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Interferometry with Interacting Bose-Einstein Condensates in by Tarik Berrada

By Tarik Berrada

This thesis demonstrates a whole Mach–Zehnder interferometer with interacting Bose–Einstein condensates limited on an atom chip. It depends upon the coherent manipulation of atoms trapped in a magnetic double-well capability, for which the writer built a singular kind of beam splitter. Particle-wave duality permits the development of interferometers for subject waves, which counterpoint optical interferometers in precision size units, either for technological functions and basic assessments. This calls for the advance of atom-optics analogues to beam splitters, part shifters and recombiners.

Particle interactions within the Bose–Einstein condensate bring about a nonlinearity, absent in photon optics. this can be exploited to generate a non-classical nation with decreased atom-number fluctuations contained in the interferometer. This country is then used to check the interaction-induced dephasing of the quantum superposition. The ensuing coherence instances are came across to be an element of 3 longer than anticipated for coherent states, highlighting the opportunity of entanglement as a source for quantum-enhanced metrology.

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The second line describes the tunneling of one particle between the two modes, with the coupling strength: J =− 2 dr 2m ∇φ L ∇φ R + φ L V φ R . 79) J does not explicitly depend on the interaction strength g3D , but the wavefunctions φ L and φ R usually do. The minus sign is chosen such that J is positive, as will appear below. The last two lines correspond to interaction-induced transfers of particle between the two modes. In Ref. [28], the authors derived a consistent “improved” two-mode description of the BJJ where they retained all these terms, showing that they could be responsible for significant deviations from the “standard” 2MM generally used in literature.

4. 5 They correspond to a situations where all the atoms are in the ground (respectively the first excited) state. In principle, this choice is not critical as long as the interactions do not significantly modify the spatial modes. As discussed in Sect. 3, this is likely to be a good approximation in the case of elongated double-well potentials. Secondly, as time evolves, a linear superposition of ground and excited state will not remain in the subspace spanned by φg and φe . Still, it is reasonable to restrict the dynamics to the two lowest-lying states as long as no higher-energy state is accessible.

76) We assume without loss of generality that φ L and φ R are real functions. Here again, we omit the hats on the operators a L and a R . 77) Following Ref. [25], we insert Eq. 78) where E i0 is the sum of the mean kinetic and potential energy in the mode i and j I (i, j) = g3D φiL φ R dr . Note that each term of the Hamiltonian conserves the total atom number N = n L + n R . The first line corresponds to the total energy of the left 6 Note that although the modes are labeled left and right, we don’t need at this stage to assume that they are localized.

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