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Self-amplifying spin measurement in a long-lived spin-squeezed state

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

Published Jul 7, 2020• 9 citations
OpenAlex

Abstract

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 $2\times 10^4$ 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.

Related papers

Long-lived spin-squeezed states in an trapped-atom clock on a chip

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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 $2times 10^4$ 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.

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

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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.

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Towards a quantum-enhanced atomic clock on a chip

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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.

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Compression et dynamique de spin dans une horloge à atomes piégés

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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.

•Sep 17, 2019•1 citation

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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.

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Direct comparison of two spin squeezed optical clocks below the quantum projection noise limit

John Martin Robinson, Maya Miklos, Yee Ming Tso +5 more

Building scalable quantum systems that demonstrate genuine performance enhancement based on entanglement is a major scientific goal for fields including computing, networking, simulations, and metrology. The tremendous challenge arises from the fragility of entanglement in increasingly larger sized quantum systems. Optical atomic clocks utilizing a large number of atoms have pushed the frontier of measurement science, building on precise engineering of quantum states and control of atomic interactions. However, today's state-of-the-art optical atomic clocks are limited by the quantum projection noise (QPN) defined by many uncorrelated atoms. Pioneering work on producing spin squeezed states of atoms has shown a path towards integrating entanglement into the best performing clocks. However, to directly demonstrate advantage of quantum entanglement in a working clock we must prevent backaction effects that degrade quantum coherence and introduce uncontrolled perturbations, as well as minimize the influence of technical noise arising from the interrogating clock laser. Here we present a new optical clock platform integrated with collective strong-coupling cavity QED for quantum non-demolition (QND) measurement. Optimizing the competition between spin measurement precision and loss of coherence, we measure a Wineland parameter of -1.8(7) dB for 1.9x10$^4$ atoms, thus verifying the presence of entanglement. Furthermore, a moving lattice allows the cavity to individually address two independent sub-ensembles, enabling us to spin squeeze two clock ensembles successively and compare their performance. This differential comparison between the two squeezed clocks directly verifies enhanced clock stability of 2.0(3) dB below QPN, and 0.6(3) dB above the standard quantum limit (SQL), at the measurement precision level of 10$^{-17}$, without subtracting any technical noise contributions.

arXiv:2211.08621•Nov 16, 2022•5 citations
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.
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 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.
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.
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.
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.
Building scalable quantum systems that demonstrate genuine performance enhancement based on entanglement is a major scientific goal for fields including computing, networking, simulations, and metrology. The tremendous challenge arises from the fragility of entanglement in increasingly larger sized quantum systems. Optical atomic clocks utilizing a large number of atoms have pushed the frontier of measurement science, building on precise engineering of quantum states and control of atomic interactions. However, today's state-of-the-art optical atomic clocks are limited by the quantum projection noise (QPN) defined by many uncorrelated atoms. Pioneering work on producing spin squeezed states of atoms has shown a path towards integrating entanglement into the best performing clocks. However, to directly demonstrate advantage of quantum entanglement in a working clock we must prevent backaction effects that degrade quantum coherence and introduce uncontrolled perturbations, as well as minimize the influence of technical noise arising from the interrogating clock laser. Here we present a new optical clock platform integrated with collective strong-coupling cavity QED for quantum non-demolition (QND) measurement. Optimizing the competition between spin measurement precision and loss of coherence, we measure a Wineland parameter of -1.8(7) dB for 1.9x104^44 atoms, thus verifying the presence of entanglement. Furthermore, a moving lattice allows the cavity to individually address two independent sub-ensembles, enabling us to spin squeeze two clock ensembles successively and compare their performance. This differential comparison between the two squeezed clocks directly verifies enhanced clock stability of 2.0(3) dB below QPN, and 0.6(3) dB above the standard quantum limit (SQL), at the measurement precision level of 10−17^{-17}−17, without subtracting any technical noise contributions.