Non-Markovian dynamics of the giant atom beyond the rotating-wave approximation

TL;DR

This work investigates non-Markovian dynamics of a giant artificial atom coupled to a 1D SAW bath beyond the rotating-wave and weak-coupling limits by employing the hierarchical equations of motion (HEOM). An optimized ESPRIT-based exponential decomposition of the bath correlation function enables accurate, nonperturbative simulations, validated against zero-temperature RWA results and perturbative Redfield theory. The results show persistent memory effects at finite temperature, enhanced memory with stronger coupling, and the formation of atom–field bound states at zero temperature for two coupling points. These findings establish giant atoms as a versatile platform for studying non-Markovian open quantum dynamics with potential applications in quantum information processing and quantum thermodynamics.

Abstract

Superconducting qubits coupled to meandering transmission lines or surface acoustic waves may realize giant artificial atoms, whose spatially separated coupling points give rise to long-lived non-Markovian dynamics. Previous studies were limited to the zero-temperature, weak-coupling regime, where the rotating-wave approximation applies and only single-phonon processes contribute. Here we go beyond these limits using the hierarchical equations of motion (HEOM). We show that HEOM accurately captures the exact dynamics at zero temperature and weak coupling, whereas perturbative Redfield theory fails due to long bath memory times. The non-Markovian effects persist at finite temperatures. In the strong-coupling regime, they are further enhanced, and we observe bound-state formation at zero temperature with only two coupling points. These results establish giant atoms as a powerful platform for exploring non-Markovian open quantum dynamics and their applications in quantum information and thermodynamics.

Figures (5)

• Figure 1: Two-level giant atom coupled to the left- and right- propagating modes in a 1D acoustic waveguide via multiple contacts, with a separation of $\Delta x$.
• Figure 2: (a) Effective bath spectral density of the SAW field at zero temperature; (b) The corresponding bath correlation function as function of time. Here and in the subsequent plots, we consider an Ohmic spectral density of the SAW environment, $\gamma(\omega) = \eta \omega e^{-\omega/\omega_c}$, with the coupling strength and cutoff frequency parameters set as $\eta = 1 \times 10^{-2}$, $\omega_c/\omega_0 = 2$ and $\omega_0\tau /2\pi = 20$.
• Figure 3: Excited-state probability of the giant atom as a function of time, obtained from the RWA analytical solution, the Redfield master equation, and from HEOM simulations at zero temperature. We compare three different time delays $\tau$: (a) zero time delay, which amounts to a single contact point; (b) time delay comparable to the atomic relaxation time; (c) time delay longer than the atomic relaxation time. The other parameters are chosen as in Fig. \ref{['SD_BCF_plot']}.
• Figure 4: (a) Real part of the thermal BCF for the SAW field as a function of time at various temperatures, along with their corresponding ESPRIT fits (dashed). (b) Rescaled thermal BCFs. All other parameters are the same as in Fig. \ref{['SD_BCF_plot']}.
• Figure 5: Time evolution of the excited-state population $P_{ee}$ [panels (a), (b)] and coherence $|P_{eg}|$ [panels (c), (d)] of a two-level giant atom at different temperatures. Results are shown for weak coupling ($\eta = 1\times10^{-2}$, left column) and stronger coupling ($\eta = 5\times 10^{-2}$, right column). All other parameters are the same as in Fig. \ref{['SD_BCF_plot']}.