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arXiv:0806.1553 · Physical Review A

Amplification of fluctuations in a spinor Bose-Einstein condensate

Sabrina R. Leslie, Jennie Guzman, Mukund Vengalattore, Jay Deep Sau, Marvin L. Cohen, Dan Stamper-Kurn

Published Apr 28, 2009• 125 citations
arXivHTMLPDF

Abstract

Dynamical instabilities in a $^{87}\text{R}\text{b}$ $F=1$ spinor Bose-Einstein condensate are used as a parametric amplifier of quantum spin fluctuations. We demonstrate the spectrum of this amplifier to be tunable, in quantitative agreement with theory. We quantify the microscopic spin fluctuations of the initially paramagnetic condensate by applying this amplifier and measuring the resulting macroscopic magnetization. The variance of these fluctuations agrees with predictions of a beyond-mean-field theory. This spin amplifier is thus shown to be nearly quantum limited at a gain as high as 30 dB.

DOI
10.1103/physreva.79.043631

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We develop theory for fluctuations in atom number and spin within finite-sized cells of a spinor Bose-Einstein condensate. This theory provides a model of measurements that can be performed in current experiments using finite resolution in situ imaging. We develop analytic results for quantum and thermodynamic limits of the fluctuations and apply our theory to the four equilibrium phases of a spin-1 condensate. We then validate these limits and examine the behavior over a wide parameter regime using numerical calculations specialized to the case of a spinor condensate confined to be quasi-two-dimensional.
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For quantum fluids, the role of quantum fluctuations may be significant in several regimes such as when the dimensionality is low, the density is high, the interactions are strong, or for low particle numbers. In this paper, we propose a fundamentally different regime for enhanced quantum fluctuations without being restricted by any of the above conditions. Instead, our scheme relies on the engineering of an effective attractive interaction in a dilute, two-component Bose-Einstein condensate (BEC) consisting of thousands of atoms. In such a regime, the quantum spin fluctuations are significantly enhanced (atom bunching with respect to the noninteracting limit) since they act to reduce the interaction energy, a remarkable property given that spin fluctuations are normally suppressed (antibunching) at zero temperature. In contrast to the case of true attractive interactions, our approach is not vulnerable to BEC collapse. We numerically demonstrate that these quantum fluctuations are experimentally accessible by either spin or single-component Bragg spectroscopy, offering a useful platform on which to test beyond-mean-field theories. We also develop a variational model and use it to analytically predict the shift of the immiscibility critical point, finding good agreement with our numerics.