Bose-Einstein condensate (BEC) is an extreme state of matter that may occur when bosonic neutral atoms are cooled to very low temperatures (~100 nK). When a BEC is trapped in a magnetic potential, the spin of each atom is oriented in the direction of the magnetic field. The spin degrees of freedom are frozen and the BEC is described by a scalar order parameter. When the BEC is trapped using an optical potential, the spin of each atom is free to evolve. The order parameter of describing a spin-f BEC has 2f+1 component and the BEC is referred to as a spinor BEC. This research project focuses on using spinor BEC for generating metrological useful entangled states.

Recent results

Deterministic entanglement generation from driving through quantum phase transitions^[1]

For a ⁸⁷Rb BEC of zero magnetization in the F=1 ground hyperfine manifold, the spinor ground state of the system exhibits three quantum phases, namely the Polar (P), Broken-axis symmetry (BA), and Twin-Fock (TF) phases. The polar phase is equivalent to a pure BEC with only one m_F=0 component. This phase can be prepared readily in experiment. By tuning the relative strength between the (m_F=0 to m_F=±1) spin-mixing rate (c₂) and the quadratic Zeeman energy (q) of the BEC, we can efficiently drive a polar BEC across two quantum critical points, resulting in a highly entangled TF BEC, a quantum state that allows phase measurement precision beyond the standard quantum limit. The experiment highlights the potential of generating entanglement by driving a system through quantum phase transitions.

[1].  Luo, X. Y., Zou, Y. Q., Wu, L. N., Liu, Q., Han, M. F., Tey, M. K., & You, L. Science 355, 620-623 (2017).

Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms^[2]

Dicke states form an important class of highly entangled states which are common eigenstates |l,m〉 of the collective spin operators L² and L_z. Here L≡(L_x,L_y,L_z), L_k = Σ_j=1^N s_k^(j) with s_k^(j) representing the spin operator of the jth particle along the k(=x,y,z) direction. Most Dicke states produced so far are limited to pseudospin-1/2 (two-level) particles. In this work, we deterministically generate balanced spin-1 Dicke states in the close vicinity of |l=N,m=0〉 with N~11700, by driving a spin-1 condensate through a quantum phase transition. The prepared states are characterized to exhibit a collective spin length of l>0.99N and their entanglement breadth is inferred to be more than 10000 on average and at least ~630 atoms at 1 standard deviation. Compared to our previously reported twin-Fock state (spin-1/2 Dicke state), this spin-1 Dicke state takes advantage of all three spin components and offers higher interferometric sensitivity. Using the prepared states, we demonstrate enhanced measurement precision beyond the three-mode standard quantum limit (SQL).

Figure (A) shows the Bloch sphere representation (left) of the three-mode Dicke state. Figure (B) shows the enhancement of measured angular sensitivity over the three-mode SQL using the prepared states.

[2].  Yi-Quan Zou, Ling-Na Wu, Qi Liu, Xin-Yu Luo, Shuai-Feng Guo, Jia-Hao Cao, Meng Khoon Tey, and Li You Proceedings of the National Academy of Sciences (2018): 201715105.