Abstract
Recent progress in generating entangled spin states of neutral atoms provides opportunities to advance quantum sensing technology. In particular, entanglement can enhance the performance of accelerometers and gravimeters based on light-pulse atom interferometry. We study the effects of error sources that may limit the sensitivity of such devices, including errors in the preparation of the initial entangled state, imperfections in the laser pulses, momentum spread of the initial atomic wave packet, measurement errors, spontaneous emission, and atom loss. We determine that, for each of these errors, the expectation value of the parity operator $\Pi$ has the general form, $\overline{\langle \Pi \rangle} = \Pi_0 \cos( N \phi )$, where $\phi$ is the interferometer phase and $N$ is the number of atoms prepared in the maximally entangled Greenberger--Horne--Zeilinger state. Correspondingly, the minimum phase uncertainty has the general form, $\Delta\phi = (\Pi_0 N)^{-1}$. Each error manifests itself through a reduction of the amplitude of the parity oscillations, $\Pi_0$, below the ideal value of $\Pi_0 = 1$. For each of the errors, we derive an analytic result that expresses the dependence of $\Pi_0$ on error parameter(s) and $N$, and also obtain a simplified approximate expression valid when the error is small. Based on the performed analysis, entanglement-enhanced atom interferometry appears to be feasible with existing experimental capabilities.
Highlights
Neutral atoms are used in some of the most precise, state-of-the-art quantum sensors, including atomic clocks [1,2,3,4], optical atomic magnetometers [5,6,7], and atom interferometers (AIs) [8,9,10,11]
Looking forward, an ambitious goal is to harness the power of quantum entanglement to decrease the phase uncertainty in these atomic sensors [12], first, beyond the standard quantum limit (SQL), N −1/2, which arises in measurements with independent atoms, and, as close as possible to the Heisenberg limit (HL), N −1, where N is the number of atoms used in the measurement
We provide a detailed analysis of a lightpulse AI utilizing ultracold atoms that have been prepared in the GHZ spin state
Summary
Neutral atoms are used in some of the most precise, state-of-the-art quantum sensors, including atomic clocks [1,2,3,4], optical atomic magnetometers [5,6,7], and atom interferometers (AIs) [8,9,10,11]. The most promising method for generating high-fidelity entangled states of atomic spins is by using Rydberg-mediated interactions in arrays of ultracold, optically trapped neutral atoms [26]. We characterize the relevant noise sources in terms of error parameters and analyze how the phase uncertainty scales as a function of the number of entangled atoms N in the initial GHZ state. We develop a detection scheme that allows for a measurement of the interferometric phase φ, with a number of measurements that scales linearly with N , in contrast to the exponential scaling of the Hilbert space dimension for a system of N entangled atoms This is possible because a measurement of the parity of the final N -atom spin state, which provides a sufficient amount of information to determine φ, can be performed via a state-selective detection [59,60,61] with only N + 1 possible outcomes, instead of needing to distinguish between the 2N possible final states. If the total number of experiments (AI cycles) is fixed, a decrease in the number of lossless experiments can be interpreted as an effective deterioration of phase uncertainty per one experiment
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