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arXiv:2007.01964 · PRX Quantum

Observing Spin-Squeezed States under Spin-Exchange Collisions for a Second

Meng-Zi Huang, Jose Alberto de la Paz, Tommaso Mazzoni, Konstantin Ott, P. Rosenbusch, Alice Sinatra, Carlos L. Garrido Alzar, Jakob Reichel

Published May 8, 2023• 19 citations
arXivHTMLPDF

Abstract

Using the platform of a trapped-atom clock on a chip, we observe the time evolution of spin-squeezed hyperfine clock states in ultracold rubidium atoms on previously inaccessible time scales up to 1 s.The spin degree of freedom remains squeezed after 0.6 s, which is consistent with the limit imposed by particle loss and is compatible with typical Ramsey times in state-of-the-art microwave clocks.The results also reveal a surprising spin-exchange interaction effect that amplifies the cavity-based spin measurement via a correlation between spin and external degrees of freedom.These results open up perspectives for squeezing-enhanced atomic clocks in a metrologically relevant regime and highlight the importance of spin interactions in real-life applications of spin squeezing.

DOI
10.1103/prxquantum.4.020322

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Using the platform of a trapped-atom clock on a chip, we observe the time evolution of spin-squeezed hyperfine clock states in ultracold rubidium atoms on previously inaccessible time scales up to 1 s.The spin degree of freedom remains squeezed after 0.6 s, which is consistent with the limit imposed by particle loss and is compatible with typical Ramsey times in state-of-the-art microwave clocks.The results also reveal a surprising spin-exchange interaction effect that amplifies the cavity-based spin measurement via a correlation between spin and external degrees of freedom.These results open up perspectives for squeezing-enhanced atomic clocks in a metrologically relevant regime and highlight the importance of spin interactions in real-life applications of spin squeezing.
Using the platform of a trapped-atom clock on a chip, we have generated spin-squeezed states and observed their time evolution on unprecedented timescales, showing that metrological spin squeezing is preserved for one second. We observe up to 8.1(9) dB of metrological squeezing in a cloud of 2times1042times 10^42times104 ultracold alkali atoms by quantum nondemolition (QND) measurement in a fiber Fabry-Perot microcavity. The experiment also reveals a surprising amplification effect in the final cavity measurement of the spin state. It results from a subtle interplay between the cavity coupling and the spin dynamics originating from cold collisions. Spin dynamics such as these are an important factor in real atomic clocks that previous proof-of-principle squeezing experiments had not been able to address. Our results open up encouraging perspectives for squeezing-enhanced atomic clocks in a metrologically relevant stability regime.
Using the platform of a trapped-atom clock on a chip, we have generated spin-squeezed states with up to 8.1(9) dB of metrological squeezing in a cloud of 2×1042\times 10^42×104 ultracold alkali atoms by quantum nondemolition (QND) measurement in a fiber Fabry-Perot microcavity. Observing the time evolution of the squeezed state on unprecedented timescales of more than one second reveals a surprising measurement amplification effect in the final measurement of the spin state. It results from a subtle interplay between the spin dynamics of interacting indistinguishable particles and energy-dependent cavity coupling and leads to an increased cavity shift per spin, and thus to a higher signal per photon read out. Metrological spin squeezing is preserved for 1 s. Both results open up encouraging perspectives for squeezing-enhanced atomic clocks in a metrologically relevant stability regime.
Atomic sensors are among the best devices for precision measurements of time, electric and magnetic fields, and inertial forces. However, all atomic sensors that utilise uncorrelated particles are ultimately limited by quantum projection noise, as is already the case for state-of-the-art atomic clocks. This so-called standard quantum limit (SQL) can be overcome by employing entanglement, a prime example being the spin-squeezed states. Spin squeezing can be produced in a quantum non-demolition (QND) measurement of the collective spin, particularly with cavity quantum electrodynamical (cQED) interactions. In this thesis, I present the second-generation trapped-atom clock on a chip (TACC) experiment, where we combine a metrology-grade compact clock with a miniature cQED platform to test quantum metrology protocols at a metrologically-relevant precision level. In a standard Ramsey spectroscopy, the stability of the apparatus is confirmed by a fractional frequency Allan deviation of 6E-13 at 1 s. We demonstrate spin squeezing by QND measurement, reaching 8(1) dB for 1.7E4 atoms, currently limited by decoherence due to technical noise. Cold collisions between atoms play an important role at this level of precision, leading to rich spin dynamics. Here we find that the interplay between cavity measurements and collisional spin dynamics manifests itself in a quantum amplification effect of the cavity measurement. A simple model is proposed, and is confirmed by initial measurements. New experiments in this direction may shed light on the surprising many-body physics in this sytem of interacting cold atoms.
The Dick effect and quantum projection noise (QPN) are among the most stringent limiting factors for state-of-the-art atomic frequency standards, including both primary and secondary standards, as well as compact clocks. A possible solution to the Dick effect relies on Quantum Non-Destructive (QND) detection, which allows multiple interrogations with weak measurements on the same atomic ensemble. Furthermore, spin-squeezed states, which can also be prepared by such QND detection, have the potential to enable clock measurements beyond the standard quantum limit, by employing quantum correlations. Our experimental platform is a Trapped-Atom Clock on a Chip (TACC) that uses ultracold Rb atoms, having demonstrated metrological stability. In the second generation of this experiment, we target quantum enhancement by using QND detection and spin-squeezed ultra-cold atoms generated by cavity QED interactions. To reach this goal, we have integrated two fiber Fabry-Perot cavities on the clock chip, realizing a platform for cavity QED in the strong coupling and weak coupling regimes. With this new device we aim to explore spin squeezing at a metrologically relevant level of stability. Here, we report on the current status and perspectives of this project.
Abstract We analyze the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity and continuous quantum measurement of the transmitted cavity field in order to monitor the evolution of the atomic ensemble. Using analytical treatment and microscopic simulations of the dynamics, we show that one can achieve significant spin squeezing, favorably scaling with the number of atoms N. However, contrary to some previous literature, we clarify that it is not possible to obtain Heisenberg scaling without the continuous feedback that is proposed in optimal approaches. In fact, in the adiabatic cavity removal approximation and large N limit, we find the scaling behavior N − 2 / 3 for spin squeezing and N − 1 / 3 for the corresponding protocol duration. These results can be obtained only by considering the curvature of the Bloch sphere, since linearizing the collective spin operators tangentially to its equator yields inaccurate predictions. With full simulations, we characterize how spin-squeezing generation depends on the system parameters and departs from the bad cavity regime, by gradually mixing with cavity-filling dynamics until metrological advantage is lost. Finally, we discuss the relevance of this spin-squeezing protocol to state-of-the-art optical clocks.