Forced evaporative cooling

Repeated removal of high-energy trapped atoms while lowering the energy cutoff as the sample cools. Elastic rethermalization replenishes the tail. The useful outcome is increased phase-space density of an atomic gas, not temperature reduction alone.

After energy-selective loss, elastic collisions redistribute energy and refill the escaping tail. This restores a nearly thermal distribution when redistribution is fast compared with the changing cutoff and unwanted atom loss. The collision rate depends on number density, cross section, and relative speed; slowing atoms alone does not guarantee continued equilibration.

Runaway evaporative cooling is an evaporation regime in which cooling makes subsequent elastic rethermalization of a trapped atomic gas faster rather than slower. In a sufficiently confining trap, the cooling sample can become denser enough that the increasing number density outweighs the decreasing collision speed in ${\Gamma }_{\mathrm{el}}\sim n{\sigma }_{\mathrm{el}}\bar{v}$.

The growing collision rate helps replenish the high-energy tail removed by forced evaporative cooling. It is not automatic: trap weakening, unfavorable cross section changes or unwanted particle loss can instead reduce the rate. Measuring atom number, cloud size and temperature during the ramp tests whether the favorable regime is actually maintained.

A radiofrequency field induces transitions from trapped weak-field-seeking magnetic sublevels to untrapped states at a resonance surface. Atoms with sufficient energy reach that surface and leave. Sweeping the frequency changes the energy cutoff without equating every lost atom with the sample-average energy.

For a classical three-dimensional harmonic trap of fixed frequencies, $E=3N{k}_{B}T$. If each lost atom removes mean energy ${ϵ}_{\mathrm{ev}}=(\eta +\kappa )k_{B}T$, differential energy balance gives $d\ln T/d\ln N=(\eta +\kappa -3)/3$. The result assumes rapid elastic equilibration and excludes separate work from changing trap frequencies.

For a classical three-dimensional harmonic trap of fixed frequencies, $E=3N{k}_{B}T$ and $\mathcal{D}\propto N{T}^{-3}$. Combining $dE={ϵ}_{\mathrm{ev}}dN$ with these equations gives $d\ln \mathcal{D}/d\ln N=4-{ϵ}_{\mathrm{ev}}/(k_{B}T)$. Since evaporation decreases $N$, phase-space density of an atomic gas increases only when the removed mean energy exceeds $4k_{B}T$. Merely lowering temperature requires only ${ϵ}_{\mathrm{ev}}>3k_{B}T$. Changing confinement adds trap work and changes these formulas.

The ratio of an evaporation cutoff to thermal energy. Keeping the cutoff fixed while lowering temperature increases this ratio and reduces population in the escaping tail.