Unified laboratory-frame analysis of atomic gravitational-wave sensors

TL;DR

This work develops a unified laboratory-frame framework to analyze how atomic clocks and atom interferometers respond to gravitational waves, accounting for all leading GW couplings to massive particles and light. It shows that atomic clocks rely on geodesic motion to sense GWs via light-pulse readouts of position, while atom interferometers exploit spatial superpositions to probe the GW potential directly; mass-defect and light propagation corrections are also incorporated. The authors introduce composite interrogation protocols—hyper-echo for clocks and large-momentum-transfer for interferometers—demonstrating how a common pulse-sequence approach enhances sensitivity and suppresses noise. The results illuminate how terrestrial and space-based implementations differ in feasibility and sensitivity, and they provide a route to networks of GW detectors using atomic sensors with potentially Hz to sub-Hz target frequencies.

Abstract

Atomic sensors using light-matter interactions, in particular atomic clocks and atom interferometers, have the potential to complement optical gravitational-wave detectors in the mid-frequency regime. Although both rely on interference, the interfering components of clocks are spatially colocated, whereas atom interferometers are based on spatial superpositions. Both the electromagnetic fields that drive the transitions and generate superpositions, while propagating through spacetime, as well as the atoms themselves as massive particles are influenced by gravitational waves, leading to effective potentials that induce phase differences inferred by the sensor. In this work, we analyze the effects of these potentials on atomic clocks and atom interferometers in the laboratory frame. We show that spatial superpositions in atom interferometers, both light-pulse and guided ones, give rise to a gravitational-wave signal. Although these spatial superpositions are suppressed for clocks, we show that the light pulses driving internal transitions measure the spatial distance between the centers of two separate clocks. We highlight that this mechanism only yields a sensitivity if both clocks, including possible trapping setups, move on geodesics given by the gravitational wave. While such configurations are natural for satellite free-fliers, terrestrial optical clocks usually rely on stationary traps, rendering them insensitive to leading order. Moreover, we show that both sensors can be enhanced by composite interrogation protocols in a common framework. To this end, we propose a pulse sequence that can be used for large-momentum-transfer atom interferometers and for hyper-echo atomic clocks, leading to a signal enhancement and noise suppression.

Figures (3)

• Figure 1: Gravitational potential $\hat{V}_\text{G}$ induced by a GW in the laboratory frame in space and time (density plot). The harmonic potential (shown on the top for $t=0$) oscillates between positive and negative values in phase with the strain of the GW (shown on the right). The light cones for pulses traveling in a GW background from the left ($+$) and right ($-$) are modified as well. The phase perturbation $\chi_\pm^{(1)}$ of the respective light beam is shown by the hue color scale along the light cone. If evaluated at the time and position where the light interacts with the atom, this perturbation translates into the potentials $\hat{V}_{\omega,\text{G}}$ and $\hat{V}_{k,\text{G}}$.
• Figure 2: Spacetime diagrams of differential setups for detecting a GW with the strain shown on the left. The two sensors are separated by a distance $L$ and driven by common $\pi/2$ and $\pi$ pulses (red). Traps are drawn in yellow. (a) For two stationary traps, the atom in the trap away from the origin oscillates with a suppressed amplitude (shown on the bottom) due to the strong confinement of the trap. (b) In contrast, when moving on geodesics, both the atom and trap move as a consequence of the equivalence principle, so that the oscillation amplitude (shown on the bottom) is larger and in phase with the GW. (c) Light-pulse atom interferometers, shown as Mach--Zehnder schemes, probe the potential $\hat{V}_\text{G}$ induced by the GW (density plot).
• Figure 3: Composite interrogation protocol using single-photon transitions for both atom interferometers and atomic clocks (traps highlighted in yellow). The large-momentum-transfer Mach--Zehnder interferometer consists of generalized beam-splitter pulses (a $\pi/2$ pulse in red accompanied by $N-1$ gray $\pi$ pulses) and a generalized mirror pulse (a $\pi$ pulse in red sandwiched by $N-1$ gray $\pi$ pulses). The resonance is tuned such that, except for the red pulses, only one arm is addressed and the internal state is changed (blue: ground state and green: excited state). The same sequence is used for clocks, however, in that case, both interfering components are always resonant. The interrogation time $T$ separates the red pulses, where gray pulses are separated by a time $2\tau_\text{B}$.