Fermionic Suppression of Dipolar Relaxation

We observe the suppression of inelastic dipolar scattering in ultracold Fermi gases of the highly magnetic atom dysprosium: the more energy that is released, the less frequently these exothermic reactions take place, and only quantum spin statistics can explain this counterintuitive effect. Inelastic dipolar scattering in nonzero magnetic fields leads to heating or to loss of the trapped population, both detrimental to experiments intended to study quantum many-body physics with strongly dipolar gases. Fermi statistics, however, is predicted to lead to a kinematic suppression of these harmful reactions. Indeed, we observe a 120-fold suppression of dipolar relaxation in fermionic versus bosonic Dy, as expected from theory describing universal inelastic dipolar scattering, though never before experimentally confirmed. Similarly, low inelastic cross sections are observed in spin mixtures, also with striking correspondence to predictions. The suppression of relaxation opens the possibility of employing fermionic dipolar species in studies of quantum many-body physics involving, e.g., synthetic gauge fields and pairing.

Figure 1

(a)–(c) Single-spin-flip dipolar relaxation of spin-polarized states into spin mixtures. Arrow points from the incoming to the outgoing spin population. (d) and (e) Single-spin-flip dipolar relaxation of spin mixtures into spin-polarized states. (f) Single-spin-flip dipolar relaxation of a spin mixture into a different spin mixture.

Figure 2

Population decay of fermionic ${}^{161}\mathrm{Dy}$ at $B=0.410(5)\mathrm{G}$, $T=390(30)\mathrm{nK}$, and ${\overline{n}}_0=7(2)\times {10}^{12}{\mathrm{cm}}^{-3}$ for $m_F=+21/2$ (triangles), $-19/2$ (circles), and $-17/2$ (diamonds) as well as bosonic ${}^{162}\mathrm{Dy}$ at $B=0.100(5)\mathrm{G}$, $T=450(30)\mathrm{nK}$, and ${\overline{n}}_0=3(1)\times {10}^{13}{\mathrm{cm}}^{-3}$ for $m_F=+8$ (squares). The solid curves are fits to the data using Eq. (3) [36]. (Inset) Stern-Gerlach images of initial states.

Figure 3

Dipolar relaxation as depicted in Fig. 1 for bosonic ${}^{162}\mathrm{Dy}$ ($m_F=+8$) and fermionic ${}^{161}\mathrm{Dy}$ ($m_F=+21/2$). (a)–(b) Two-body-loss lifetimes versus magnetic field. (c)–(d) Atom loss spectra presented as normalized atom number. Locations of Feshbach resonances appear as dips in the atom loss. (e) Two-body collisional loss rates for ${}^{162}\mathrm{Dy}$ (squares) and ${}^{161}\mathrm{Dy}$ (triangles) at the same fields as in (a)–(d). See Fig. 2 caption and Ref. [27] for initial densities and temperatures. Curves are collisional loss rates calculated using the expressions for ${\sigma }_1$ and ${\sigma }_2$ in Eq. (2) and in Ref. [27], respectively, and correspond to ${}^{162}\mathrm{Dy}$ (top), ${}^{161}\mathrm{Dy}$ (bottom) and distinguishable particles (middle) at $T=450(30)\mathrm{nK}$ (top, middle) and 390(30) nK (bottom) with no free parameters. Thickness represents temperature error [27, 36].

Figure 4

Dipolar relaxation of spin mixtures. Curves are fits to coupled two-body-loss rate equations; see Ref. [27]. (a) Population decay of fermionic ${}^{161}\mathrm{Dy}$ in the $m_F=-19/2$ (circles) and $m_F=-21/2$ (triangles) states at $T=450(20)\mathrm{nK}$ and $B=0.410(5)\mathrm{G}$. (b) ${}^{161}\mathrm{Dy}$ population decay in the $m_F=-17/2$ (diamonds) and $m_F=-19/2$ (circles) states at $T=380(20)\mathrm{nK}$ and 0.488(5) G. This inelastic collision proceeds more rapidly than panel (a)’s due to different quantum statistics; see text. Initial density of each spin state is $2(1)\times {10}^{12}{\mathrm{cm}}^{-3}$ [36]. (Insets) Averages of 18 Stern-Gerlach images.