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arXiv:1409.6089 · Physical Review A

Spin squeezing by tensor twisting and Lipkin-Meshkov-Glick dynamics in a toroidal Bose-Einstein condensate with spatially modulated nonlinearity

Tomáš Opatrný, Michal Kolář, Kunal K. Das

Published May 15, 2015• 41 citations
arXivHTMLPDF

Abstract

We propose a scheme for spin squeezing in the orbital motion of a Bose-Einstein condensate in a toroidal trap. A circular lattice couples two counterrotating modes and squeezing is generated by the nonlinear interaction spatially modulated at half the lattice period. By varying the amplitude and phase of the modulation, various cases of the twisting tensor can be directly realized, leading to different squeezing regimes. These include the one-axis twisting and two-axis countertwisting that are often discussed as the most important paradigms for spin squeezing. Our scheme naturally realizes the Lipkin-Meshkov-Glick model with the freedom to vary all its parameters simultaneously.

DOI
10.1103/physreva.91.053612

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We propose a scheme for spin squeezing in the orbital motion of a Bose-Einstein condensate in a toroidal trap. A circular lattice couples two counterrotating modes and squeezing is generated by the nonlinear interaction spatially modulated at half the lattice period. By varying the amplitude and phase of the modulation, various cases of the twisting tensor can be directly realized, leading to different squeezing regimes. These include the one-axis twisting and two-axis countertwisting that are often discussed as the most important paradigms for spin squeezing. Our scheme naturally realizes the Lipkin-Meshkov-Glick model with the freedom to vary all its parameters simultaneously.
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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.
We theoretically investigate a scheme to enhance relative number squeezing and spin squeezing in a two-component Bose-Einstein condensate (BEC) by utilizing the inherent mean-field dynamics of the condensate. Due to the asymmetry in the scattering lengths, the two components exhibit large density oscillations where they spatially separate and recombine. The effective nonlinearity responsible for the squeezing is increased by up to 3 orders of magnitude when the two components spatially separate. We perform a multimode simulation of the system using the truncated Wigner method and show that this method can be used to create significant squeezing in systems where the effective nonlinearity would ordinarily be too small to produce any significant squeezing in sensible time frames, and we show that strong spatial dynamics resulting from large particle numbers aren't necessarily detrimental to generating squeezing. We develop a simplified semianalytic model that gives good agreement with our multimode simulation and will be useful for predicting squeezing in a range of different systems.
Spin squeezing, as a crucial quantum resource, plays a pivotal role in quantum metrology, enabling us to achieve high-precision parameter estimation schemes. Here, we investigate the spin squeezing and the quantum phase transition in an anisotropic central spin system. We find that this kind of central spin system can be mapped to the anisotropic Lipkin-Meshkov-Glick model in the limit where the ratio of transition frequencies between the central spin and the spin bath tends towards infinity. This property can induce a one-axis twisting interaction and provides another possibility for generating spin squeezing. We consider the generation of spin-squeezed states through the ground state and the dynamical evolution of the central spin model, respectively. The results show that the dynamical approach is more effective, and the spin-squeezing parameter improves as the anisotropy parameter decreases, while its value scales with system size as ${N}^{\ensuremath{-}2/3}$. Furthermore, we obtain the critical exponent of the quantum Fisher information around the critical point by numerical simulation, and find its value tends to 4/34/34/3 as the frequency ratio and the system size approach infinity. This paper offers a promising scheme for generating spin-squeezed state and paves the way for potential advancements in quantum sensing.
We examine the dynamics of circulating modes of a Bose-Einstein condensate confined in a toroidal lattice. Nonlinearity due to interactions leads to criticality that separates oscillatory and self-trapped phases among counterpropagating modes which however share the same physical space. In the mean-field limit, the criticality is found to substantially enhance sensitivity to rotation of the system. Analysis of the quantum dynamics reveals the fluctuations near criticality are significant, which we explain using spin-squeezing formalism visualized on a Bloch sphere. We utilize the squeezing to propose a Ramsey interferometric scheme that suppresses fluctuation in the relevant quadrature sensitive to rotation.
The twist-and-turn dynamics of spin squeezing results from the interplay of the one-axis-twisting (nonlinear in the collective-spin operators) and the transverse-field turning (linear) term in the underlying Lipkin-Meshkov-Glick-type Hamiltonian, both with constant (time-independent) prefactors. Using shortcuts to adiabaticity (STA) and the recently developed enhanced version thereof (eSTA), we demonstrate here that dynamics of this type can be utilized for a fast and robust preparation of spin-squeezed states in internal bosonic Josephson junctions, i.e., condensates of cold bosonic atoms in two different internal (hyperfine) states (single-boson modes) coupled through Rabi rotations. Assuming that the initial state of this system is its ground state for a given initial value of the (time-dependent) linear coupling strength and that the nonlinear coupling strength remains constant, we set out to determine the time dependence of the linear (Rabi) coupling strength that allows for the generation of spin-squeezed states using the STA- and eSTA-based approaches. We then characterize the modified twist-and-turn dynamics of this system by evaluating the coherent spin-squeezing and number-squeezing parameters, as well as the fidelity of the target spin-squeezed states. In this way, we show that the eSTA approach allows for a particularly robust realization of strongly spin-squeezed states in this system, consistently outperforming its adiabatic and STA-based counterparts, even for systems with several hundred particles. Our method could also be employed for the generation of metrologically-useful non-Gaussian states.