By Li You, Tsinghua University
An important direction of atomic quantum gas research concerns the generation of large entangled states. In addition to their applications in quantum information and quantum simulation, entangled states are useful for enhanced metrological precisions beyond the standard quantum limit (SQL) 1/N1/2 of N uncorrelated atoms. Metrologically useful spin squeezed states have been extensively explored and generated in various systems, including in Bose Einstein Condensate (BEC) through collisional interactions and in atomic vapors based on quantum nondemolition measurements.
Twin-Fock state (TFS) with equal number of particles in two orthogonal modes, can provide near Heisenberg limit (HL) precision of 1/N, relying on correlations from particle exchange symmetries. A mixture of TFSs can be created from waiting for spin mixing dynamics to evolve in atomic condensate through elementary spin exchange collisions whereby two atoms in the m_F=0 component oscillate into one atom each in the m_F=±1 components and vice versa. In 2011, three experiments detected such quantum correlations based on spin mixing dynamics in 87Rb spinor BEC [1-3], respectively revealed by a reduced fluctuation in the population difference between the m_F=±1 components , two-mode quadrature squeezing through an atomic homodyne detection , and the creation of large TFS ensembles of up to 104 atoms and a claimed interferometric sensitivity -1.61dB below the SQL .
An important characteristic for the TFS ensemble prepared this way is the broad distribution for the total number of atoms (N) in m_F=±1. To overcome this inherent fluctuation, one post selects experimental data sets whereby a narrow range of N is adopted. Such an approach however significantly reduces the experimental efficiency on top of the already non-optimal conversion efficiency of the TFS. Furthermore, TFS generated from spin mixing dynamics is sensitive to experimental imperfections and external noises during the evolution.
We shall discuss our recent work of deterministic generation of TFS in the F=1 ground hyperfine manifold of 87Rb BEC through quantum phase transitions. By manipulating the net quadratic Zeeman shift, which is the sum of a shift from a bias static magnetic field and the ac-Zeeman shift from a dressing microwave, we drive the ground state condensate initially of all atoms in the m_F=0 component into twin-Fock state with near unity efficiency. The striking narrow distribution of N allows us to beat the quantum shot noise (QSN) limit without post-selection. Specifically, the fluctuations in the population difference between the two modes of the TFS samples are observed to be highly squeezed, at -9.9(2) dB below the QSN. Subtracting detection noise leads to an improved squeezing of -11.8(3) dB, which together with the measured collective spin length of 0.99(1) N/2, translates into an entanglement depth of 640 atoms, primarily limited by the loss of atoms.
We anticipate our results will establish a benchmark for producing entangled atomic BECs, which will provide previously unavailable opportunities to study their properties and to clarify their metrological implications.
We acknowledge the support by MOST (No. 2013CB922004) of the National Key Basic Re-search Program of China, and by NSFC (No. 91121005, No. 91421305, and No. 11374176).
1. E. M. Bookjans et al, Phys. Rev. Lett. 107, 210406 (2011).
2. C. Gross et al, Nature 480, 219 (2011).
3. B. Lucke et al, Science 334, 773 (2011).