Giant atom with disorders: Effects from imperfect couplings

TL;DR

This work analyzes how disorder in coupling positions and strengths affects giant-atom physics in waveguide QED. By modeling N coupling points and deriving both the single-atom equation of motion and a master equation for braided atoms, it shows that DFI and BICs are robust in the Markovian regime to either type of disorder, while non-Markovian dynamics are more sensitive to coupling-position disorder, with coupling-strength disorder showing quadratic scaling and position disorder exhibiting extended-Debye behavior. The study also demonstrates that coupling-phase fluctuations preserve the general robustness of dark-state/BIC phenomena, though they increase decay rates quadratically with the phase noise. Overall, the results guide experimental design by outlining precision requirements for observing non-Markovian giant-atom effects and DFI.

Abstract

The study of giant atoms goes beyond the local interaction paradigm in the conventional quantum optics, and predicts novel phenomena, such as oscillating bound states in the continuum (BICs) and decoherence-free interaction (DFI) that do not exist in small atoms, for some particular parameter settings of coupling positions and strengths. However, in the realistic experiments to implement giant-atom systems, there is always some level of disorder both in coupling positions and strengths. In this work, we investigate the effects of disorder on the phenomena related to giant atoms. We find that the giant-atom related phenomena are robust to both disorders of coupling positions and strengths in the Markovian regime, but more sensitive to the disorder of coupling positions in the non-Markovian regime. Our work shows that, to observe the non-Markovian phenomenon such as (oscillating) BICs in giant-atom systems, more precision is needed to control the disorder of coupling positions than that of the coupling strengths in the experiments.

Figures (6)

• Figure 1: Sketch of two-level giant atom(s) coupled to an open 1D waveguide at multiple $N$ coupling points $x_i$ with coupling strength $g_i$ : (a) One giant atom with $N = 3$ coupling points; (b) Two braided giant atoms with total $N = 4$ coupling points. In both figures, the disorders of coupling positions and coupling strengths are illustrated by the envelope and the transparency of the blue wave packets, respectively.
• Figure 2: Parameter space of giant atom spanned by the dimensionless parameters $\Omega\tau$ (size effect) and $\gamma\tau$ (time delay effect) with $\Omega$ the atomic transition frequency, $\tau$ the travel time between two neighboring coupling points, and $\gamma$ the relaxation rate of single coupling point.
• Figure 3: The excitation probability of a typical non-Markovian giant atom as a function of evolution time. The atomic probability saturates at some finite values in the long-time limit when the dark state condition (\ref{['eq-DS']}) is satisfied (black line) with parameters: $\Omega\tau/2\pi=2.22$ and $\gamma\tau/2\pi=0.13$, but continues to decay when the condition (\ref{['eq-DS']}) is broken by the imposed disorders of coupling positions and strengths (red line) with parameters: $\Omega\tau_1/2\pi=2.231,\ \Omega\tau_2/2\pi=2.184$, $\gamma\tau_1/2\pi=0.1299,\ \gamma\tau_2/2\pi=0.1286$ and $\gamma\tau_3/2\pi=0.1329$.
• Figure 4: Disorder effects on the dark state and BIC. (a1) Averaged decay rate of giant atom $\overline{\kappa_{min}}$, cf. Eq. (\ref{['eq-kappamin']}), as functions of the coupling-strength disorder deviation $\sigma_g$ and the coupling-position disorder deviation $\sigma_x$. (a2) Averaged decay rate $\overline{\kappa_{min}}$ as a function of the coupling-strength disorder deviation $\sigma_g$ for the zero position disorder deviation $\sigma_x = 0$ with the log-log plot shown in the insert. (a3) Averaged decay rate $\overline{\kappa_{min}}$ as a function of the coupling-position disorder deviation $\sigma_x$ for the zero coupling-strength disorder deviation $\sigma_g = 0$ with the log-log plot shown in the insert. For the plots in (a1)-(a3), parameters are chosen as $\gamma \tau / 2 \pi = 1.59 \times 10^{-4},\ \Omega \tau / 2 \pi = 0.33$ and the average of the decay rate is calculated over $200$ disorder samples. (b1)-(b3) Same plots as shown in (a1)-(a3) for the parameter setting $\gamma \tau / 2 \pi = 0.13,\ \Omega \tau / 2 \pi = 2.22$ and the average over $100$ disorder samples. In the insert of (b3), $\sigma_x$ is extended to 0.4.
• Figure 5: Disorder effects of the coupling phase. (a) Averaged decay rate $\overline{\kappa_{min}}$ as a function of the coupling-phase disorder $\sigma_{\phi}$ for different coupling and position disorder settings (indicated by different colors) in the Markovian regime with parameters: $\gamma \tau / 2 \pi = 1.59 \times 10^{-4},\ \Omega \tau / 2 \pi = 0.33$. (b) Plot of $\overline{\kappa_{min}}$ as a function of $\sigma_{\phi}$ in the non-Markovian regime with the parameters: $\gamma \tau / 2 \pi = 0.13,\ \Omega \tau / 2 \pi = 2.22$. In both figures, the data are calculated over $100$ disorder samples.