mass and particle number [@Dalfovo1999; @Leggett2001]. This has allowed a series of innovative experiments to probe the emergence of quantum fluctuations by approaching the high-density regime from the dilute limit [@Shin2008; @Lopes2017; @Navon2010; @Navon2011; @Papp2008A; @Armijo2012; @Altmeyer2007; @Pollack2009; @Chang2016]. More recently, experimental groups were able to create dilute, self-bound droplets with liquid properties using dipolar [@Schmitt2016; @Chomaz2016] and two-component condensates [@Cabrera2017; @Semeghini2017]. Remarkably, these are stabilized against collapse by quantum fluctuations thanks to an almost complete cancellation of the various mean-field contributions [@Petrov2015; @Wachtler2016; @Lima2011; @Bisset2016; @Saito2016].

Quantum fluctuations can also be important for the regime of very small particle number $N$, typically when $N\sim10$. Several groups have proposed using ultra-dilute quantum gases to investigate these in different ways, including: vortex nucleation in slowly rotating traps [@Parke2008; @Dagnino2009]; the transition between Rabi-oscillation and self-trapped regimes in double well potentials [@JuliaDiaz2010]; the generation of macroscopic state superpositions in rotating ring superlattices [@Nunnenkamp2008]; as well as few-boson systems in one dimension [@Garcia2014; @Garcia2014A]. Furthermore, the enhancement of quantum fluctuations near the superfluid to Mott-insulator phase transition occurs for small atom number per lattice site [@Greiner2002; @Jaksch1998].

In this paper, we propose an alternative regime for enhancing quantum fluctuations that does not require 