Figure 4: Suppression of P(FM) with increasing number of spins.
From: Onset of a quantum phase transition with a trapped ion quantum simulator
(a–d) Ferromagnetic order P(FM)=P(0)+P(N) is plotted vs B/|J| for N=2 to N=9 spins. The circles are experimental data, and the lines are theoretical results including decoherence and imperfect initialization. As this quantity includes only two of 2N basis states, random spin-flips and other errors degrade it much faster than the magnetization and Binder cumulant. The representative detection error bars are shown on a few points for each N. The P(FM) reduces from ∼0.9 to ∼0.55 as the system size is increased from two to nine. The principle contribution to this degradation is decoherence, predominantly due to spontaneous emission from intermediate 2P1/2 states in the Raman transition and additional dephasing, primarily due to intensity fluctuations in Raman beams. Shown in d is an estimated breakdown of the suppression of P(FM) from various effects for N=9 spins. Non-adiabaticity due to finite ramping speed, and spontaneous emission and additional dephasing due to fluctuating Raman beams suppress P(FM) by ∼8%, ∼18% and ∼24% respectively from unity (B/|J|→0).
