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arXiv:2202.01349

Twist and Turn Squeezing in a Multi-Mode Bose-Einstein Condensate

Junbang Liu, Bartlett, Thomas, J. J. Hope, Simon A. Haine

Published Feb 3, 2022• 0 citations
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Abstract

Here we examine the generation of Twist and Turn (TNT) Squeezing in a large atom-number Bose-Einstein Condensate for the purposes of generating quantum-enhanced states for atom interferometry. Unlike previous analysis, we examine situations where the multi-mode dynamics is significant, and cannot be captured by a simple single-mode model. We find that in some regimes, with careful choice of the rotation parameter, we can still obtain squeezing much more rapidly than via one-axis twisting (OAT).

DOI
10.48550/arxiv.2202.01349

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Here we examine the generation of Twist and Turn (TNT) Squeezing in a large atom-number Bose-Einstein Condensate for the purposes of generating quantum-enhanced states for atom interferometry. Unlike previous analysis, we examine situations where the multi-mode dynamics is significant, and cannot be captured by a simple single-mode model. We find that in some regimes, with careful choice of the rotation parameter, we can still obtain squeezing much more rapidly than via one-axis twisting (OAT).
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 introduce a spin-squeezing technique that is a hybrid of two well-established spin-squeezing techniques, quantum nondemolition measurement (QND), and one-axis twisting (OAT). This hybrid method aims to improve spin-squeezing over what is currently achievable using QND and OAT. In practical situations, the strength of both the QND and OAT interactions is limited. We find that, in these situations, the hybrid scheme performed considerably better than either OAT or QND used in isolation. As QND and OAT have both been realized experimentally, this technique could be implemented in current atom interferometry setups with only minor modifications to the experiment.
Free-fall atom interferometers offer a powerful platform for accurate, absolute gravitational sensing. Szigeti et al. [Phys. Rev. Lett. 125, 100402 (2020)] recently proposed a quantum-enhanced scheme that uses a spin-squeezed Bose-Einstein condensate as an input state to improve the phase sensitivity of the interferometer. The spin squeezing, generated via one-axis twisting interactions, was limited by condensate expansion. Here we present an improved state preparation in which a sudden trapping potential -- a delta kick -- is initially applied to focus the condensate. The resulting increase in density enhances the one-axis-twisting interactions and produces greater spin squeezing. Using multimode truncated-Wigner simulations, we quantify the performance of the interferometer and find that, for an optimal kick strength, the phase sensitivity surpasses the standard quantum limit by a factor of ∼20\sim 20∼20. This represents a fourfold improvement over the original scheme without the delta kick and is well captured by a two-mode approximation.
The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to SU(2)\text{SU}(2)SU(2) rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a nonlinear Hamiltonian. We introduce a method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in SU(4)\text{SU}(4)SU(4), thereby creating the opportunity for dynamics not possible in typical SU(2)\text{SU}(2)SU(2) one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multiparameter or auxiliary measurement schemes than those prepared by standard spin squeezing.
We develop a framework for describing the effects of systematic state-preparation error in quantum-enhanced atom interferometry on sensing performance. We do this in the context of both spin-squeezed and non-Gaussian states for the two-axis-twisting (TAT), one-axis-twisting (OAT), and twist-and-turn (TNT) state-preparation schemes, and derive general conditions for robustness and susceptibility of quantum states to state-preparation error. In the spin-squeezing regime, we find that OAT is more susceptible to state-preparation error than TAT due to its parameter-dependent phase-space rotation. In the non-Gaussian regime, we find that OAT is robust to state-preparation errors, which can be explained by a small ratio of off-diagonal to diagonal elements in its Fisher-covariance matrix. In contrast, TNT does not exhibit this robustness. We find that the single-parameter unbiased estimators that are habitually used in quantum-enhanced atom interferometry are not always optimal, and that there may be occasions where biased estimators, or two-parameter unbiased estimators, lead to lower net error.
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.