Efimov effect in non-integer dimensions induced by an external field

The Efimov effect can be induced by means of an external deformed one-body field that effectively reduces the allowed spatial dimensions to less than three. To understand this new mechanism, conceptually and practically, we employ a formulation using non-integer dimension, which is equivalent to the strength of an external oscillator field. The effect most clearly appears when the crucial two-body systems are unbound in three, but bound in two, dimensions. We discuss energy variation, conditions for occurrence, and number of Efimov states, as functions of the dimension. We use practical examples from cold atom physics of $^{133}$Cs-$^{133}$Cs-$^{133}$Cs, $^{87}$Rb-$^{87}$Rb-$^{87}$Rb, $^{133}$Cs-$^{133}$Cs-$^{6}$Li, and $^{87}$Rb-$^{87}$Rb-$^{39}$K. Laboratory tests of the effect can be performed with two independent parameters, i.e. the external one-body field and the Feshbach two-body tuning. The scaling and (dis)appearance of these Efimov states occur precisely as already found in three dimensions.