BEC Coherence Time

BEC Coherence Time is the coherence duration of a Bose-Einstein condensate in the book's account, which grows with the number of atoms as the two-thirds power of their ratio to a critical number, through collective synchronization with the substrate. In chapter 7, collective coherence is enhanced when many atoms synchronize with the substrate, with a scaling the book ties to the frequencies of collective modes. τ▱ is the fixed substrate coherence time, the coherence time at the critical atom number (τ≋,BEC = τ▱ at N⚛ = N⨶); above it the coherence time grows as N⚛^(2/3), so doubling the atoms multiplies it by 2^(2/3) ≈ 1.59. The two-thirds power is the law's statement of collective enhancement; dimensional analysis alone cannot fix it, since N⚛/N⨶ is dimensionless. Coherence is lost to the environment at a rate Γ≋⦰ = γ◌ (T◌/T▱)² (ρ◌/ρ▱) [𝕋⁻¹], quadratic in the temperature ratio and linear in the density ratio, where γ◌ is the environmental coupling. The book writes τ≋,BEC = τ▱ (N⚛/N⨶)^(2/3), where τ≋,BEC is the BEC Coherence Time [𝕋], τ▱ the substrate coherence time [𝕋], N⚛ the atom number [∅] and N⨶ the critical atom number [∅]. A time times a pure number stays [𝕋]. BEC Coherence Time connects to Scaling Quantum Coherence, Mass-Dependent Coherence Time, Decoherence Mechanisms, Operational Coherence Time and Macroscopic Coherence.