Fundamental Limits of Large Momentum Transfer in Optical Lattices

Abstract

Large-momentum-transfer techniques are instrumental for the next generation of atom interferometers as they significantly improve their sensitivity. State-of-the-art implementations rely on elastic scattering processes from optical lattices such as Bloch oscillations or sequential Bragg diffraction, but their performance is constrained by imperfect pulse efficiencies. Here we develop a Floquet-based theoretical framework that provides a unified description of elastic light-atom scattering across all relevant regimes. Within this formalism, we identify practical regimes that exhibit orders of magnitude reduced losses and improved phase accuracy compared to previous implementations. The model's validity is established through direct comparison with exact numerical solutions of the Schrödinger equation and through quantitative agreement with recent experimental benchmark results. These findings delineate previously unexplored operating regimes for large-momentum-transfer beam splitters and open new perspectives for precision atom-interferometric measurements in fundamental physics, gravity gradiometry or gravitational wave detection.

Figures (4)

• Figure 1: (a) Space-time diagram of a Large-momentum-Transfer-enhanced Mach-Zehnder atom interferometer. The sequence consists of two beam splitter and a mirror pulse. Each interferometer arm is accelerated and decelerated using LMT sequences in an optical lattice, resulting in a larger momentum separation compared to a standard Mach-Zehnder atom interferometer (dashed lines). (b) Control parameters (acceleration and lattice potential) for Bloch Oscillation and Sequential Bragg Diffraction LMT.
• Figure 2: (a) Density map of the tunneling loss rate $\Gamma_0$ of the Floquet-groundstate at quasi-momentum $\kappa = 0$$\vert \phi_0(\kappa = 0)\rangle$ versus Floquet period $T_F$ and interpolation parameter $\eta$ (cf. \ref{['eq:lattice_param']}) for a lattice depth of $V_0 = 50E_r$. The color bar is cut off at $10^{-7}$ to increase the contrast. (b) Cut through the density map (a) in SBD limit at $\eta=100$ (solid blue line) corresponding to $\kappa=0$, results of exact numerical simulations (blue points), tunneling loss rate in SBDs limit for $\kappa=k_L$ (orange line) and overall loss rate of state-of-the-art experiment Toulouse2 (orange star). The experimental loss rate deviates from its fundamental limit at $\kappa=k_L$ due pulse-to-pulse fluctuations and spontaneous emission losses. (c) Cut through the density map (a) in BO limit at $\eta=0.1$ (solid blue line) and results of exact numerical simulations (blue points). The exact numerical simulations are performed with the 'Universal Atom Interferometer Simulator' (UATIS) UATIS.
• Figure 3: Phase uncertainty induced by lattice depth differences versus lattice depth $V_0$ for a Floquet period of $T_F=5.3 \mu s$. The specific Floquet period was chosen to cover the experiment Toulouse2 at a lattice depth of $V_0 = 50E_r$ in the limit of SBDs. The phase uncertainty is determined for the first five Floquet bands in the limit of BOs $\eta=0.1$ (a) and the limit of SBDs $\eta=100$ (b). The average AC Stark shift is suppressed here.
• Figure 4: (a) Schematic illustration of lattice acceleration in arbitrary units versus time $t$ for adiabatic preparation of Floquet state $\lvert\phi_0(\kappa)\rangle$ and SBDs LMT pulse. The pulse sequence is split into distinct steps: $t\in [0, \tau_1]$ adiabatic ramping of lattice potential; $t \in (\tau_1, \tau_2]$ adiabatic ramping of lattice acceleration; $t \in (\tau_2, \tau_3]$ BOs controlling the quasi-momentum $\kappa$; $t \in (\tau_3, \tau_4]$ adiabatic change of lattice acceleration function $\eta$; $t \in (\tau_4, \tau_5]$ SBDs LMT pulse. Note that the first two steps correspond to adiabatic Bloch state preparation adiabatic-AI. (b) Momentum representation probability amplitude of wavefunction in arbitrary units at time-steps $t=0, \tau_1, \tau_2, \tau_3, \tau_4, \tau_5$ in the co-moving lattice frame.