Zero-temperature thermodynamics of asymmetric Fermi gases at unitarity

The equation of state of a dilute two-component asymmetric Fermi gas at unitarity is subject to strong constraints, which affect the spatial density profiles in atomic traps. These constraints require the existence of at least one nontrivial partially polarized (asymmetric) phase. We determine the relation between the structure of the spatial density profiles and the $T=0$ equation of state, based on the most accurate theoretical predictions available. We also show how the equation of state can be determined from experimental observations.

Figure 1

(Color online) Grand-canonical phase diagram of a two-component Fermi gas at unitarity and $T=0$. Various phases are separated by phase transitions along the straight lines extending from the origin with constant slopes $y_x$. The dotted line follows the sequence of phases in a sample trap.

Figure 2

(Color online) Example of a function $h\left(y\right)$ and the corresponding function $g\left(x\right)$ shown as thick lines. Maxwell’s construction for phase coexistence leads to a linear $g\left(x\right)$ for $x∊(0.5,1.0)$, interpolating between the two pure phases shown with lighter lines. This corresponds to the kink and/or first-order phase transition at $y=y_1$ in $h\left(y\right)$. Various other sample functions are lightly sketched within the allowed (dotted) triangular region.

Figure 3

(Color online) Measured transition radii from Ref. 3. The upper plot shows the normalized data (crosses) on top of data generated from several randomly generated functions $h\left(y\right)$. The lower plot shows the parameter $\gamma$ defined in Eq. (14).