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Red detuned capillary guiding involves coupling a Gaussian beam into the fibre core which excites Hermitian (HE) modes suitable for atom guidance. The coupling angle and mode matching quality play a strong role in determining the quality of mode generated within the fibre. Typically ~30-50% of the guide laser power is lost due to mode mismatch, this scattering obstructs atom entry and diminishes effective guiding length. This must be anticipated and compensated for prior to flux guidance calculations. The scatter, can only be minimised by better mode matching.

Atoms travelling in the fibre guide do so in a manner similar to light propagating in a multimode fibre, that is, motion along the fibre axis is unconstrained whereas grazing incidence modes provide a series of coherent reflections in the transverse axis defined by the dipole-potential well generated. As expected, a stronger guide dipole potential can confine greater transverse atomic momenta.

The primary drawback of red-detuned capillary guides, is a rapid attenuation of the guide intensity in the core, particularly in narrow core fibres. The following approximation describes this attenuation, it is a critical, and stifling, transmission characteristic of hollow-core fibres:

2 3 4 . 2 1 λ a l e ≈ 1.26

where the hollow-core radius is a, the guide wavelength is λ, and l1/e is the length at which guide light falls to 1/e of its input intensity.

Elaboration on this and a review of experimental work on red-detuned fibre guides is discussed in chapter 3. Further experimental concerns regarding atom heating during transit are also discussed in context there. Since evanescent fibre guiding was not performed in St Andrews and in the interest of brevity, blue detuned capillary guiding is not discussed here, however thorough descriptions can be found in the works of Ito61,69 and Muller & Cornell75_.

However, scatter further along the fibre is less easy to minimise; imperfections can siphon off annulus coupled light anywhere along the fibre length. Thus the best method of reduction employs the hitherto negative attribute of fibre attenuation. The severe attenuation of grazing incidence modes associated with narrow diameter HC’s rapidly eliminates extraneous modes. Both modes induced via facet or imperfection scatter can be strongly suppressed by the HC’s inherent attenuation rate.

Another difference between red and blue capillary guides is highlighted by Muller & Cornell et al. They state that, with dipole potential optimised, guiding efficiency is not actually a maximum when coupling efficiency is greatest. Instead guiding is enhanced when the speckle pattern in the evanescent field is engineered to

minimise the number of “unprotected” regions on the annulus surface. That is, the speckle pattern which occurs due to interference between multiple laser modes within the annular core (AC) which sporadically stifles the evanescent field along the fibre walls, should be minimised such that no gaps appear in the evanescent field. This represents a fundamental impediment to blue-detuned fibre guides.

Coherent Guidance

The applicability of blue-detuned capillary guidance to coherent atom transport comes from the practical possibility of very narrow diameter guide paths. The chief impediment to red detuned coherent transport was field attenuation, blue detuned guidance does not suffer from this problem. However the requisite narrowing of the HC and the dependence on evanescent leakage for an atomic grazing incidence path brings attractive VDW forces much closer to the atom flux. This risks a higher loss rate, particularly in fibres with multiple modes in the annular core. Nevertheless, intuitively, if a guide laser can be tuned far enough from resonance to reduce spontaneous emission, if sufficient intensity can be coupled into a fibre annulus to maintain a high level of evanescent repulsive dipole potential, and if speckle can be removed, then blue detuned guidance will, in principle, be the most efficient form of capillary guidance.

However it must be stated that, to the authors knowledge, blue detuned capillary guidance of atoms, has not yet been demonstrated within single-optical mode HC fibres; despite the reductions in both speckle and requisite laser power, the narrow annulus core, typically only a few guide wavelengths in diameter, inflicts optical mode coupling difficulties and subsequent optical blockage of the flux path into the HC. That is, light coupled from the front or rear of the fibre presents excessive scatter76 _{or rapidly} converging annuli modes which seal within a few tens of microns77,78_{, both of which} serve to obstruct atom entry to the HC.

Figure 1.19 shows the intensity profile of an LP01 mode on exit from a capillary annulus capable of supporting only the lowest order mode; the mode on exit from the fibre (important for establishing correct guide launch profile) can be seen to have completely filled, by diffraction, within 100μm’s from the fibre facet. Following the recent work of M.Hautakorpi, et al.79 _{future work in this field is likely to involve}

launching LPm,p modes of order m≠0, where the mode output yields a hollow beam

more suitable for flux loading.

Figure 1.19 : The spatial profile of light output from a capillary fibre capable of supporting only a single optical mode in its annular core. Data given at a) the fibre exit facet and b) 100μm from the fibre facet. Fibre dimensions are 6μm hollow-core diameter, 3μm annular thickness and 50mm length. Diagram reproduced from Dall et al.