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Implementation of Cavity Squeezing of a Collective Atomic Spin

Vladan Vuletić, Monika Schleier-Smith, Ian D. Leroux

Published Feb 1, 2010• 0 citations
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Abstract

We squeeze unconditionally the collective spin of a dilute ensemble of laser-cooled superscript 87]Rb atoms using their interaction with a driven optical resonator. The shape and size of the resulting spin uncertainty region are well described by a simple analytical model [M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, arXiv:0911.3936 [Phys. Rev. A (to be published)]] through 2 orders of magnitude in the effective interaction strength, without free parameters. We deterministically generate states with up to 5.6(6) dB of metrologically relevant spin squeezing on the canonical [superscript 87]Rb hyperfine clock transition.

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We squeeze unconditionally the collective spin of a dilute ensemble of laser-cooled superscript 87]Rb atoms using their interaction with a driven optical resonator. The shape and size of the resulting spin uncertainty region are well described by a simple analytical model [M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, arXiv:0911.3936 [Phys. Rev. A (to be published)]] through 2 orders of magnitude in the effective interaction strength, without free parameters. We deterministically generate states with up to 5.6(6) dB of metrologically relevant spin squeezing on the canonical [superscript 87]Rb hyperfine clock transition.
We squeeze unconditionally the collective spin of a dilute ensemble of laser-cooled 87Rb atoms using their interaction with a driven optical resonator. The shape and size of the resulting spin uncertainty region are well described by a simple analytical model [M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, arXiv:0911.3936 [Phys. Rev. A (to be published)]] through 2 orders of magnitude in the effective interaction strength, without free parameters. We deterministically generate states with up to 5.6(6) dB of metrologically relevant spin squeezing on the canonical 87Rb hyperfine clock transition.
We propose and analyze a simple method to squeeze dynamically and unconditionally the collective spin of a dilute atomic ensemble by interaction with a driven mode of an optical resonator, as recently demonstrated [I. D. Leroux, M. H. Schleier-Smith, and V. Vuleti\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. Lett. 104, 073602 (2010)]. We show that substantial squeezing can be achieved in the regime of strong collective ensemble-resonator coupling. The squeezing is ultimately limited either by photon emission into free space or by the curvature of the Bloch sphere. We derive both limits and show where each prevails.
The unconditional squeezing of the collective spins of an atomic ensemble in a laser driven optical cavity [I. D. Leroux, M. H. Schleier-Smith, and V. Vuleti\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. Lett 104, 073602 (2010)] is studied and analyzed theoretically. Surprisingly, we find that the largely detuned driving laser can improve the scaling of cavity squeezing from ${S}^{\ensuremath{-}2/5}$ to ${S}^{\ensuremath{-}2/3}$, where SSS is the total atomic spin. Moreover, we also demonstrate that the experimental imperfection of photon scattering into free space can be efficiently suppressed by detuning.
Deterministic light-induced spin squeezing in an atomic gas is limited by photon shot noise or, equivalently, by atomic state information escaping with the light field mediating the effective atom-atom interaction. We show theoretically that the performance of cavity spin squeezing [M. H. Schleier-Smith, I. D. Leroux, and V. Vuleti\ifmmode \acute{c}\else \'{c}\fi{}, Phys. Rev. A 81, 021804(R) (2010)] can be substantially improved by erasing the light-atom entanglement, and propose several methods for doing so. Accounting for light scattering into free space, quantum erasure improves the scaling of cavity squeezing from ${S}^{\ensuremath{-}1/2}$ to ${S}^{\ensuremath{-}2/3}$, where SSS is the total atomic spin.
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.
We utilize multilevel atoms trapped in a driven resonant optical cavity to produce scalable multimode squeezed states for quantum sensing and metrology. While superradiance or collective dissipative emission by itself has been typically a detrimental effect for entanglement generation in optical cavities, in the presence of additional drives it can also be used as an entanglement resource. In a recent work [B. Sundar, D. Barberena, A. M. Rey, and A. Pi\~neiro Orioli, companion paper, Phys. Rev. Lett. 132, 033601 (2024)], we described a protocol for the dissipative generation of two-mode squeezing in the dark state of a six-level system with only one relevant polarization. There we showed that up to two quadratures can be squeezed. Here, we develop a generalized analytic treatment to calculate the squeezing in any multilevel system where atoms can collectively decay by emitting light into two polarization modes in a cavity. We show that in this more general system up to four spin squeezed quadratures can be obtained. We study how finite-size effects constrain the reachable squeezing, and analytically compute the scaling with NNN. Our findings are readily testable in current optical cavity experiments with alkaline-earth-like atoms.