The fact that the divergence is diffraction-limited means that the lens does not cause aberrations, so that the product of the beam width and beam divergence is as small as possible. This can be true regardless of how big the beam divergence is, and instead has to do with the beam quality. A diffraction-limited beam (e.g., a Gaussian) is one for which this product is equal to the smallest value allowed by the uncertainty principle.

What is beamdivergence

As others have mentioned, even if that source existed, you would then be defeated by wave optics which would disallow a perfectly collimated beam anyway.

Lens centering error: 3~5'. Waveband: 400-1100nm. Surface finish: Grade 3-4.

Divergence angleof beam

EDIT: It's actually more simple than that. I originally used the wrong definition of what a perfectly collimated beam would be. If you wanted a completely collimated beam (all rays traveling parallel to the optical axis), that would mean your marginal and chief ray angles would be zero, which would make the value of your Lagrange invariant zero, which means you'd have zero light.

Perfect collimation would require that the chief ray angle be zero and the marginal ray height be nonzero angle be zero. If your chief ray angle is zero, that means your beam came from a source of zero size.

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Lowdivergencelaser

For cases where the paraxial approximation applies the minimum beam waist is $2 w_0=\frac{4 \lambda f}{\pi d}$ for focal length $f$ and collimating lens diameter $d$. http://www.ophiropt.com/laser-measurement-instruments/beam-profilers/knowledge-center/tutorial/what-is-m2

Practically speaking, however, you can generally pick beam diameters sufficiently large to produce "zero" divergence as far as your application is concerned.

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Gaussian beamdivergence

Laser beamdivergenceand spot size

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Gaussian beamdivergencecalculator

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From radiometry we know that would require a source of infinite radiant exitance. Outside that exception, there would be no energy in the perfectly collimated beam.

Divergence anglecalculator

In most lenses, spherical aberration is considered an undesirable technical flaw. However, in the past, controlled spherical aberration was intentionally used ...

Divergence $\theta=0$ is not possible -- from a quantum mechanical perspective, it would violate the Heisenberg uncertainty principle for position and momentum of a photon. "Collimated" is not really a technical term; it is a qualitative description of a beam with a relatively small divergence angle.

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"A thin lens of focal length f is used to collimate the light emerging from an optical fibre. The fibre has small core diameter and numerical aperture NA. It achieves a diffraction limited divergence angle θ for the collimated beam."

Divergence angleformula

I am wondering how can there be a "diffraction limited divergence angle θ"? If the lens is placed at exactly focal length f away from the end of the optical fibre, shouldn't all the light be properly collimated with θ=0?

Also, a diffraction limited divergence is in contrast to a worse performing beam. If you have a non-Gaussian beam (i.e. M^2 > 1) the beam will diverge more.

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