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arXiv:1408.1266 · Physical Review Letters

Generation and Detection of a Sub-Poissonian Atom Number Distribution in a One-Dimensional Optical Lattice

J.-B. Béguin, Eva Bookjans, S. L. Christensen, H. L. Sørensen, Jörg Helge Müller, Eugene Simon Polzik, J. Appel

Published Dec 30, 2014• 90 citations
arXivHTMLPDF

Abstract

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance -14 dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of ±8 atoms on an ensemble of some 10(3) atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum nondemolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice.

DOI
10.1103/physrevlett.113.263603

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We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance -14 dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of ±8 atoms on an ensemble of some 10(3) atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum nondemolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice.
We present experimental techniques and recently demonstrated results related to the optimization and characterization of our recently demonstrated nanofiber-based atom trap. The atoms are confined in an optical lattice that is created using a two-color evanescent field surrounding the optical nanofiber. For this purpose, the polarization state of the trapping light fields has to be properly adjusted. We demonstrate that this can be accomplished by analyzing the light scattered by the nanofiber. Furthermore, we show that loading the nanofiber trap from a magneto-optical trap leads to sub-Doppler temperatures of the trapped atomic ensemble and yields a sub-Poissonian distribution of the number of trapped atoms per trapping site.
Abstract The analysis of entangled atomic ensembles and their application for interferometry beyond the standard quantum limit requires an accurate determination of the number of atoms. We present an accurate fluorescence detection technique for atoms that is fully integrated into an experimental apparatus for the production of many-particle entangled quantum states. Number-resolved fluorescence measurements with single-atom accuracy for 1 up to 30 atoms are presented. According to our noise analysis, we extrapolate that the single-atom accuracy extends to a limiting atom number of 390(20) atoms. We utilize the accurate atom number detection for a number stabilization of the laser-cooled atomic ensemble. For a target ensemble size of 7 atoms prepared on demand, we achieve a 92(2)% preparation fidelity and reach number fluctuations 18(1) dB below the shot noise level using real-time feedback on the magneto-optical trap.
We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first principles stochastic master equation to model the squeezing as function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of ~5 dB is achievable with current technology for ~2500 atoms trapped 180 nm from the surface of a nanofiber with radius a=225 nm.
We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first-principles stochastic master equation to model the squeezing as a function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of $\ensuremath{\sim}5$ dB is achievable with current technology for $\ensuremath{\sim}2500$ atoms trapped 180 nm from the surface of a nanofiber with radius a=225a=225a=225 nm.
The analysis of entangled atomic ensembles and their application for interferometry beyond the standard quantum limit requires an accurate determination of the number of atoms. We present an accurate fluorescence detection technique for atoms that is fully integrated into an experimental apparatus for the production of many-particle entangled quantum states. Single-particle resolving fluorescence measurements for 111 up to 303030 atoms are presented. According to our noise analysis, we extrapolate that the single-atom resolution extends to a limiting atom number of 390(20)390(20)390(20) atoms. We utilize the accurate atom number detection for a number stabilization of the laser-cooled atomic ensemble. For a target ensemble size of 777 atoms prepared on demand, we achieve a 92(2) %92(2)\,\%92(2)% preparation fidelity and reach number fluctuations 18(1) dB18(1)\,\mathrm{dB}18(1)dB below the shot noise level using real-time feedback on the magneto-optical trap.
We have recently demonstrated a new experimental platform for trapping and optically interfacing laser-cooled cesium atoms. The scheme uses a two-color evanescent field surrounding an optical nanofiber to localize the atoms in a one-dimensional optical lattice 200 nm above the nanofiber surface [1]. In order to use this fiber-coupled ensemble of trapped atoms for applications in the context of quantum communication and quantum information processing, non-classical states of the atomic spins have to be prepared and should live long enough to allow one to apply successive quantum gates. The close proximity of the trapped atoms to the nanofiber surface and the strong polarization gradients of nanofiber-guided light fields are potentially important sources of decoherence. Here, we present our latest experimental results on the coherence properties of atomic spins in our nanofiber-based trap. Using a microwave field to drive the clock transition, we determine inhomogeneous and homogeneous dephasing times by Ramsey and spin echo techniques, respectively. Our results constitute the first measurement of the coherence properties of atoms trapped in the vicinity of a nanofiber and represent a fundamental step towards establishing nanofiber-based traps for cold atoms as a building block in a quantum network.