Multiparameter quantum metrology with bright solitons

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Abstract

We consider the problem of quantum metrology with simultaneous measurement of several phase parameters in the framework of current tendencies of development of alternative navigation. The fundamental limits of linear and nonlinear metrology are studied. The effect of losses on the accuracy of quantum metrology for several parameters is revealed. A realistic scenario for preparing three-mode NooN states using atomic bright solitons is proposed.

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About the authors

A. P. Alodjants

ITMO National Research University; Southern Ural State University

Author for correspondence.
Email: alexander_ap@list.ru
Russian Federation, Saint Petersburg; Chelyabinsk

D. V. Tsarev

ITMO National Research University; Southern Ural State University

Email: alexander_ap@list.ru
Russian Federation, Saint Petersburg; Chelyabinsk

S. V. Osipov

Cherepovets State University

Email: alexander_ap@list.ru
Russian Federation, Cherepovets

M. S. Podoshvedov

Southern Ural State University; Kazan National Research Technical University

Email: alexander_ap@list.ru
Russian Federation, Chelyabinsk; Kazan

S. P. Kulik

Southern Ural State University; Lomonosov Moscow State University

Email: alexander_ap@list.ru
Russian Federation, Chelyabinsk; Moscow

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Supplementary files

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2. Fig. 1. Scheme of multiparameter quantum metrology with solitons. |ψin> is a trial multiparticle state of quantum solitons, which evolves with the accumulation of phases φj containing information about the measured parameters χj (j = 1, ..., d). The operator denotes the linear transformations that allow the construction of a procedure for measuring and estimating the unknown parameters. Details are given in the text

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3. Fig. 2. TMSDK ground state distributions at (a) Λ = 0; (b) Λ = Λcr = 3.34087496; (c) Λ = 3.345. N = 40

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4. Fig. 3. Dependence of the ultimate measurement error σ(1) on the control parameter Λ in the vicinity of the critical point Λ = Λcr for linear quantum metrology using solitons. The particle loss is characterised by the deviation of the FDP transparency coefficient η from unity. The number of particles is N = 40. The limit linear quantum metrology is characterised by the SCP and CIP, which are indicated by the dashed lines. The black dotted line denotes the accuracy of linear metrology achieved using optimal states, while the thin solid black line corresponds to the PG σPG = 1 / N

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