High-contrast double Bragg interferometry via detuning control

TL;DR

The paper tackles the challenge of achieving high-contrast, large-momentum-transfer atom interferometry with double Bragg diffraction under external acceleration. It introduces a tri-frequency detuning strategy to compensate Doppler shifts and develops a five-level S-matrix framework to quantify performance under realistic imperfections. By systematically comparing conventional, constant-detuning, linear-detuning-sweep, and OCT-augmented detuning protocols, the study shows that OCT provides the highest robustness, maintaining contrasts above 95% across typical momentum spreads and lattice-depth fluctuations, with DS-DBD offering strong performance for well-collimated ensembles. These findings enable practical high-contrast DBD interferometers and suggest a pathway to extending large-momentum-transfer interferometry for precision sensing, including potential integration with Bloch oscillations to achieve very large $k$-momenta in terrestrial and space-based platforms.

Abstract

We propose high-contrast Mach-Zehnder atom interferometers based on double Bragg diffraction (DBD) operating under external acceleration. To mitigate differential Doppler shifts and experimental imperfections, we introduce a tri-frequency laser scheme with dynamic detuning control. We evaluate four detuning-control strategies-conventional DBD, constant detuning, linear detuning sweep (DS-DBD), and a hybrid protocol combining detuning sweep with optimal control theory (OCT)-using exact numerical simulations and a five-level S-matrix model. The OCT strategy provides the highest robustness, maintaining contrast above 95\% under realistic conditions, while the DS-DBD strategy sustains contrast above 90\% for well-collimated Bose-Einstein condensates. These results offer practical pathways to high-contrast, large-momentum-transfer DBD-based interferometers for precision quantum sensing and fundamental physics tests.

Figures (6)

• Figure 1: Schematics of a double Bragg atom interferometer under microgravity. Left: Experimental setup of a DBD pulse using counter-propagating optical lattices $L_1$ (red shaded) and $L_2$ (blue shaded) with orthogonal polarizations $\hat{\sigma}_1$ and $\hat{\sigma}_2$. Right: Atomic density evolution in the twin-lattice center-of-mass frame $|\psi(z,t)|^2$, normalized to its initial maximum $|\psi_{max}|^2=\max_{z}|\psi(z,0)|^2$ and shown in decibel units, for conventional (C-DBD) and optimized (OCT) Mach-Zehnder interferometers with phase shifts $\Delta \phi =0$ (left column) and $\pi$ (right column), adjusted via the interrogation time $T$. Atomic densities are obtained from exact numerical simulations, with red-shaded regions indicating the three DBD pulses. Only the visibly populated diffracted ports are labeled in the right panel after the last DBD pulse.
• Figure 2: (a) Tri-frequency laser configuration enabling double Bragg diffraction of atoms under a strong constant acceleration $\bm{g} = g \hat{z}$, with dynamic Doppler shift compensation. The red box highlights four beams that resonantly drive DBD as the Doppler shift increases. (b) Corresponding energy-level diagram including Doppler and AC-Stark shifts. Upward and downward Bragg transitions are driven by frequency differences $\Delta \omega_{1,2} = \omega_b - \omega_a \pm \nu_D$, where $\nu_D$ is dynamically tuned to compensate the Doppler shift $\nu_g = 2k_L g t$. In (b), the solid lines indicate resonant transitions, whereas dashed lines represent off-resonant couplings.
• Figure 3: Comparison of beam-splitter (BS) and mirror (M) inefficiencies ($1-\eta_{BS| M}$) for four strategies: conventional DBD (C-DBD), constant-detuning DBD (CD-DBD), linear-detuning-sweep DBD (DS-DBD), and a hybrid strategy combining DS-BS with OCT-M (OCT). BS and M efficiencies $\eta_{BS| M}$ are evaluated for an input Gaussian wave packet with a momentum width $\sigma_p=0.05\,\hbar k_L$, centered at $p_0 = 0$ for BS and $p_0 = 2\,\hbar k_L$ for M without polarization error ($\varepsilon_{pol}=0$).
• Figure 4: (a) Effective two-level system representing first-order DBD developed in Ref. Li-PRR-2024. (b) Linear detuning sweep mimicking adiabatic passage for robust population transfer. The initial and final states of an ideal double Bragg beam-splitter are given by $|0\rangle=|0\hbar k_L\rangle$ and $|1\rangle=(|2\hbar k_L\rangle + |-2\hbar k_L\rangle)/\sqrt{2}$, respectively.
• Figure 5: (a) Mach-Zehnder atom interferometer in momentum space implemented with three DBD pulses. Input and output ports are labeled by indices $i=1,2,3$, corresponding to momentum states $|p\rangle$, $|p+2\hbar k_L\rangle$, and $|p-2\hbar k_L\rangle$, respectively. Higher-order momentum states (e.g., $|\pm 4\hbar k_L\rangle$) are not shown for clarity but are included in the population calculations. (b) T-scan fringe in the $|\pm 2\hbar k_L\rangle$-port using the DS-DBD strategy shows 97% contrast under an effective acceleration $g = 0.000357 k_L^{-1}\omega_{\mathrm{rec}}^{2}$ with an initial momentum width $\sigma_p=0.05\hbar k_L$ and COM momentum $p_0=0$. (c) Contrast degradation in the CD-DBD protocol due to a large initial COM momentum $p_0=0.1\hbar k_L$ and a momentum width $\sigma_p=0.01\hbar k_L$. (d) Contrast versus momentum width $\sigma_p$ with vanishing COM momentum and polarization error. (e) Contrast versus initial COM momentum $p_0$ with a momentum width $\sigma_p=0.05\hbar k_L$ and no polarization error. (f) Contrast versus polarization error $\varepsilon_{pol}$ with an initial momentum width $\sigma_p=0.05\hbar k_L$ and vanishing COM momentum. In subplots (d–f), exact numerical results are shown as symbols, while solid curves represent predictions from the five-level S-matrix theory.