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Bulletin of the Russian Academy of Sciences Physics

Multiparameter Quantum Metrology with Bright Solitons

A. P. Alodjants, Dmitriy V. Tsarev, S. G. Osipov, Mikhail S. Podoshvedov, S. P. Kulik

Published Jun 1, 2024• 0 citations
Publisher

Abstract

Abstract A quantum metrology problem of simultaneous measurement and estimation of several phase parameters was considered in the framework of current tendencies of development of alternative navigation. The fundamental limits of both linear and nonlinear metrology were studied. The effect of losses on the accuracy of quantum metrology of several phase parameters was analyzed. A method to prepare three-mode N00N- states using atomic bright solitons was proposed.

DOI
10.1134/s1062873824706676

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Abstract A quantum metrology problem of simultaneous measurement and estimation of several phase parameters was considered in the framework of current tendencies of development of alternative navigation. The fundamental limits of both linear and nonlinear metrology were studied. The effect of losses on the accuracy of quantum metrology of several phase parameters was analyzed. A method to prepare three-mode N00N- states using atomic bright solitons was proposed.
We consider a multiparameter quantum metrology problem with bright soliton networks in the presence of weak losses. We introduce the general Heisenberg limit (GHL) ${\ensuremath{\sigma}}_{\mathbit{\ensuremath{\chi}}}=1/{N}^{k}$ that characterizes fundamental limitations for unknown parameter measurement and estimation accuracy ${\ensuremath{\sigma}}_{\mathbit{\ensuremath{\chi}}}$ within linear (k=1k=1k=1) and nonlinear (k=3k=3k=3) quantum metrology approaches to solitons. We examine multipartite NOON states specially prepared for the improvement of multiparameter estimation protocols. As a particular example of producing such states, we propose a three-mode soliton Josephson-junction (TMSJJ) model as a three-mode extension for the soliton Josephson-junction bosonic model, which we previously proposed. The energy spectrum of the TMSJJ exhibits sharp phase transition peculiarities for the TMSJJ ground state. The transition occurs from a Gaussian-like (coherent) state to the superposition of entangled Fock states, which rapidly approach the three-mode NOON state. We show that in the presence of weak losses the TMSJJ enables saturation scaling relevant to the optimal state limit close to the GHL. Our findings open prospects for quantum network sensorics with atomtronic circuits.
The estimation of some parameters with super-Heisenberg (SH) sensitivity, i.e. beyond Heisenberg limit, is one of the principal problems for current quantum metrology. We propose to use Bose–Einstein condensate quantum bright solitons for this purpose. We have shown that solitons, as quantum nonlinear structured field objects, allow SH phase estimation even with coherent probes in the framework of a nonlinear metrology approach. To achieve ultimate scaling in nonlinear phase estimation, which is 1/ N 3 , we examine soliton phase shift occurring due to interaction of weakly coupled 1D solitons. We have shown that steady states of coupled solitons can be used for the formation of maximally path-entangled N 00 N -state providing minimal propagation error of solitons’ relative distance, momentum, and atom–atom scattering length parameter.
By considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition states and maximally path entangled N00N-states. We examine Mach- Zehnder interferometer in the context of parity measurements, in order to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio between two-body scattering length and intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of a single measurement optimally extracting information from the probe state on all the parameters, and (iii) statistical independence of the estimated parameters. We consider the situation when these concerns present no obstacle, and for every estimated parameter the variance obtained in the multiparameter scheme is equal to that of an optimal scheme for that parameter alone, assuming all other parameters are perfectly known. We call such models compatible. In establishing a rigorous theoretical framework for investigating compatibility, we clarify some ambiguities and inconsistencies present in the literature and discuss several examples to highlight interesting features of unitary and nonunitary parameter estimation, as well as deriving new bounds for physical problems of interest, such as the simultaneous estimation of phase and local dephasing.