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Optical and Quantum Sensing and Precision Metrology II

Analyzing spin states of a Bose-Einstein condensate with number-resolved counting

Carsten Klempt, Mareike Hetzel, Lucca Pezzè, Cebrail Pür, Martin Quensen, Andreas Hüper, J. Kruse, Augusto Smerzi

Published Mar 9, 2022• 0 citations
Publisher

Abstract

A tomography of many-body quantum states of indistinguishable particles is generally performed by engineering couplings between the involved states and a subsequent counting of the occupation numbers. While precise couplings belong to the standard experimental toolbox, an accurate number counting presents a considerable challenge for both photonic and atomic quantum states. Here we present an application of a number-resolving atom counting [New J. Phys. 23, 113046 (2021)] for the state reconstruction of an atomic coherent spin state. We generate the coherent spin state by driving a Rabi frequency between two hyperfine states of an ultracold Rubidium ensemble.The result is analyzed by a number-resolving fluoresence detection setup. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. The results offer an exciting perspective for a high-fidelity tomography of entangled states and can be applied for the future demonstration of Heisenberg-limited atom interferometry.

DOI
10.1117/12.2617229

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A tomography of many-body quantum states of indistinguishable particles is generally performed by engineering couplings between the involved states and a subsequent counting of the occupation numbers. While precise couplings belong to the standard experimental toolbox, an accurate number counting presents a considerable challenge for both photonic and atomic quantum states. Here we present an application of a number-resolving atom counting [New J. Phys. 23, 113046 (2021)] for the state reconstruction of an atomic coherent spin state. We generate the coherent spin state by driving a Rabi frequency between two hyperfine states of an ultracold Rubidium ensemble.The result is analyzed by a number-resolving fluoresence detection setup. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. The results offer an exciting perspective for a high-fidelity tomography of entangled states and can be applied for the future demonstration of Heisenberg-limited atom interferometry.
The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting perspective for the high-fidelity reconstruction of entangled states and can be applied for a future demonstration of Heisenberg-limited atom interferometry.
High data acquisition rates and low-noise detection of ultracold neutral atoms present important challenges for the state tomography and interferometric application of entangled quantum states in Bose-Einstein condensates. In this paper, we present a high-flux source of 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensates combined with a number-resolving detection. We create Bose-Einstein condensates of $2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ atoms with no discernible thermal fraction within 3.3 s using a hybrid evaporation approach in a magnetic and optical trap. For the high-fidelity tomography of many-body quantum states in the spin degree of freedom [M. Hetzel, et al., arXiv:2207.01270], it is desirable to select a single mode for a number-resolving detection. We demonstrate the low-noise selection of subsamples of up to 16 atoms and their subsequent detection with a counting noise below 0.2 atoms. The presented techniques offer an exciting path towards the creation and analysis of mesoscopic quantum states with improved fidelities and towards their exploitation for fundamental and metrological applications.
Atom interferometers belong among today's most precise sensors and offer a broad range of possible metrological applications. Given their ability to measure accelerations and rotations precisely, they are suitable for inertial sensing, navigation and geodesy. Beyond this, they proved indispensible for time-keeping as well as fundamental research. This explains why the improvement of achievable sensitivities of atom interferometers is of particular interest. However the sensitivity of atom interferometers is fundamentally restricted by the standard quantum limit. The standard quantum limit can only be surpassed by employing entangled many-partice states. Entangled states, such as the twin-Fock state, allow atom interferometers to improve the phase sensitivity beyond the standard quantum limit, but they are reliant on an accurate detection of the interferometric out come. In this work, an experimental apparatus is designed and set up that will allow for routine generation of highly entangled twin-Fock states in a Rubidium-87 spinor Bose-Einstein condensate. As the main feature of this apparatus, an accurate atom counting fluorescence detection has been implemented. This detection achieves single-particle resolving fluorescence measurements for 1 up to 30 atoms. According to the noise analysis the single-atom resolution extends to a limiting atom number of 390(20) atoms. The implemented quadrupole coils with their strong gradient of up to 300 G/cm offer a tight confinement that in combination with the 55 W optical dipole trap laser will enable a fast repetition rate of the creation of highly entangled quantum states.
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.
Bose-Einstein condensates are coherent matter waves, produced by cooling gaseous atomic clouds to ultra-low temperatures. For applications in atom interferometry and precision measurements, Bose-condensed sources present an intriguing alternative to thermal atoms. Although the current sensitivity achievable with interferometers using coherent atoms is not comparable to thermal beam machines (mainly due to the lower flux), there are promising ways to utilise the potential of Bose-condensed sources for atom interferometry. Among those is the low momentum width of Bose-Einstein condensates, which can generally be well controlled and is advantageous for increased interferometric sensitivities by implementing large momentum transfer beam splitters. As part of this thesis, experimental and theoretical investigations are presented to investigate the potential of Bose-Einstein condensates for such applications. We shall present the quantum projection noise limited performance of a Ramsey interferometer operating on the atomic clock transition of a freely expanding cloud of Bose-condensed rubidium 87 atoms. The results include Ramsey fringes of high visibility, not measurably affected by atomic interaction-induced dephasing effects. The achievement and detection of the quantum projection noise limit rely critically on the precision and accuracy of both the imaging setup and the coupling scheme in the interferometric beam splitters. The stabilisation of the beam splitters via an optical Sagnac interferometer is the basis for the quantum projection noise limited performance of the interferometer presented. For an increase of bandwidth and flux in atom interferometric measurements, it is advantageous to use a continuous atomic beam. A truly continuous coherent atom source has not been realised to date, and we present results on a pumping mechanism in this thesis, as a decisive step towards a continuous atom laser. By the investigation of different momentum resonances, we find that the pumping scheme relies on a Raman superradiance-like process. Finally, the thesis demonstrates two interaction measurements in rubidium. The strong mean field interactions due to the high densities in Bose-Einstein condensates are used to probe the potential of a rubidium 87 condensate with an atom laser. The measurement allows a determination of the scattering length between the two atomic states involved. In addition to this two-body scattering scheme, we present a measurement of three-body loss coefficients, extracted from loss curves in rubidium 85 Bose-Einstein condensates. The measurement provides new upper bounds on the three-body loss coefficients at the scattering lengths considered.