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arXiv:0911.3936 · Physical Review A

Squeezing the collective spin of a dilute atomic ensemble by cavity feedback

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

Published Feb 24, 2010• 178 citations
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Abstract

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.

DOI
10.1103/physreva.81.021804

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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.
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 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.
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.
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.
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.
We theoretically investigate the entangled states of an atomic ensemble that can be obtained via cavity feedback, varying the atom-light coupling from weak to strong, and including a systematic treatment of decoherence. In the strong-coupling regime for small atomic ensembles, the system is driven by cavity losses into a long-lived, highly entangled many-body state that we characterize analytically. In the weak-coupling regime for large ensembles, we find analytically the maximum spin-squeezing that can be achieved by optimizing both the coupling and the atom number. This squeezing is fundamentally limited by spontaneous emission to a constant value, which is independent of the atom number.