Quantum decoherence is a central concept in physics. Applications such as quantum information processing depend on understanding it; there are even fundamental theories proposed that go beyond quantum mechanics1, 2, 3, in which the breakdown of quantum theory would appear as an ‘intrinsic’ decoherence, mimicking the more familiar environmental decoherence processes4. Such applications cannot be optimized, and such theories cannot be tested, until we have a firm handle on ordinary environmental decoherence processes. Here we show that the theory for insulating electronic spin systems can make accurate and testable predictions for environmental decoherence in molecular-based quantum magnets5. Experiments on molecular magnets have successfully demonstrated quantum-coherent phenomena6, 7, 8 but the decoherence processes that ultimately limit such behaviour were not well constrained. For molecular magnets, theory predicts three principal contributions to environmental decoherence: from phonons, from nuclear spins and from intermolecular dipolar interactions. We use high magnetic fields on single crystals of Fe8 molecular magnets (in which the Fe ions are surrounded by organic ligands) to suppress dipolar and nuclear-spin decoherence. In these high-field experiments, we find that the decoherence time varies strongly as a function of temperature and magnetic field. The theoretical predictions are fully verified experimentally, and there are no other visible decoherence sources. In these high fields, we obtain a maximum decoherence quality-factor of 1.49 × 106; our investigation suggests that the environmental decoherence time can be extended up to about 500 microseconds, with a decoherence quality factor of ~6 × 107, by optimizing the temperature, magnetic field and nuclear isotopic concentrations.
Figures at a glance
Figure 1: Typical ESR spectra, showing echo intensity as a function of transverse magnetic field,H⊥. 
Data are shown for two different samples, at different temperatures and orientations of field, and at ωESR = 240 GHz. a, Sample 1. Solid red line,
, T = 1.58 K; dashed blue line, 
, T = 1.67 K. Top inset, sample dimensions are approximately z: x: y = 1,000: 700: 250 µm. Lower left inset, the low-T spin structure of the Fe8 molecule. Lower right inset, the directions of the easy (z), hard (x) and intermediate (y) axes of an Fe8 molecule ( 
approximately gives the direction of the crystallographic vector a). b, Sample 2. Solid red line, 
, T = 1.7 K; dashed blue line, 
, T = 1.23 K. Top inset, sample dimensions are approximately z: x: y = 900: 800: 400 µm. Bottom inset, tunnelling splitting, 2Δo, as a function of transverse field at 
(solid red line) and at 
(dashed blue line).
Figure 2: Calculated contributions to the decoherence coming from the coupling to nuclear spins, phonons and magnons. 
a, The three individual contributions which sum to give the dimensionless decoherence rate γφ =
/T2Δo, as a function of the qubit splitting in the case 
. b, The three corresponding contributions to the decoherence time, T2. In both panels: brown dashed lines, nuclear contribution (short-dashed brown lines are for the natural isotopic concentrations, long-dashed brown lines for the deuterated system); solid lines of different colours, magnon contributions at different temperatures (shown) from 0.1 to 1.6 K; long-dashed lines of different colours, phonon contributions, shown for the same temperatures as in the magnon case.
Figure 3: Measured and calculated decoherence times T2 in samples 1 and 2, as a function of temperature. 
a, Results for
. Main panel: thin red line with diamonds, measured using sample 1, Hy = 9.845 T; thin green line with circles, measured using sample 2, Hy = 9.875 T; vertical and horizontal error bars, standard errors of T2 data fits and uncertainty in temperature (ΔT = ± 0.05 K), respectively. Thick blue line, calculations including phonon and magnon contributions, Hy = 9.5 T. Inset: partial contributions calculated for 
(solid line) from magnons (dashed line) and phonons (long-dashed line), together with the corresponding experimental results for the two samples (diamonds and circles). The scale on the right-hand side of the main panel indicates the decoherence Q-factor, Qφ = π/γφ = πT2Δo/ 
; the right-hand scale on the inset shows γφ. b, As for a, but now for 
. The experimental curves were measured at Hx = 10.865 T (sample 1) and Hx = 11.953 T (sample 2). The theoretical curves are obtained at Hx = 11.3 T.
