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arXiv:2208.04019 · Physical Review A

Accelerating many-body entanglement generation by dipolar interactions in the Bose-Hubbard model

Marlena Dziurawiec, Tanausú Hernández Yanes, Marcin Płodzień, Mariusz Gajda, Maciej Lewenstein, Emilia Witkowska

Published Jan 24, 2023• 18 citations
arXivHTMLPDF

Abstract

The spin-squeezing protocols allow the dynamical generation of massively correlated quantum many-body states, which can be utilized in entanglement-enhanced metrology and technologies. We study a quantum simulator generating twisting dynamics realized in a two-component Bose-Hubbard model with dipolar interactions. We show that the interplay of contact and long-range dipolar interactions between atoms in the superfluid phase activates the anisotropic two-axis countertwisting mechanism, accelerating the spin-squeezing dynamics and allowing the Heisenberg-limited accuracy in spectroscopic measurements.

DOI
10.1103/physreva.107.013311

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The spin-squeezing protocols allow the dynamical generation of massively correlated quantum many-body states, which can be utilized in entanglement-enhanced metrology and technologies. We study a quantum simulator generating twisting dynamics realized in a two-component Bose-Hubbard model with dipolar interactions. We show that the interplay of contact and long-range dipolar interactions between atoms in the superfluid phase activates the anisotropic two-axis countertwisting mechanism, accelerating the spin-squeezing dynamics and allowing the Heisenberg-limited accuracy in spectroscopic measurements.
Generation, storage, and utilization of correlated many-body quantum states are crucial objectives of future quantum technologies and metrology. Such states can be generated by the spin-squeezing protocols, i.e., one-axis twisting and two-axis countertwisting. In this Letter, we show activation of these two squeezing mechanisms in a system composed of ultracold atomic fermions in the Mott insulating phase by a position-dependent laser coupling of atomic internal states. Realization of both the squeezing protocols is feasible in the current state-of-the-art experiments.
We study the generation of metrologically useful entanglement in a three-level (spin-1) system naturally realized in arrays of dipole-interacting Rydberg atoms confined in optical tweezers. In the spin-quadrupolar operator basis, the interaction Hamiltonian decomposes into effective SU(2) subspaces, within which quench dynamics from product initial states generate scalable spin-nematic squeezing. For symmetric interactions, we identify a mapping to effective one-axis twisting within bright and dark manifolds and demonstrate that the squeezing parameter scales as ξ2∝N−2/3ξ^{2}\propto N^{-2/3}ξ2∝N−2/3 (ξ2∝N−0.5ξ^{2}\propto N^{-0.5}ξ2∝N−0.5) with system size for all-to-all (two-dimensional dipolar) couplings. In both cases the quantum Fisher information reaches FQ∝N2F_Q\propto N^{2}FQ​∝N2. For antisymmetric interactions supplemented by a microwave drive we find a distinct two-axis countertwisting mechanism. This results in squeezing ξ2∝N−0.7ξ^{2}\propto N^{-0.7}ξ2∝N−0.7 for all-to-all interactions and moderate squeezing for dipolar interactions in 2D. Our results constitute a first theoretical step beyond the well-studied qubit setting toward scalable entanglement generation in qudit systems with dipolar interactions, directly relevant to current Rydberg tweezer experiments.
We study a bulk fermionic dipolar molecular gas in the quantum degenerate regime confined in a two-dimensional geometry. Using two rotational states of the molecules, we encode a spin 1/2 degree of freedom. To describe the many-body spin dynamics of the molecules, we derive a long-range interacting XXZ model valid in the regime where motional degrees of freedom are frozen. Because of the spatially extended nature of the harmonic oscillator modes, the interactions in the spin model are very long ranged, and the system behaves close to the collective limit, resulting in robust dynamics and generation of entanglement in the form of spin squeezing even at finite temperature and in the presence of dephasing and chemical reactions. We discuss how the internal state structure can be exploited to realize time reversal and enhanced metrological sensing protocols.
The scalable production of multipartite entangled states in ensembles of qubits is a crucial function of quantum devices, as such states are an essential resource both for fundamental studies on entanglement, as well as for applied tasks. Here we focus on the U(1) symmetric Hamiltonians for qubits with dipolar interactions-a model realized in several state-of-the-art quantum simulation platforms for lattice spin models, including Rydberg-atom arrays with resonant interactions. Making use of exact and variational simulations, we theoretically show that the nonequilibrium dynamics generated by this Hamiltonian shares fundamental features with that of the one-axis-twisting model, namely, the simplest interacting collective-spin model with U(1) symmetry. The evolution governed by the dipolar Hamiltonian generates a cascade of multipartite entangled states-spin-squeezed states, Schrödinger's cat states, and multicomponent superpositions of coherent spin states. Investigating systems with up to N=144 qubits, we observe full scalability of the entanglement features of these states directly related to metrology, namely, scalable spin squeezing at an evolution time O(N^{1/3}) and Heisenberg scaling of sensitivity of the spin parity to global rotations for cat states reached at times O(N). Our results suggest that the native Hamiltonian dynamics of state-of-the-art quantum simulation platforms, such as Rydberg-atom arrays, can act as a robust source of multipartite entanglement.
Spin squeezing is both a fundamental witness of quantum entanglement and a key resource for quantum-enhanced metrology. While all-to-all interactions provide a paradigmatic route to generate spin squeezing, many programmable quantum simulators naturally realize finite-range interactions that induce coupling between collective spin dynamics and finite-momentum spin-wave modes, thereby degrading the achievable squeezing. Here we develop an optimization-based global-control strategy for enhancing spin squeezing in a two-dimensional XX model with dipolar interactions. By combining rotor-spin-wave theory with an extension to open boundary conditions, we enable efficient optimization of control protocols for large finite-range interacting systems. We show that a single collective transverse field generates squeezing beyond the conventional two-axis-twisting benchmark across system sizes accessible to numerical benchmarking. The optimized dynamics exploits squeezing-axis reorientation while suppressing spin-wave excitations, thereby stabilizing strong squeezing over extended times. We further implement the optimized protocol in a two-dimensional Rydberg-atom array and experimentally observe enhanced, long-lived spin squeezing in good agreement with theory.
The spin-squeezing dynamics of a quasi-one-dimensional dipolar Bose gas trapped in a double-well potential is studied by employing the method of the multiconfigurational time-dependent Hartree for bosons. We find that optimal squeezing generated by the dipolar interaction can be improved over the one-axis twisting limit, and this squeezing is much stronger than that obtained by the contact interaction. Moreover, natural orbital-related squeezing can be controlled by the direction of the dipole moment, which provides control for storing the optimal spin squeezing. The origin of the squeezing as well as the relationship between spin squeezing and the two-order correlation function are also discussed.