubit. (a) Ramsey oscillations of a transmon qubit simulated using an RTN flux noise model with a $1/f$ noise spectrum. The inset shows the pulse sequence of a typical Ramsey experiment. (b) Similar to panel (a), but incorporating an additional strong flux noise source characterized by a fixed switching frequency. The Ramsey fringes exhibit a beating pattern due to this additional noise component. (c) Regular Ramsey oscillation fringe of a transmon qubit device (qubit-1). Blue line represents the experimental result, while yellow line depicts the Ramsey oscillation fitted by the function $(1+\cos(\Delta \omega \tau)\exp(-\Gamma \tau))/2$, and green line highlights the envelope $\exp(-\Gamma t)$. (d) Similar to panel (c) but with a beating envelope. The fitting function is modified to $(1+\cos(\Delta \omega \tau)\exp(-\Gamma \tau)|\cos(\delta \omega \tau/2)|)/2$ according to Eq. \ref{['eq-15']}. The frequency detuning $\Delta\omega$ in panel (d) is set to a larger value compared to that in panel (c) in order to more clearly display the beating pattern.
• Figure 3: Extracted qubit state vector XY-modulus (i.e., $E(t)$ or $E^\prime(t)$) from the Ramsey experiment as a function of qubit frequency $f_{01}$ and the time interval $\tau$. (a) and (c) show experimental results for qubit-1 and qubit-2. For both qubits, the Ramsey fringe envelope exhibits exponential decay at all frequencies. Red dots represent the decoherence time $T_2^*$ obtained by fitting the Ramsey envelopes, with the mean and maximum values of $T_2^*$ labeled. $T_2^*$ decreases significantly when the qubit is far from the optimal point. (b) and (d) are similar to panels (a) and (c), but they exhibit a beating phenomenon across the entire tunable frequency range. (e) shows the numerically simulated $E(t)$ spectrum when only $1/f$ noise is applied to the transmon qubit. (f) is similar to panel (e) but includes an additional strong RTN. The simulations are in excellent agreement with the experimental results.
• Figure 4: Ramsey fringes induced by multiple strong flux-RTN sources. (a) Ramsey fringes in the presence of $1/f$ noise and $N$ flux-RTN sources, where $N = 2, 3$. (b) Simulated $E(t)$ for Ramsey process as a function of $N$. From left to right, the amplitude of the additional flux-RTN is distributed among $N$ individual sources. For each $N$, the amplitudes of individual flux-RTN sources $b_i (i=1,2,\ldots,N)$ are randomly generated while their total sum remains constant, i.e., $\sum\limits_{i=1}^N{b_i}=b_0$. The spectra demonstrate how the beating pattern evolves into a typical exponential decay pattern as the influence of the additional strong flux-RTN is averaged out. ($\lambda=50\ {\rm Hz}$, $b_0=8\times 10^{-5}\ \Phi_0$, $\Phi_b=0.0966\ \Phi_0$)
• Figure S1: Sketch of the measurement setup. The superconducting qubit chip is measured in a dilution refrigerator with a base temperature of approximately 20 mK. Each readout channel consists of a HEMT amplifier powered by a DC-current source. The beating Ramsey interference pattern appears when the current source is positioned at location A, and disappears when the current source is placed at location B.