Cooling by Spontaneous Decay of Highly Excited Antihydrogen Atoms in Magnetic Traps

An efficient cooling mechanism of magnetically trapped, highly excited antihydrogen ($\overline{\mathrm{H}}$) atoms is presented. This cooling, in addition to the expected evaporative cooling, results in trapping of a large number of $\overline{\mathrm{H}}$ atoms in the ground state. It is found that the final fraction of trapped atoms is insensitive to the initial distribution of $\overline{\mathrm{H}}$ magnetic quantum numbers. Expressions are derived for the cooling efficiency, demonstrating that magnetic quadrupole (cusp) traps provide stronger cooling than higher order magnetic multipoles. The final temperature of $\overline{\mathrm{H}}$ confined in a cusp trap is shown to depend as $\sim 2.2T_{n_0}{n}_0^{-2/3}$ on the initial Rydberg level $n_0$ and temperature $T_{n_0}$.

Figure 1

Gas dynamics due to a changing external potential (from solid to dashed lines). The standard evaporative cooling is shown in (a). In (b), the decreasing potential energy of trapped atoms, results in collisionless cooling during the radiative cascade of Rydberg atoms. The shaded areas indicate the distribution of decay events under the assumption of field-free $\overline{\mathrm{H}}$s (light area) and accounting for magnetic field effects (dark area). DIC is more efficient in the latter case.

Figure 2

Time evolution of the number of trapped atoms (a) and the atomic temperature (b) for $n_0=44$, $m_0=43$. The solid and dashed curves refer to $100\%$ low-field seeking ground state atoms and an equal mixture of $e^{+}$ spin orientations, respectively. The inset shows the initial (open circles) and final (closed circles) velocity distribution fitted to Maxwellian curves with temperatures $T(0)=15\mathrm{K}$ and $T(\infty )=0.4\mathrm{K}$, respectively. The cusp trap has a $B$-field difference of 4 T. (c) Ratio of energy loss due to evaporation and DIC.

Figure 3

Fraction of trapped atoms as functions of time [(a),(c)] and average principal quantum number [(b),(d)], for $n_0=44$ and different initial $33\le m_0\le 43$ [in (a) and (b) at $T(0)=10\mathrm{K}$] and circular Rydberg atoms with $36\le n_0\le 44$ [in (c) and (d) at $T(0)=12\mathrm{K}$]. Different curves are steps of two in $m_0$ and $n_0$. The inset shows the linear $n_0$ dependence of the fraction of trapped atoms (open circles), which disappears when strong magnetic field effects are neglected (closed circles). The trap parameters are identical to Fig. 2.

Figure 4

$n$ dependence of the atomic temperature of circular Rydberg states for $n_0=44$, $T(0)=15\mathrm{K}$, $\gamma =1$ (a), and $\gamma =5$ (b). The open circles show the numerical results neglecting the diamagnetic term in the atomic Hamiltonian, and the closed circles result from the full calculations. The solid line is obtained for the adiabatic cascade from Eq. (8), while the dotted and dashed lines indicate the temperature decrease due to the sudden deexcitation according to Eq. (6).