We present investigations of the superconductor to insulator transition (SIT) of uniform a-Bi films using a technique sensitive to Cooper pair phase coherence. The films are perforated with a nanohoneycomb array of holes to form a multiply connected geometry and subjected to a perpendicular magnetic field. Film magnetoresistances on the superconducting side of the SIT oscillate with a period dictated by the superconducting flux quantum and the areal hole density. The oscillations disappear close to the SIT critical point to leave a monotonically rising magnetoresistance that persists in the insulating phase. These observations indicate that the Cooper pair phase coherence length, which is infinite in the superconducting phase, collapses to a value less than the interhole spacing at this SIT. This behavior is inconsistent with the gradual reduction of the phase coherence length expected for a bosonic, phase fluctuation driven SIT. This result starkly contrasts with previous observations of oscillations persisting in the insulating phase of other films implying that there must be at least two distinct classes of disorder tuned SITs. 1 arXiv:1301.6155v2 [cond-mat.supr-con] 4 Feb 2013Superconductor to insulator quantum phase transitions (SIT) can be induced in a wide range of quasi two-dimensional superconducting systems, including elemental films, high T c superconductors, organic superconductors and superconductor graphene composites [1][2][3][4][5][6][7][8]. Remarkably, these transitions occur, nearly universally, at a critical normal state resistance, R Nc ≃ R Q = h (2e) 2 , and film resistances often show scaling behavior around this critical point. The most prominent theories that can account for these behaviors view the SIT as a Cooper pair or boson localization transition, rather than a Cooper pair breaking transition [9][10][11][12][13][14]. Recent experiments that probe films near the SIT in new ways have provided more details that support this "bosonic" picture of the SIT [15][16][17][18][19]. For example, scanning tunneling microscopy (STM) has revealed that spatial inhomogeneities develop in the order parameter on approaching the SIT suggesting that Cooper pairs localize into islands [19,20]. High frequency transport measurements indicate that a finite superfluid density persists in non-superconducting films [21]. Here, we describe experiments employing a technique that is uniquely sensitive to the length scale that diverges at a bosonic SIT: the phase coherence length ξ φ . This technique previously revealed that Cooper pairs maintain their phase coherence over 100's of nanometers through the SITs of two distinct film systems [15,22].For this work, we investigate a third film system [23][24][25] that is likely to provide the most stringent test of whether the bosonic SIT is generic to thin films. This phase sensitive technique requires patterning films with an array of nanometer-scale holes.The hole patterning creates a simply connected geometry that leads to Little-Parks-like (LP) oscillations...