Decay of quantum sensitivity due to three-body loss in Bose-Einstein condensates

Dennis Rätzel and Ralf Schützhold

Phys. Rev. A 103, 063321 – Published 28 June 2021

Abstract

In view of the coherent properties of a large number of atoms, Bose-Einstein condensates (BECs) have a high potential for sensing applications. Several proposals have been put forward to use collective excitations such as phonons in BECs for quantum-enhanced sensing in quantum metrology. However, the associated highly nonclassical states tend to be very vulnerable to decoherence. In this article, we investigate the effect of decoherence due to the omnipresent process of three-body loss in BECs. We find strong restrictions for a wide range of parameters, and we discuss possibilities to limit these restrictions.

Received 29 January 2021
Accepted 8 June 2021

DOI:https://doi.org/10.1103/PhysRevA.103.063321

Physics Subject Headings (PhySH)

Bose-Einstein condensates Phonons Quantum metrology

Atomic, Molecular & Optical

Authors & Affiliations

Dennis Rätzel ^1,* and Ralf Schützhold^2,3

¹Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
²Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
³Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany

^*dennis.raetzel@physik.hu-berlin.de

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Vol. 103, Iss. 6 — June 2021

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Images

Figure 1
Sketch (not to scale) of the main idea of quantum enhanced sensing (with single-mode squeezing) in the displacement scheme and its deterioration due to decoherence. Depicted are the Wigner representations of the initial ground state (top left) and the coherent state (top right) displaced in the $X$ -direction $X \to X + δ$ due to the interaction representing the measurement. However, if this displacement $δ$ is smaller than the initial quantum uncertainty $Δ X$ (radius of the blue circles), the coherent state (full blue circle in top right diagram) cannot be distinguished unambiguously from the initial ground state, i.e., the measurement is not conclusive. To overcome this problem, one can start with an initial squeezed state (middle left) with a reduced uncertainty $Δ X$ such that the displacement $δ$ is larger than $Δ X$ (middle right). In the presence of decoherence, however, this reduced initial uncertainty $Δ X$ grows between initialization (bottom left) and final read-out (bottom right) such that the state after the interaction (full blue ellipse in bottom right diagram) can again not be distinguished unambiguously from the state without this interaction (dashed blue ellipse in bottom right diagram).
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Figure 2
Sketch (not to scale) of the main idea of quantum enhanced sensing (with single-mode squeezing) in the rotation scheme and its deterioration due to decoherence in analogy to Fig. 1. The left panels depict the Wigner representations of the initial squeezed states. Without decoherence, the rotated squeezed state (solid blue ellipse in top right panel) has little overlap with the state in the absence of rotation (dashed blue ellipse in top right panel). With decoherence, however, their overlap becomes much larger (bottom right panel), and thus it is much harder to distinguish them. In the squeezing scheme (Sec. 5c), we get a qualitatively similar picture.
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Figure 3
Total damping constant $γ_{k}^{-}$ (blue solid line) and the total noise constant $γ_{k}^{+}$ (green dashed line) are plotted as functions of $| k | L / π$ , where $L$ is the length of the elongated direction of the cuboid BEC, based on the parameters mentioned in the text. For low momenta, the $k$ -independent $γ_{3 b}$ due to three-body loss dominates. For higher quasiparticle momenta, Beliaev damping starts to dominate due to its proportionality to ${| k |}^{5}$ . In the presented regime of very low temperatures, Landau damping is completely suppressed. The difference between $γ_{k}^{-}$ and $γ_{k}^{+}$ is strongly pronounced for small momenta where $| α_{k} |$ becomes large.
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