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arXiv:2009.07372 · Physical Review A

Twist-and-store entanglement in bimodal and spin-1 Bose-Einstein condensates

Artur Niezgoda, Emilia Witkowska, Safoura Sadat Mirkhalaf

Published Nov 16, 2020• 1 citation
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Abstract

A scheme for dynamical stabilization of entanglement quantified by the quantum Fisher information is analyzed numerically and analytically for bimodal and spin-1 Bose-Einstein condensates in the context of atomic interferometry. The scheme consists of twisting dynamics followed by a single rotation of a state which limits further evolution around stable center fixed points in the mean-field phase space. The resulting level of entanglement is of the order or larger than at the moment of rotation. It is demonstrated that the readout measurement of parity quantifies the level of entanglement during the entire evolution.

DOI
10.1103/physreva.102.053315

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A scheme for dynamical stabilization of entanglement quantified by the quantum Fisher information is analyzed numerically and analytically for bimodal and spin-1 Bose-Einstein condensates in the context of atomic interferometry. The scheme consists of twisting dynamics followed by a single rotation of a state which limits further evolution around stable center fixed points in the mean-field phase space. The resulting level of entanglement is of the order or larger than at the moment of rotation. It is demonstrated that the readout measurement of parity quantifies the level of entanglement during the entire evolution.
We analyze a scheme for storage of entanglement quantified by the quantum Fisher information in the two-axis countertwisting model. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of the four stable center and two unstable saddle fixed points in the mean-field phase portrait. The entangled state is generated dynamically from an initial spin-coherent state located around an unstable saddle fixed point. At an optimal moment of time the state is shifted to a position around the stable center fixed points by a single rotation, where its dynamics and properties are approximately frozen. We also discuss evolution with noise. In some cases the effect of noise turns out to be relatively weak, which is explained by parity conservation.
We demonstrate dynamic stabilization of a strongly interacting quantum spin system realized in a spin-1 atomic Bose-Einstein condensate. The spinor Bose-Einstein condensate is initialized to an unstable fixed point of the spin-nematic phase space, where subsequent free evolution gives rise to squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that rotate the spin-nematic many-body fluctuations and limit their growth. The stability diagram for the range of pulse periods and phase shifts that stabilize the dynamics is measured and compares well with a stability analysis.
We demonstrate experimentally an alternative method for the dynamic generation of atomic spin squeezing, building on the interplay between linear coupling and nonlinear phase evolution. Since the resulting quantum dynamics can be seen as rotation and shear on the generalized Bloch sphere, we call this scheme twist-and-turn. This is closely connected to an underlying instability in the classical limit of this system. The short-time evolution of the quantum state is governed by a fast initial spreading of the quantum uncertainty in one direction, accompanied by squeezing in the orthogonal axis. We find an optimal value of ${\ensuremath{\xi}}_{\mathrm{S}}^{2}=\ensuremath{-}7.1(3)$ dB in a single Bose-Einstein condensate and scalability of the squeezing to more than 104{10}^{4}104 particles with ${\ensuremath{\xi}}_{\mathrm{S}}^{2}=\ensuremath{-}2.8(4)$ dB.
Implementation of the quantum interferometry concept to spin-1 atomic Bose–Einstein condensates is analyzed by employing a polar state evolved in time. In order to identify the best interferometric configurations, the quantum Fisher information (QFI) is maximized. Three optimal configurations are identified, among which one was not reported in the literature yet, although it gives the highest value of the QFI in experimentally achievable short time dynamics. Details of the most optimal configurations are investigated based on the error-propagation formula which includes the interaction-based readout protocol to reduce the destructive effect of detection noise. In order to obtain Heisenberg scaling accessible by present day experimental techniques, an efficient measurement and a method for the inversion of dynamics were developed, as necessary for the protocol’s implementation.
We revisit in detail the non-mean-field ground-state phase diagram for a binary mixture of spin-1 Bose-Einstein condensates including quantum fluctuations. The noncommuting terms in the spin-dependent Hamiltonian under the single-spatial-mode approximation make it difficult to obtain exact eigenstates. Utilizing spin-z-component conservation and total spin angular momentum conservation, we numerically derive information on the building blocks and evaluate the von Neumann entropy to quantify the ground states. The mean-field phase boundaries are found to remain largely intact, yet the ground states show fragmented and entangled behaviors within large parameter spaces of interspecies spin-exchange and singlet-pairing interactions.
We theoretically investigate the effect of multimode dynamics on the creation of macroscopic superposition states (spin-cat states) in Bose-Einstein condensates via one-axis twisting. A two-component Bose-Einstein condensate naturally realizes an effective one-axis twisting interaction, under which an initially separable state will evolve toward a spin-cat state. However, the large evolution times necessary to realize these states is beyond the scope of current experiments. This evolution time is proportional to the degree of asymmetry in the relative scattering lengths of the system, which results in the following trade-off: faster evolution times are associated with an increase in multimode dynamics, and we find that generally multimode dynamics reduce the degree of entanglement present in the final state. However, we find that highly entangled catlike states are still possible in the presence of significant multimode dynamics and that these dynamics impose a speed limit on the evolution of such states.