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We propose a scheme to obtain the Heisenberg-limited parameter estimationprecision by immersing atoms in a thermally equilibrated quasi-one-dimensionaldipolar Bose-Einstein condensate reservoir. We show that the collisions betweenthe dipolar atoms and the immersed atoms can result in a controllable nonlinearinteraction through tuning the relative strength and the sign of the dipolarand contact interaction. We find that the repulsive dipolar interactionreservoir is preferential for the spin squeezing and the appearance of anentangled non-Gaussian state. As a useful resource for quantum metrology, wealso show that the non-Gaussian state results in the phase estimation precisionin the Heisenberg scaling, outperforming that of the spin-squeezed state.

Near-Heisenberg-limited parameter estimation precision by a dipolar-Bose-gas reservoir engineering