By Tarik Berrada

This thesis demonstrates a whole Mach–Zehnder interferometer with interacting Bose–Einstein condensates constrained on an atom chip. It is determined by the coherent manipulation of atoms trapped in a magnetic double-well strength, for which the writer built a unique form 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 exams. This calls for the improvement of atom-optics analogues to beam splitters, part shifters and recombiners.

Particle interactions within the Bose–Einstein condensate result in a nonlinearity, absent in photon optics. this is often exploited to generate a non-classical nation with decreased atom-number fluctuations contained in the interferometer. This nation is then used to check the interaction-induced dephasing of the quantum superposition. The ensuing coherence occasions are chanced on 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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**Extra resources for Interferometry with Interacting Bose-Einstein Condensates in a Double-Well Potential**

**Example text**

N −→ n=−N /2 N /2 . . φ p −→ p=−N /2 ∞ −∞ dn . . |n , N +1 2π ∞ −∞ dφ . . φ p . 97). Similarly, the quadrature operators are defined by 1 iφ e + e−iφ , 2 1 iφ sin φ = e − e−iφ . 2 Bose-Einstein Condensate in a Double Well: Two-Mode Theory … 29 ˆ n], the commutation relation [φ, ˆ let us introduce the phenomenological uncertainty relation between relative phase and half-number difference9 1 nˆ φˆ ≥ . 106) In Sect. 4, we will show that a N-particle two-mode system can be described by an effective spin verifying angular momentum commutation relations.

106). 106) implies that the number difference and the relative phase of the BJJ cannot be measured simultaneously with arbitrary accuracy. 104). In the Fock basis, the matrix elements of the tunneling operator read (see Eq. 108) while that of the cosine operator read m| cos φ |n = We see that for n, m 9 Note 1 δm,n+1 + δm,n−1 . 109) N/2, one can identify both operators: that in the following, unless stated, its standard deviation. F 2 represents the variance of the quantity F, and F 30 1 Introduction and Theoretical Background m| a L† a R + a †R a L |n ≈ N m| cos φ |n .

2 Bose-Einstein Condensate in a Double Well: Two-Mode Theory … 29 ˆ n], the commutation relation [φ, ˆ let us introduce the phenomenological uncertainty relation between relative phase and half-number difference9 1 nˆ φˆ ≥ . 106) In Sect. 4, we will show that a N-particle two-mode system can be described by an effective spin verifying angular momentum commutation relations. 106) when the number and phase spread are small enough. In Sect. 5, we will present a mean-field model valid in the “continous limit” N → ∞ and show that the halfnumber difference and the phase are canonical conjugate variables linked by n = −i ∂ .