Preserving quantum coherence in thermal noisy systems via qubit frequency modulation

TL;DR

The paper addresses preserving quantum coherence of a frequency-modulated qubit in thermal, phase-covariant environments. It develops a time-local master equation for a driven qubit coupled to dissipative and dephasing baths, with a modulated frequency $\omega(t)$ and specified spectral densities. The main findings are that frequency modulation strongly protects coherence against thermal dissipative noise, is ineffective for pure dephasing due to commutation with the qubit Hamiltonian, and can provide protection under mixed noise only when the dephasing coupling $\alpha$ remains below a temperature-dependent threshold $\alpha_{\mathrm{th}}$ that decreases with temperature. These results yield practical guidelines for FM parameter choices and illuminate the limits of FM-based coherence protection in realistic, thermal quantum devices such as superconducting qubits.

Abstract

Quantum coherence is a key resource underpinning quantum technologies, yet it is highly susceptible to environmental decoherence, especially in thermal settings. While frequency modulation (FM) has shown promise in preserving coherence at zero temperature, its effectiveness in realistic, noisy thermal environments remains unclear. In this work, we investigate a single frequency-modulated qubit interacting with a thermal phase-covariant reservoir composed of dissipative and dephasing channels. We demonstrate that FM significantly preserves coherence in the presence of thermal dissipation while being ineffective under thermal pure-dephasing noise due to commutation between system and interaction Hamiltonians. When both noise channels are present, FM offers protection only for weak dephasing coupling. Our findings clarify the limitations and potential of FM-based coherence protection under thermal noise, supplying practical insights into designing robust quantum systems for quantum applications.

Figures (6)

• Figure 1: A sketch of the driven qubit system. A qubit (two-level atom) interacts with two independent types of ideal noise: dissipative noise at temperature $T_1$ and phase noise at temperature $T_2$. The transition frequency of the qubit $\omega_0$ is modulated sinusoidally by an externally applied field, characterized by a modulation amplitude $\delta$ and a modulation frequency $\Omega$. $R$ and $\alpha$ represent the dimensionless coupling strengths between the qubit and the dissipative and dephasing reservoirs, respectively.
• Figure 2: (a) Qubit coherence $\zeta(t)$ and (b) excited state population $P_e(t)$ as functions of scaled dimensionless time $\gamma t$ under a low-temperature reservoir with $K_B T_1 = 2.6 \times 10^{-3} \hbar \omega_0$. The results are shown for optimal amplitude and frequency modulations with $\delta = 2.40483 \Omega$, $\Omega = 5 \gamma$ (dotted red line), and for the case of no driving field $\Omega=0$ (solid blue line). The qubit is in the strong coupling regime with $R = 100$.
• Figure 3: (a) Qubit coherence $\zeta(t)$ and (b) excited state population $P_e(t)$ as functions of the scaled time $\gamma t$ under an intermediate-temperature reservoir with $K_B T_1 = 2.6 \hbar \omega_0$. The results are shown for optimal amplitude and frequency modulations with $\delta = 2.40483 \Omega$, $\Omega = 5 \gamma$ (dotted red line), and for the case of no driving field $\Omega=0$ (solid blue line). The qubit is in the strong coupling regime with $R = 100$.
• Figure 4: (a) Qubit coherence $\zeta(t)$ and (b) excited state population $P_e(t)$ as functions of scaled time $\gamma t$ under a high-temperature reservoir with $K_B T_1 = 260 \hbar \omega_0$. The results are shown for optimal amplitude and frequency modulations with $\delta = 2.40483 \Omega$, $\Omega = 5 \gamma$ (dotted red line), and for the case of no driving field $\Omega=0$ (solid blue line). The qubit is in the strong coupling regime with $R = 100$.
• Figure 5: Qubit coherence $\zeta(t)$ as a function of scaled time $\gamma t$ for different values of the dephasing coupling $\alpha$. The values of other parameters are: $R=100$, $\delta = 0$, $\Omega = 0$. Both dissipative and dephasing reservoirs are set to zero temperature ($T_1 = T_2 = 0$).