Design of Robust Raman Pulses for Cold Atom Interferometers Based on the Krotov Algorithm

Abstract

The performance of high-precision cold-atom interferometers, which are important for applications in gravimetry and fundamental physics, is often limited by noise and imperfections in the driving laser system. To address this, we propose and numerically demonstrate a method for designing robust Raman pulses using the Krotov quantum optimal control algorithm. We establish a theoretical model for the atom-laser interaction and detail the implementation of the Krotov method to optimize the temporal shape of the pulse's amplitude and phase. Numerical simulations indicate that, compared to standard pulses, the optimized pulses maintain high atomic manipulation fidelity over an extended range of laser frequency detunings and intensity fluctuations. Furthermore, in simulations of a full interferometer sequence, this robustness translates to a significant enhancement in the final fringe contrast under a systematic detuning. This work demonstrates that quantum optimal control is a promising pathway for suppressing experimental noise and improving the signal-to-noise ratio and precision of next-generation atomic sensors.

Figures (8)

• Figure 1: Energy level diagram for a two-photon stimulated Raman transition in an alkali atom (rubidium as an example). Two laser fields (with wave vectors $\mathbf{k}_1$ and $\mathbf{k}_2$) coherently couple the ground-state hyperfine levels. $\delta$ is the two-photon detuning, which corresponds to the detuning term in the effective two-level model.
• Figure 2: Spacetime path diagram for a Mach-Zehnder atom interferometer. The interferometer is formed by a $\pi/2$-$\pi$-$\pi/2$ sequence of Raman pulses, with a time interval of $T$ between pulses. The purple solid lines represent the two classical paths of the atomic wave packet under the influence of the gravitational field (g). Here, $|g, \mathbf{p}\rangle$ denotes the ground-state atom and $|e, \mathbf{p}+\hbar\mathbf{k}_L\rangle$ denotes the excited-state atom. The black curve below shows the timing of the Raman pulses, and $\Omega_R$ is the Rabi frequency.
• Figure 3: Convergence process of the Krotov algorithm for different step-size parameters $\lambda$. The three rows, from top to bottom, correspond to $\lambda = 0.1, 0.5,$ and $1.0$, respectively. The left column shows a magnified view of the first 10 iterations, while the right column shows the complete iterative process. In the plots, the black curves represent the average cost functional, $J_T(\text{avg})$, and the colored curves represent the cost functionals for different perturbation parameters. The results show that $\lambda=0.5$ achieves the optimal balance between convergence speed and stability.
• Figure 4: Final pulse waveforms obtained from optimizations with different step-size parameters $\lambda$. The three columns, from left to right, correspond to $\lambda = 0.1$ (KR1), $0.5$ (KR2), and $1.0$ (KR3), respectively. The top row shows the time evolution of the pulse amplitude, and the bottom row shows the time evolution of the pulse phase. The red curves are the robust pulses optimized by the Krotov algorithm, while the black curves represent the initial non-robust pulse for comparison.
• Figure 5: Comparison of the robustness of different pulses against laser frequency detuning. In the plots, the horizontal axis is the normalized detuning, and the vertical axis is the atomic transition probability. The top three rows show the Krotov-optimized pulses (KR1, KR2, KR3), while the bottom three rows show the standard pulses (Gaussian, super-Gaussian, and rectangular).