By Christian Groß
Interferometry, the main unique size approach identified this present day, exploits the wave-like nature of the atoms or photons within the interferometer. As anticipated from the legislation of quantum mechanics, the granular, particle-like beneficial properties of the separately self sustaining atoms or photons are answerable for the precision restrict, the shot noise restrict. even if this “classical” sure isn't really primary and it's the objective of quantum metrology to beat it via making use of entanglement one of the debris. This paintings studies at the consciousness of spin-squeezed states compatible for atom interferometry. Spin squeezing was once generated at the foundation of motional and spin levels of freedom, wherein the latter allowed the implementation of an entire interferometer with quantum-enhanced precision.
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Extra info for Spin Squeezing and Non-linear Atom Interferometry with Bose-Einstein Condensates
The theoretical description of weakly interacting dilute Bose gases was introduced 1947 by Bogoliubov. The key idea is to replace the annihilation (and creation) operators aˆ 0 √ for the macroscopically occupied ground state by a complex number aˆ 0 → n 0 eiϕ0 . 1 2 2π is Planck’s constant and m the atomic mass. The exact value depends on the density of states. 3) 2 Here g = 4πm a is the coupling constant proportional to the s-wave scattering length a. 3) describes a weakly interaction Bose–Einstein condensate in the mean field limit.
5 kHz (illustrated by the shading). For greater barriers the local Josephson energies are comparable to the Charging energies and the system is close to the Fock regime (see Fig. 12 shows the eigenmodes in the lowest band of our few-well trap for 5,300 atoms. The calculation was done in harmonic—phonon—approximation (m) treating the system as coupled oscillators with different masses (E C ) and spring constants (E J (m) ). Exact numerical diagonalization following reference  reveals the eigenmodes.
In Fig. 2 the two approaches to calculate the Josephson energy E J are compared. In a harmonic trap the fastest possible tunneling time is bounded by the inverse trap frequency ωz−1 since the trap frequency sets the minimal time for the atoms to move from one side of the trap to the other. 2b shows that the “capacitor” method to calculate E J gives correct results in the regime V0 < μ since the tunnel frequency ω pl approaches the trap frequency ωz in the limit of vanishing barrier height (see Sect.
Spin Squeezing and Non-linear Atom Interferometry with Bose-Einstein Condensates by Christian Groß