Angular momentum in quantum physics: theory and application by L. C. Biedenharn

By L. C. Biedenharn

This article develops the speculation of angular momentum from the perspective of a primary symmetry in nature and exhibits how this idea pertains to utilized components of study in smooth quantum physics.

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A. Regal -9 10 -10 σ (cm2 ) 10 -11 10 -12 10 -13 10 160 180 200 220 240 260 B (gauss) Fig. 19. 4 μK [95]. Between the peak and dip in σ, the interaction is attractive; everywhere else it is repulsive. ) The exponential time constant for energy transfer between the two radial directions, τ , was measured as a function of magnetic field. τ is related to the s-wave collision cross-section through 1/τ = 2 n σv/α. v = 4 kB T /πm is the mean relative speed between colliding fermions and n = N1tot n7 (r) n9 (r) d3 r is the densityweighted density.

3 GHz +7/2 -9/2 -7/2 -5/2 +9/2=mf f=9/2 Fig. 8. – 40 K ground state level diagram, with exaggerated Zeeman splittings. The two levels represent the hyperfine structure, which originates from the coupling of the nuclear spin (I = 4) with the electron spin (S = 1/2). Note that the hyperfine structure of 40 K is inverted. Since evaporative cooling requires collisions to rethermalize the gas, a mixture of two distinguishable particles is required to cool fermions. 40 K provides an elegant solution to this problem.

4 2. Molecule binding energy. – While suggestive of molecule creation, the measured atom loss was not conclusive proof for the existence of Feshbach molecules. We therefore developed a spectroscopic technique to probe the molecules. First, we created the molecules with a magnetic-field ramp across the Feshbach resonance that stopped at a magnetic field Bhold . f. f. frequency was chosen so that the photon energy was near the energy splitting between the mf = −5/2 and mf = −7/2 atom states. The resulting population in the mf = −7/2 state, which was initially unoccupied, was then probed selectively either by separating the spin states spatially using a strong magnetic-field gradient during free expansion (SternGerlach imaging) or by leaving the magnetic field high (215 G) and taking advantage of non-linear Zeeman shifts.

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