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arXiv:2009.09728 · Physical Review A

Critically enhanced spin-nematic squeezing and entanglement in dipolar spinor condensates

Qing-Shou Tan, Yixiao Huang, Qiongtao Xie, Xiaoguang Wang

Published Oct 7, 2020• 3 citations
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Abstract

We study the quantum critical effect enhanced spin-nematic squeezing and quantum Fisher information (QFI) in the spin-1 dipolar atomic Bose-Einstein condensate. We show that the quantum phase transitions can improve the squeezing and QFI in the nearby regime of the critical point, and the Heisenberg-limited high-precision metrology can be obtained. The different properties of the ground squeezing and entanglement under even and odd number of atoms are further analyzed, by calculating the exact analytical expressions. We also demonstrate the squeezing and entanglement generated by the spin-mixing dynamics around the phase-transition point. It is shown that the steady squeezing and entanglement can be obtained, and the Bogoliubov approximation can well describe the dynamics of spin-nematic squeezed vacuum state.

DOI
10.1103/physreva.102.043307

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We study the quantum critical effect enhanced spin-nematic squeezing and quantum Fisher information (QFI) in the spin-1 dipolar atomic Bose-Einstein condensate. We show that the quantum phase transitions can improve the squeezing and QFI in the nearby regime of the critical point, and the Heisenberg-limited high-precision metrology can be obtained. The different properties of the ground squeezing and entanglement under even and odd number of atoms are further analyzed, by calculating the exact analytical expressions. We also demonstrate the squeezing and entanglement generated by the spin-mixing dynamics around the phase-transition point. It is shown that the steady squeezing and entanglement can be obtained, and the Bogoliubov approximation can well describe the dynamics of spin-nematic squeezed vacuum state.
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We study spin-nematic squeezing in a spinor Bose-Einstein condensate and use it to probe dynamical quantum phase transitions. We show that the quench dynamics of the spin-nematic squeezing exhibits a nonanalytical change with respect to a final quadratic Zeeman energy, and demonstrate that the squeezing detects not only the ground state phase diagram, but also the excited state quantum phase transition. We further analyze the dynamic stabilization of the system and present its relation to the dynamical quantum phase transitions. Our results are applicable to the spinor condensates with both of the sodium and rubidium atoms.
Abstract We propose a simple scheme to realize the persistent spin-nematic squeezing in a spinor Bose–Einstein condensate by rapidly turning-off the external magnetic field at a time that maximal spin-nematic squeezing occurs. We observe that the optimal spin-nematic squeezing can be maintained in a nearly fixed direction. For a proper initial magnetic field, the optimal squeezing can be obviously enhanced. We further construct a spin-mixing interferometer, where the quantum correlation of the squeezed state (generated by our scheme) is fully utilized in the phase measurement, and show the phase sensitivity of the interferometer has a significant enhancement.
We investigate spin squeezing (SS) and the quantum Fisher information (QFI) for the Jaynes-Cummings Dicke (JC-Dicke) model in a two component atomic Bose-Einstein condensate (BEC) inside an optical cavity. Analytical expressions for spin squeezing and the reciprocal of the quantum Fisher information per particle (RMQFI) are derived using the frozen spin approximation. It is shown that in the superradiant phase near the critical point, maximum squeezing and maximum quantum entanglement occurs. The present study is relevant to quantum information processing and precision spectroscopy.
Entanglement lies at the core of emergent quantum technologies such as quantum-enhanced metrology, quantum communication and cryptography, and quantum simulation and computing. Spinor Bose-Einstein condensates (BECs) offer a promising platform for the generation and application of entangled states. For example, a spin-1 BEC has served for the proof-of-principle demonstration of a quantum-enhanced atomic clock. Ferromagnetic spin-1 BECs with zero magnetization exhibit three ground-state quantum phases with different entanglement properties. The control parameter can be tuned by a magnetic field or by microwave dressing. As already experimentally demonstrated, an entangled ground state can be reached from a well accessible, non-entangled one by driving the control parameter across quantum phase transitions (QPTs). We investigate which of the entangled ground states afford quantum-enhanced interferometry. The interferometric usefulness is quantified by the quantum Fisher information (QFI), which we analyze throughout all ground-state phases. A large QFI at about half the Heisenberg limit, and thus far above the standard quantum limit, is attained by the well-known Twin-Fock state and by the central broken-axisymmetry (CBA) state. We detail how the CBA state can be used as a probe for quantum-enhanced interferometry. Furthermore, we observe that the large QFI of the CBA state can be traced back to enclosed macroscopic superposition states (MSSs). Measuring the atom number in one out of three modes generates, with high probability and heralded by the measurement outcome, a MSS similar to a NOON state. Our proposal promises NOON-like MSSs of unprecedentedly many atoms. Both proposed applications of the adiabatically prepared CBA state depend only on existent technology. Our numerical results show that they tolerate a reasonably swift quasiadiabatic passage in the presence of atom loss as well as uncertainties of atom counting. Excited-state quantum phase transitions (ESQPTs) extend the concept of QPTs beyond the ground state. While they have been extensively investigated theoretically, there are only few experimental results. From the perspective of quantum-state engineering, it is furthermore surprising how rarely order parameters of ESQPTs are discussed in the literature. Mean-field models for spinor BECs imply ESQPTs, to which some experimental observations on the mean-field dynamics can be attributed. However, so far, neither theoretical nor experimental studies have specifically addressed ESQPTs in spinor BECs. We extend the ground-state phase diagram of ferromagnetic spin-1 BECs with zero magnetization across the spectrum. There are three excited-state phases, corresponding to one ground-state phase each. The ESQPTs are signaled by a diverging density of states. The mean-field phase-space trajectories can be characterized by a winding number that is in one-to-one correspondence to the excited-state phases. We derive a closely related order parameter encoded in the dynamics of coherent states and discuss how this order parameter can be interferometrically measured in current experiments. Remarkably, the mean-field model governing the ESQPTs in spin-1 BECs with zero magnetization is encountered also, e. g., in molecular and nuclear physics. Because of the superior experimental control, spinor BECs can be considered as simulators of the ESQPTs in those systems. Our results contribute to quantum-state engineering and quantum-enhanced interferometry in spinor BECs and to the characterization of excited-state quantum phases. The latter may, in turn, lead on to applications in quantum-state engineering.
Abstract We study the effect of dephasing on the spin-mixing dynamics of a spinor Bose–Einstein condensate. We focus on a short-time dynamics and derive an analytical dynamics equations for the system by using mean-field approximation. We show the spin-mixing is suppressed via a quantum Zeno effect (QZE) in which the phase-noise intensity is much stronger than the inverse correlation time of the stimulated process. We also investigate the spin-nematic squeezing in the process of spin-mixing dynamics and show the squeezing is restrained by the QZE.