Abstract
Active interferometers are designed to enhance phase sensitivity beyond the standard quantum limit by generating entanglement inside the interferometer. An atomic version of such a device can be constructed by means of a spinor Bose–Einstein condensate with an F = 1 groundstate manifold in which spin-changing collisions (SCCs) create entangled pairs of m = ±1 atoms. We use Bethe Ansatz techniques to find exact eigenstates and eigenvalues of the Hamiltonian that models such SCCs. Using these results, we express the interferometer’s phase sensitivity, Fisher information, and Hellinger distance in terms of the Bethe rapidities. By evaluating these expressions we study scaling properties and the interferometer’s performance under the full Hamiltonian that models the SCCs, i.e., without the idealising approximations of earlier works that force the model into the framework of SU(1,1) interferometry.
Highlights
Atom interferometry uses the wave character of atoms, and in particular the superposition principle, to detect phase differences and perform high-precision measurements in a variety of fields, ranging from measurements of the fine structure constant to gravimetry and atomic clocks [1]
The Hamiltonian (4) satisfies the conditions of a Richardson–Gaudin model [20,21,22] and its exact eigenstates and eigenvalues can be determined by techniques that fall into the broader class of the algebraic Bethe Ansatz
We have theoretically analysed the performance of an active atomic interferometer based on spin-changing collisions (SCCs) in a three-species Bose–Einstein condensate by making use of Bethe Ansatz techniques
Summary
Atom interferometry uses the wave character of atoms, and in particular the superposition principle, to detect phase differences and perform high-precision measurements in a variety of fields, ranging from measurements of the fine structure constant to gravimetry and atomic clocks [1]. The Heisenberg limit Δφ 1/N, which is a fundamental constraint resulting from Heisenberg’s uncertainty principle, may be approached [3] Another strategy to surpass the standard quantum limit goes back to Yurke, McCall, and Klauder [4], and consists of exchanging passive beam splitters by active components. In the present paper we show that an analytic treatment of the full Hamiltonian (2) is possible without any additional assumptions by exploiting Bethe-Ansatz integrability We use this method to compute exact eigenstates and eigenvalues of the spin-changing Hamiltonian (2), and for semi-analytic calculations of phase sensitivities and other quantities of interest for several variants of active atom interferometers. By analysing the scaling properties of phase sensitivities we are able to identify parameter regimes in which the standard quantum limit can be surpassed
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