Anomalous loss behavior in a single-component Fermi gas close to a $p$-wave Feshbach resonance

We theoretically investigate three-body losses in a single-component Fermi gas near a $p$-wave Feshbach resonance in the interacting, nonunitary regime. We extend the cascade model introduced by Waseem et al. [M. Waseem, J. Yoshida, T. Saito, and T. Mukaiyama, Phys. Rev. A 99, 052704 (2019)] to describe the elastic and inelastic collision processes. We find that the loss behavior exhibits a $n^3$ and an anomalous $n^2$ density dependence for a ratio of elastic-to-inelastic collision rate larger and smaller than 1, respectively. The corresponding evolutions of the energy distribution show collisional cooling or evolution toward low-energetic nonthermalized steady states, respectively. These findings are particularly relevant for understanding atom loss and the energetic evolution of ultracold gases of fermionic lithium atoms in their ground state.

Figure 1

Schematic depiction of the $p$-wave scattering process for two-channel scattering. The figure shows the potential of the incoming scattering atoms at energy $E$ and the closed channel with a resonant dimer state at energy $E_{\text{r}}$. Incoming atoms can tunnel through the centrifugal barrier and create weakly bound dimers at a rate $L_{\text{M}}n$, with $n$ the density of the atoms. Weakly bound dimers can, in return, decay into two free atoms with rate ${\mathrm{\Gamma }}_{\text{r}}\left(E\right)$. This elastic scattering process leads to energy redistribution, i.e., thermalization. When weakly bound dimers collide with a free atom, they collapse into a deeply bound dimer at a rate ${\mathrm{\Lambda }}_{\text{ad}}n$. This inelastic process leads to a loss since the binding energy converted to kinetic energy is large compared to the trap depth of the atomic trap.

Figure 2

(a) The temperature $T$ in units of the initial temperature $T_{\text{0}}=T(t=0)$ and (b) the phase-space density $\rho$ in units of ${\rho }_{\text{0}}=\rho (t=0)$ as a function of time t and the truncation parameter $E_{\text{r}}/\left(k_{\text{B}}{T}_{\text{0}}\right)$. The temperature decreases for ${\eta }_{\text{0}}>3/2$ and the phase-space density increases for ${\eta }_{\text{0}}>9/2$.

Figure 3

The kinetic energy distribution $f\left(E_v\right)$ of a gas in the nonthermalized regime in units of $E_{\text{r}}^{-1}$ for a truncation parameter ${\eta }_{\text{0}}=4$ after a hold time $t$ in units of the loss timescale ${\tau }_{\text{2}}$ in a box potential. Initially, $f$ is a normalized Maxwell-Boltzmann distribution of temperature $E_{\text{r}}/\left(4k_{\text{B}}\right)$ and the three-body losses lead to a decrease and reshaping of the kinetic energy distribution. After the axis break, at $t=10{\tau }_{\text{2}}$, the distribution does not have an exponential tail of energies $E_v>E_{\text{r}}/2$ anymore. The inset shows the density in units of the initial density changing due to a decrease of the kinetic energy distribution (solid line) and the projected $n^2$-dependent loss for a gas of constant kinetic energy distribution (dashed line).

Figure 4

The three-body loss coefficient $L_{\text{3}}$ close to the $p$-wave Feshbach resonance at $B_{\text{0}}=159.17\left(5\right)\mathrm{G}$ from the publication [19] for three different sets of temperatures of $2.7\mu \mathrm{K}$, $3.9\mu \mathrm{K}$, and $5.7\mu \mathrm{K}$ shown as squares, circles, and triangles, respectively. The arrows mark the points where $E_{\text{r}}/\left(k_{\text{B}}{T}_{\text{0}}\right)=10$, separating the interacting and noninteracting regime. The solid curves, describing the crossover between the two regimes, are a fit of Eq. (A2) to the data of the three temperatures with a fit result for the vibrational quenching rate coefficient of ${\mathrm{\Lambda }}_{\text{ad}}=3.6\left(6\right)\times {10}^{-14}{\mathrm{m}}^3{\mathrm{s}}^{-1}$. The dashed curves show the loss coefficient of only the cascade model with the fit result ${\mathrm{\Lambda }}_{\text{ad}}$ included in Eq. (A1).

Figure 5

The cascade process rates of Eqs. (1) and (2) as a function of the magnetic field detuning $B-B_{\text{0}}$. The three colors correspond to the rates for the densities and temperatures of the loss measurements depicted with the same colors in Fig. 4. The magnetic field detuning spans the range corresponding to $E_{\text{r}}/\left(k_{\text{B}}{T}_{\text{0}}\right)$ ranging from 3/2 to 10, which is the interacting, nonunitary regime as defined in Sec. 2. The dimer breakup rate ${\mathrm{\Gamma }}_{\text{r}}$ (solid line) has a ${(B-B_{\text{0}})}^{3/2}$ dependence, the inelastic loss rate ${\mathrm{\Lambda }}_{\text{ad}}{n}_{\text{0}}$ (dotted lines) is constant with $n_{\text{0}}$ the initial density of the three scenarios, the dimer creation rate is $L_{\text{M}}{n}_{\text{0}}$ (dash-dotted lines), and the loss rate of observer atoms is ${\mathrm{\Lambda }}_{\mathrm{ad}}{n}_{\mathrm{D},0}$ (dashed lines) with $n_{\text{D,0}}$ the initial dimer density.