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arXiv:1109.2185 · Physical Review Letters

Strong Quantum Spin Correlations Observed in Atomic Spin Mixing

Eva Bookjans, Christopher D. Hamley, Michael Chapman

Published Nov 18, 2011• 73 citations
arXivHTMLPDF

Abstract

We have observed sub-Poissonian spin correlations generated by collisionally induced spin mixing in a spin-1 Bose-Einstein condensate. We measure a quantum noise reduction of $\ensuremath{-}7\text{ }\text{ }\mathrm{dB}$ ($\ensuremath{-}10\text{ }\text{ }\mathrm{dB}$ corrected for detection noise) below the standard quantum limit for the corresponding coherent spin states. The spin fluctuations are detected as atom number differences in the spin states using fluorescent imaging that achieves a detection noise floor of 8 atoms per spin component for a probe time of $100\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$.

DOI
10.1103/physrevlett.107.210406

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We have observed sub-Poissonian spin correlations generated by collisionally induced spin mixing in a spin-1 Bose-Einstein condensate. We measure a quantum noise reduction of \ensuremath−7  dB\ensuremath{-}7\text{ }\text{ }\mathrm{dB}\ensuremath−7  dB (\ensuremath−10  dB\ensuremath{-}10\text{ }\text{ }\mathrm{dB}\ensuremath−10  dB corrected for detection noise) below the standard quantum limit for the corresponding coherent spin states. The spin fluctuations are detected as atom number differences in the spin states using fluorescent imaging that achieves a detection noise floor of 8 atoms per spin component for a probe time of 100  \ensuremathμs100\text{ }\text{ }\ensuremath{\mu}\mathrm{s}100  \ensuremathμs.
The quantum properties of matter waves, in particular quantum correlations and entanglement are an important frontier in atom optics with applications in quantum metrology and quantum information. In this thesis, we report the first observation of sub-Poissonian fluctuations in the magnetization of a spinor 87Rb condensate. The fluctuations in the magnetization are reduced up to 10 dB below the classical shot noise limit. This relative number squeezing is indicative of the predicted pair-correlations in a spinor condensate and lay the foundation for future experiments involving spin-squeezing and entanglement measurements. We have investigated the limits of the imaging techniques used in our lab, absorption and fluorescence imaging, and have developed the capability to measure atoms numbers with an uncertainly < 10 atoms. Condensates as small as ≈ 10 atoms were imaged and the measured fluctuations agree well with the theoretical predictions. Furthermore, we implement a reliable calibration method of our imaging system based on quantum projection noise measurements. We have resolved the individual lattice sites of a standing-wave potential created by a CO2 laser, which has a lattice spacing of 5.3 µm. Using microwaves, we site-selectively address and manipulate the condensate and therefore demonstrate the ability to perturb the lattice condensate of a local level. Interference between condensates in adjacent lattice sites and lattice sites separated by a lattice site are observed.
In this letter, we have studied sub-Poissonian distributions and quantum correlation of atoms in spinor Bose–Einstein condensates. It is found that there exists the sub-Poissonian distributions for spin-1 and spin-(-1) components, respectively. There may exist the violation of the Cauchy–Schwartz inequality. For the same atomic numbers, the regions that include violation of the Cauchy–Schwartz inequality will shift rightwards with the increment of the Rabi frequency, whereas for the same Rabi frequency, the regions will shift leftwards with the increment of the atomic numbers.
We investigate the quantum dynamics of number fluctuations inside an atomic condensate during coherent spin mixing among internal states of the ground state hyperfine manifold, by quantizing the semiclassical nonrigid pendulum model in terms of the conjugate variable pair: the relative phase and the atom number. Our result provides a theoretical basis that resolves the resolution limit, or the effective "shot-noise" level, for counting atoms that is needed to clearly detect quantum correlation effects in spin mixing.
Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3 dB.
We report dispersive spin shot noise measurement of a Bose-Einstein condensate (BEC). While dispersive probing has been used for quantum spin noise measurement of thermal and cold gases for decades, confirmative measurement of shot noise of real spin, i.e., the linear dependence of the spin variance on the number of atoms in a BEC, has been lacking. Here, we demonstrate precise spin noise measurement of a BEC of rubidium atoms at the spin shot noise level by polarization rotation using a two-color probe at optimal detunings, with power balance stabilization to suppress probe-induced excess spin noise. This work opens the possibility for the unexplored study of quantum spin fluctuations in multicomponent or spinor BECs and offers an approach to improve spin measurement precision, which is relevant to atomic spin-based sensors.