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arXiv:1810.03236 · Physical Review A

Generating macroscopic superpositions with interacting Bose-Einstein condensates: Multimode speedups and speed limits

Samuel P. Nolan, Simon A. Haine

Published Dec 4, 2018• 10 citations

Abstract

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.

DOI: 10.1103/physreva.98.063606

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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.

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.

We study theoretically the interaction-induced generation of mesoscopic coherent spin state superpositions (small-particle-number cat states) from an initial coherent spin state in bimodal Bose-Einstein condensates and the subsequent phase revival, including decoherence due to particle losses and fluctuations of the total particle number. In a full multimode description, we propose a preparation procedure of the initial coherent spin state and we study the effect of preexisting thermal fluctuations on the phase revival, and on the spin and orbito-spinorial cat-state fidelities.

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

{10}^{4}

particles with ${\ensuremath{\xi}}_{\mathrm{S}}^{2}=\ensuremath{-}2.8(4)$ dB.

We provide an experimentally viable scheme for the generation of entangled number states of Bose–Einstein condensates in multiple wells with cyclic pairwise connectivity. The condensate ground state in a multiple well trap can self-evolve, when appropriately phase engineered with specific phase differences between the neighbouring wells, to a macroscopic superposition state with controllable entanglement – as for example the multiple well generalization of double well NOON states. We demonstrate, through numerical simulations, the creation of entangled states of small numbers of particles in three and four wells and then explore the creation of entangled states where there are larger numbers of particles or a larger number of wells. In the four well case we study a novel, initially unexpected, type of entanglement produced as the particle numbers, or interaction strengths, increase.

Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.