Role of atoms in atomic gravitational-wave detectors

Recently, it has been proposed that space-based atomic sensors may be used to detect gravitational waves. These proposals describe the sensors either as clocks or as atom interferometers. Here, we seek to explore the fundamental similarities and differences between the two types of proposals. We present a framework in which the fundamental mechanism for sensitivity is identical for clock and atom interferometer proposals, with the key difference being whether or not the atoms are tightly confined by an external potential. With this interpretation in mind, we propose two major enhancements to detectors using confined atoms, which allow for an enhanced sensitivity analogous to large momentum transfer used in atom interferometry (though with no transfer of momentum to the atoms), and a way to extend the useful coherence time of the sensor beyond the atom's excited-state lifetime.

Figure 1

Optical lattice clock and atom interferometer detectors for gravitational waves. Each type of proposal relies on two ensembles of atoms, one in each satellite. Lasers transmitted between the satellites encode phase shifts due to changing optical path lengths caused by a gravitational wave. The key difference between clock and atom interferometer proposals is that in clocks atomic recoils due to the momentum of absorbed or emitted photons are suppressed by tightly confining the atoms, while in atom interferometers the atoms are free to recoil.

Figure 2

A toy model for gravitational-wave detection. (a) Two atoms ($a$ and $b$) are addressed by a single laser resonant with a transition between the ground state $|g\rangle$ and a long-lived excited state $|e\rangle$. A phase modulator mimics the effect of a gravitational wave by modifying the optical path length between the two atoms. (b) For tightly confined atoms (clocks), a simple Ramsey sequence can be used to detect changes in optical path length. A first $\pi /2$ pulse imprints the laser phase on the two atoms when the path length is shifted by $L_1$, and a second $\pi /2$ pulse acts when the path length is shifted by $L_2$. Random variations in the laser phase (${\varphi }_1$ and ${\varphi }_2$) are common to the two atoms, while phase shifts resulting from changes in path length are not. The signal from the phase modulator manifests as phase shift ${\mathrm{\Phi }}_s=k(L_2-L_1)$ between the excited-state probability oscillations of the two atoms. (c) For unconfined atoms (atom interferometers), transitions between $|g\rangle$ and $|e\rangle$ are accompanied by momentum kicks, which necessitate an additional laser $\pi$ pulse in the middle of the sequence. The phase shift between excited-state oscillations of the two atoms is now ${\mathrm{\Phi }}_s=k(L_3-2L_2+L_1)$.

Figure 3

LMT-like enhancement with confined atoms. (a) Atoms are addressed by counterpropagating lasers, both of which pass through the phase modulator that sits between the atoms. (b) Two blocks of $M$ pairs of $\pi$ pulses (blue boxes) are inserted between the $\pi /2$ pulses of the standard Ramsey sequence. Each pair of $\pi$ pulses contains a pulse originating from each direction. The duration of each block is assumed here to be short relative to the GW period, while a long evolution time (gray box) between the two blocks may be comparable to the GW period. (c) The additional pulses lead to a factor of $4M+1$ enhancement in the signal phase ${\mathrm{\Phi }}_s$ compared to simple Ramsey sequence.

Figure 4

Use of three-state system to allow atoms to stay in the ground state for much of the evolution time. (a) Our procedure utilizes two ground states, $|g_1\rangle$ and $|g_2\rangle$, and a single long-lived optically excited state $|e\rangle$. $|g_1\rangle$ and $|g_2\rangle$ can independently be coupled to $|e\rangle$ using laser pulses with different frequency and/or polarization (red and blue arrows). (b) After preparing an atomic superposition of $|g_1\rangle$ and $|e\rangle$ using a $\pi /2$ pulse from the left (atoms begin in $|g_1\rangle$), the portion of the atoms in $|e\rangle$ is transferred to $|g_2\rangle$ using a $\pi$ pulse from the right. The atoms are then in a superposition of $|g_1\rangle$ and $|g_2\rangle$ with phase dictated by the lasers and the path length $L_1$. The sequence of pulses is reversed after a long evolution time, during which time the atoms are not susceptible to excited-state decay. The phase shift in the excited-state probabilities of the two atoms ${\mathrm{\Phi }}_s=2k(L_2-L_1)$ now encodes changes in the optical path length that occurred while the atoms were in the ground states.