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The 2007 paper Comparison of the Hanbury Brown-Twiss effect for bosons and fermions by T. Jeltes and others compares polarized helium-3 fermions with helium-4 bosons. The chemical atoms occupy a metastable atomic level. Switching off magnetic trapping of neutral atoms releases them onto a microchannel plate detector with a delay-line anode, 63 cm below. Position and arrival-time readouts give three-dimensional pair separations by time-of-flight atom detection. About 1000 clouds per isotope supply histograms; normalization removes the broad cloud shape.

The pair detection correlation dips below one for helium-3 and rises above one for helium-4. The same apparatus, matched temperatures near $0.5\mu \mathrm{K}$, nearly identical trapping potentials, negligible interactions, and magnetic field gradient checks of spin polarization support an exchange-statistics interpretation. Finite detector resolution suppresses contrast; trap switch-off and resolution uncertainties limit quantitative agreement. A diverging laser lens deepens the dip, but its aberrations preclude a precise lens-model test. This detects exchange correlations, rather than measuring occupation of one selected spin orbital.^[ref]

An experimental researcher whose team produced a Bose-Einstein condensate in dilute rubidium vapor in 1995. Magnetic trapping of neutral atoms confined the cloud, while evaporative cooling removed energetic atoms. The decisive evidence was a narrow, anisotropically expanding component appearing within a broader thermal velocity distribution. Its sudden growth as the cloud cooled connected the observed images with macroscopic occupation of the trap’s lowest quantum state.^[ref]

The rubidium experiment used laser cooling, a magneto-optical trap and magnetic trapping of neutral atoms with a rotating bias field. Radio frequency transitions removed energetic atoms; elastic collisions restored thermal equilibrium. Before absorption imaging, the trap was decompressed, then nearly released with a gradient supporting against gravity. Varying the final evaporation cut revealed a narrow anisotropic core within an isotropic thermal cloud. The broad component supplied a simultaneous comparison through the same optics. Resolution and size calibration limited inference; interactions broadened the core relative to an ideal gas.^[ref]

In 2001, Andrew G. Truscott, Randall G. Hulet, and collaborators observed degeneracy pressure in trapped lithium. A Zeeman slower fed a dual magneto-optical trap; optical pumping prepared atoms for a cloverleaf apparatus for magnetic trapping of neutral atoms. Microwave evaporation removed energetic lithium-7 bosons; elastic collisions cooled lithium-6 fermions by sympathetic cooling.^[ref]

Sequential absorption imaging recorded both trapped clouds on a camera. Fits to axial profiles used the boson cloud as a thermometer. At common temperature, the nearly equal magnetic trapping potentials provided a comparison: the clouds had similar sizes near $T/T_F=1$, but the fermion cloud remained broader as cooling reached $T/T_F=0.25$. Figure 3 compared its radius with ideal Fermi gas and classical predictions.^[ref]

Varying the wait before imaging tested thermal equilibrium. Finite imaging resolution restricted the analysis to the axial direction; fits neglected interaction-induced density shifts. Cooling eventually suffered from the dwindling boson heat capacity. The result supports quantum occupation effects, without directly resolving individual occupied states or reaching zero temperature.^[ref]

These were neutral alkali atoms in a spatially varying trap. The Fermi energy of a model electron gas instead uses uniform electrons, two equally populated spin states, and the electron mass. The measured trapped-atom radii are not measurements of that electron model's $p_F$ or $E_F$; comparing their numerical Fermi energies requires the appropriate particle mass, internal-state populations, and confining potential.

Evaporative cooling of atoms selectively removes atoms with unusually high total energy, then elastic collisions rethermalize those remaining. Loss of particles alone is insufficient: the lost atoms must carry more than the mean energy per particle if the temperature is to fall. The process is open and dissipative, so it can increase the phase-space density of an atomic gas in the remaining sample while reducing its atom number. As the temperature falls, the cutoff must be lowered to keep replenishing a useful escaping tail; a fixed high cutoff eventually gives negligible evaporation.

An experimental sequence first loads laser-cooled atoms into a conservative trap and suppresses resonant-light heating. In a trap using magnetic trapping of neutral atoms, a radiofrequency evaporation knife drives a Zeeman splitting transition from a trapped weak-field-seeking state to an untrapped state on a surface where the splitting matches the radiofrequency photon energy. Only atoms energetic enough to reach that surface escape. Lowering the radiofrequency cutoff progressively removes less energetic atoms. Alternatively, lowering an optical dipole trap's depth permits energetic atoms to spill out. This changes confinement as well as the escape cutoff, so it can reduce the collision rate. Radiofrequency-selective evaporation and the need for favourable elastic-collision and background-loss rates are documented in the original condensate experiments.^[ref]

The elastic collision rate ${\Gamma }_{\mathrm{el}}\sim n{\sigma }_{\mathrm{el}}\bar{v}$ must be large enough for elastic rethermalization of a trapped atomic gas throughout evaporation, and much faster than unwanted loss and heating. A clean vacuum reduces background collisions; suitable trapping states suppress inelastic spin-changing loss, and density must not make three-body recombination dominant. The cutoff ramp should allow equilibration without taking so long that background losses dominate. A large evaporation truncation parameter $\eta ={ϵ}_{\mathrm{cut}}/(k_{B}T)$ selects energetically valuable atoms, but an excessively large value suppresses their escape rate. A very small value discards too many useful low-energy atoms. If elastic collisions become more frequent as evaporation proceeds, the resulting runaway evaporative cooling can improve efficiency; it is not automatic in a weakening optical trap.

The energy selectivity for evaporation to increase phase-space density can be made precise in a classical three-dimensional harmonic trap with fixed frequencies. Equipartition gives $E=3N{k}_{B}T$. If each escaping atom removes mean energy ${ϵ}_{\mathrm{ev}}$, energy balance is $dE={ϵ}_{\mathrm{ev}}dN$ with $dN<0$, soThe peak harmonic-trap phase-space density is $\mathcal{D}=N(\hslash \bar{\omega }/(k_{B}T){)}^3$. ThereforeCooling requires ${ϵ}_{\mathrm{ev}}>3k_{B}T$; increasing $\mathcal{D}$ despite atom loss requires the stronger condition ${ϵ}_{\mathrm{ev}}>4k_{B}T$. These inequalities assume rapid thermalization and no work from changing trap frequencies. They distinguish lower temperature from genuinely improved quantum degeneracy. Eventually quantum statistics and inelastic processes require a refinement of this classical estimate. Efficient evaporation combines energy-selective loss, rapid elastic redistribution, and low unwanted loss; it can bring a precooled gas to Bose-Einstein condensation.