Thank you for the edit! I'm going to rephrase to check that I've understood the question correctly.
The question is about whether there are any minimal pairs between the phoneme /u(ː)/ (as in "goose") and the phoneme /ʊ/ (as in "foot") in unstressed syllables. I don't know of a strict minimal pair.
The contrast between these vowels is definitely neutralized in the following context:
- the syllable is fully unstressed (i.e. it occurs in a rhythmic context where a reduced vowel such as /ə/ could occur)
- the vowel is word-final or before another vowel (or in other words, the vowel is not followed by a consonant)
In these contexts, most speakers use a quality closer to the sound of /uː/, but in some forms of English (including some forms of "RP"), the quality can be more similar to /ʊ/. Hence the varying transcription of words like "graduate" etc. with /uː/ or /ʊ/.
Sometimes words like "graduate" are transcribed with a third symbol, /u/. The use of /u/ in English phonemic transcriptions is somewhat problematic and an abuse of notation, as this unstressed vowel is not a third phoneme in contrast with /ʊ/ and /uː/; rather, it may be intended as a simple notational shorthand for 'either the phoneme /ʊ/ or the phoneme /uː/' (which we could call a "diaphonemic" transcription), or possibly as a sign indicating a neutralization of these two phonemes (which we could call an "archiphonemic" transcription).
- In this context, there is never a contrast between /ʊ/ and /uː/ independent of the contrast of rhythm/stress/reduction.
- It should not be possible for the symbols /u/ and /ʊ/ to contrast in transcriptions like this (since the transcription /u/ implicitly includes /ʊ/ as a possible realization).
- Another tricky point is that the use of the symbol "/u/" in this context should not be understood as a phonetic transcription: it doesn't mean that the vowel is necessarily [u], or a phonetically shorter version of the /uː/ sound (the phonetic length of high vowels in English is complicated, non-binary and non-phonemic, see discussion in the next section below).
A blog post by Jack Windsor Lewis, HappYland Revisited etc (2007, January 3) discusses some of these points.
In unstressed syllables before a consonant, or in contexts such as compound words where vowel reduction doesn't always apply, the situation is a little less clear. A reduced value might appear in "speculate"; alternatively, the second syllable might just have a schwa sound. Windsor Lewis mentions "bedroom, costume, granule, vacuum, volume" as words that could potentially undergo 'weakening' to "/-u-/". I'm not sure whether we can say that the contrast is fully neutralized, but I don't think I would find it very noticeable whether a speaker used /uː/ or /ʊ/ in the unstressed syllable of one of the listed words.
However, if we take a compound like "handbook", it would sound odd to my ears if someone used /uː/ in the second syllable.
A side discussion on vowel length and the use of length marks in English phonetic and phonemic transcriptions
I was a bit confused by the use of [uː] and [u] in the initial question; part of the reason why is because it isn't necessarily clear what these mean in the context of English ([sut] with no length marker would be possible as a (broad) phonetic transcription of "suit").
The phoneme often transcribed /uː/ is not always phonetically long in duration, and its length doesn't depend only on the degree of stress. In the context of the word 'suit', /uː/ would probably be relatively short phonetically (for me, roughly [ʉ]) because of the influence of the following voiceless consonant /t/. In the word "food", where it is followed by a voiced consonant phoneme, the vowel /uː/ would be phonetically longer, but would remain the same phoneme. See The Undesirability of length marks in EFL phonemic transcription (1975) (Jack Windsor Lewis).
