Nonlinear Bragg interferometer with a trapped Bose-Einstein condensate

Letter

Nonlinear Bragg interferometer with a trapped Bose-Einstein condensate

Robin Corgier, Luca Pezzè, and Augusto Smerzi

Phys. Rev. A 103, L061301 – Published 9 June 2021

Abstract

We propose a scheme for trapped-atom interferometry using an interacting Bose-Einstein condensate. The condensate is controlled and spatially split into two confined external momentum modes through a series of Bragg pulses. The proposed scheme (i) allows the generation of large entanglement in a trapped-interferometer configuration via one-axis twisting dynamics induced by interatomic interaction and (ii) avoids the suppression of interactions during the interferometer sequence by a careful manipulation of the state before and after phase encoding. The interferometer can be used for the measurement of gravity with a sensitivity beyond the standard quantum limit.

Received 15 January 2021
Accepted 5 April 2021

DOI:https://doi.org/10.1103/PhysRevA.103.L061301

Physics Subject Headings (PhySH)

Atom interferometry Bose-Einstein condensates Entanglement in quantum gases Ultracold collisions

Quantum Information, Science & TechnologyNonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

Robin Corgier, Luca Pezzè, and Augusto Smerzi

QSTAR, INO-CNR, and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy

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Issue

Vol. 103, Iss. 6 — June 2021

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Images

Figure 1
(a) Scheme of the trapped interferometer. At $t = 0$ , a $π / 2$ Bragg pulse (vertical blue $π / 2$ pulse) splits the BEC in two momentum modes. The state preparation consists of back-and-forth oscillations up to the time $t = m T$ and is optimized by a final $α$ pulse (vertical green $α$ pulse). A $π / 2$ Bragg pulse starts the interferometer sequence. To be sensitive to gravity, the trap frequency is changed from $ω_{z}$ to ${\tilde{ω}}_{z}$ . The final $π / 2$ Bragg pulse closes the interferometer and the state is further optimized by a $β$ pulse (vertical green $α$ pulse). The phase is measured by counting the number of atoms in each cloud at time $t = m T + 3 \tilde{T} / 4$ , when the two output modes are separated and the trap is turn off. (b) Main steps of the sequence shown in a Husimi $Q$ distribution on the Bloch sphere. The top row shows the initial coherent spin state at $t = 0$ and the generated spin-squeezed state at $t = m T$ . The next three rows show the state at different stages of the interferometer: after the $α$ rotation (left column), after phase accumulation (center column), and after $β$ rotation optimization (right column). Here $α_{H}$ denotes the optimal rotation of the state in the case of a linear interferometer sequence.
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Figure 2
Input state preparation. Accumulated nonlinear coefficient $τ_{1 / 2}$ (a) as a function of $ω_{z}$ and for spherical trap ( $γ = 1$ ) and (b) as a function of the trap aspect ration $γ$ , ranging from a pancake geometry ( $γ < 1$ ) to a cylindrical geometry ( $γ > 1$ ). The solid, dashed, and dot-dashed lines show $τ_{1 / 2}$ , $\tilde{τ}$ , and $τ_{opt}$ , respectively.
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Figure 3
Gain factor $G_{α, β_{opt}}$ as a function of $m$ (namely, for different spin-squeezed input states) for trap aspect ratios (a) $γ = 0.2$ (pancake shape) and (b) $γ = 1$ (spherical shape). The different lines refer to a linear interferometer (black dashed lines) and nonlinear interferometer sequence (colored lines) with $α = 0$ (red), $π / 2$ (blue), $α_{H}$ (orange), and $α_{opt}$ (green stars). The numerical results have been calculated for $m = 0, 1 / 2, 1, ...$ and curves are a guide to the eye obtained via spline interpolation. The maximum gain $G_{\max} = \max_{τ} [G_{a H}^{L} (τ)] = N^{1 / 3}$ and SQL $G = 1$ are highlighted by the horizontal dashed lines.
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Figure 4
Optimized gain factor $G_{α_{opt}, β_{opt}}$ (a) as a function of the trap aspect ratio and for a fixed trap frequency $ν_{z} = 100$ Hz and (b) as a function of the trap frequency for a spherical trap $γ = 1$ . Red and blue symbols are obtained for a nonlinear interferometer with $m = 1 / 2$ ( $τ = τ_{1 / 2}$ ) and $m = 1$ ( $τ = τ_{1}$ ), respectively. The dashed lines denote the corresponding sensitivity for a linear interferometer where $\tilde{τ} = 0$ .
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