Spatially homogeneous entanglement for matter-wave interferometry created with time-averaged measurements

Abstract

We demonstrate a method to generate spatially homogeneous entangled, spin-squeezed states of atoms appropriate for maintaining a large amount of squeezing even after release into the arm of a matter-wave interferometer or other free space quantum sensor. Using an effective intracavity dipole trap, we allow atoms to move along the cavity axis and time average their coupling to the standing wave used to generate entanglement via collective measurements, demonstrating 11(1) dB of directly observed spin squeezing. Our results show that time averaging in collective measurements can greatly reduce the impact of spatially inhomogeneous coupling to the measurement apparatus.Spin-1/2 atoms must project into either "up" or "down" when measured. For N unentangled atoms, the independent randomness in this quantum projection fundamentally limits the single-shot phase resolution of any quantum sensor to ∆φ SQL = 1/ √ N rad, the standard quantum limit (SQL) [1]. Collective measurements of atoms in optical cavities have recently produced some of the most strongly entangled, spin-squeezed states to date, directly improving the phase resolution of a quantum sensor's "clock hand" by a factor up to 60-70 (roughly 18 dB) in noise variance below the SQL [2,3].Spin-squeezed states could be used to improve a wide range of quantum sensors, with today's best atomic clocks [4][5][6] being particularly promising candidates [7,8]. In this work we focus on preparing spin-squeezed states appropriate for matter-wave atom interferometry with applications including inertial sensing [9], measurements of gravity and freefall, [10,11] and even the search for certain proposed types of dark matter and dark energy [12,13].A major challenge arises for cavity-based atom interferometry and other applications involving release of spinsqueezed atoms into free space. The problem is that the probe mode used to perform the collective measurement is a standing wave, but the atoms are trapped in a 1-dimensional lattice defined by a standing wave cavity mode with a significantly different wavelength. Some atoms will sit in lattice sites positioned near nodes and some near anti-nodes of the entanglement-generating probe light. As a result, the atoms will contribute to the collective measurement with different strengths. In this common case, the large degree of squeezing exists only for this specific coupling configuration and would be largely lost after releasing the atoms into the arm of an interferometer, since their final coupling to the cavity mode or other readout detector will be different from the original configuration [14]. In contrast, we wish to create spatially homogeneous entanglement, quantified by the amount of observed phase resolution beyond the SQL that one can achieve when every atom couples equally to the final measurement apparatus.In this Letter, we demonstrate a method to create ho- FIG. 1. (a)Optical lattice sidebands separated by one free spectral range (FSR) are injected into the cavity to create an axially homogeneous "dipole" trap. Dip...

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