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Register a new userA nonlinear Ramsey interferometer operating beyond the Heisenberg limit
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We show that a dynamically evolving two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling maps exactly onto a nonlinear Ramsey interferometer that includes a nonlinear medium. Assuming a realistic quantum state for the TBEC, namely the SU(2) coherent spin state, we find that the measurement uncertainty of the ``path-difference phase shift scales as the standard quantum limit (1/N^{1/2}) where N is the number of atoms, while that for the interatomic scattering strength scales as 1/N^{7/5}, overcoming the Heisenberg limit of 1/N.
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We propose a feasible scheme to realize nonlinear Ramsey interferometry with a two-component Bose-Einstein condensate, where the nonlinearity arises from the interaction between coherent atoms. In our scheme, two Rosen-Zener pulses are separated by an intermediate holding period of variable duration and through varying the holding period we have observed nice Ramsey interference patterns in time domain. In contrast to the standard Ramsey fringes our nonlinear Ramsey patterns display diversiform structures ascribed to the interplay of the nonlinearity and asymmetry. In particular, we find that the frequency of the nonlinear Ramsey fringes exactly reflects the strength of nonlinearity as well as the asymmetry of system. Our finding suggests a potential application of the nonlinear Ramsey interferometry in calibrating the atomic parameters such as scattering length and energy spectrum.
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