Abstract
Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11, 12], and very recently in large atomic ensembles [13, 14, 15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing.
Highlights
Many state-of-the-art atomic microwave clocks and interferometers based on atomic ensembles are limited no longer by technical noise, but rather by the fundamental quantum fluctuations of uncorrelated atoms, known as the standard quantum limit (SQL)
They can be used for realizing quantum sensors which surpass the SQL since the non-Gaussian spin distributions can possess large Fisher information
In our system, the maximum atom number of ∼ 3000 is set by the accuracy of the spin rotation, and can be increased by two orders of magnitude by better magnetic-field control [10]
Summary
Many state-of-the-art atomic microwave clocks and interferometers based on atomic ensembles are limited no longer by technical noise, but rather by the fundamental quantum fluctuations of uncorrelated atoms, known as the standard quantum limit (SQL). The atomic quantum fluctuations between |m = ±1 in the CSS randomly rotate the polarization of the input photons |v , giving rise to a nonzero√probability ∝ φ2 for an incident |v photon to emerge in the polarization |h = (|σ+ − |σ− )/ 2, orthogonal to its input polarization The detection of such a “heralding” photon projects the atomic state onto h|ψ ∝ |φ − |−φ , which is not a CSS, but an entangled state of collective spin, namely, the first excited Dicke state [18] |ψ1 along x (Figure 1a). By aligning the trap linear polarization parallel to the probe polarization, the trap light no longer contributes to the rotation
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