Figure 1

Time evolutions of pyridine’s spin-polarization operators ${\widehat{I}}_{iz}$. (a) Coherent oscillatory transfer patterns (simulated $\to$ solid or dashed lines, experimental data $\to$ spin $I_1$, blue triangles, spin $I_2$, green circles, spin $I_3$, red squares) driven by ${\widehat{H}}_J$ between the spin sites in pyridine (structure shown; $J$ couplings taken from 8). A selective initial state concerning the spins ${\widehat{I}}_2$ (a),(b) and ${\widehat{I}}_1$ (c) is prepared, followed by an ${\widehat{H}}_J$ evolution. (b),(c) Diagrams illustrating the switch of the dynamics shown in (a) to quasimonotonic polarization transfers, as a result of introducing repeated projective measurements. These calculated curves involved instantaneous erasements of the off-diagonal density-matrix terms at intervals $\tau =31.7\mathrm{ms}$ (optimal transfer), $\tau =12.7\mathrm{ms}$ (intermed.), $\tau =0.63\mathrm{ms}$ (Zeno) for panel (b) and $\tau =63.5\mathrm{ms}$ (optimal transfer), $\tau =26.6\mathrm{ms}$ (intermed.), $\tau =3.17\mathrm{ms}$ (Zeno) for panel (c). Points in panel (a) (and all remaining data in this work) were acquired on a 600 MHz NMR spectrometer using $50\mathrm{m}M$ pyridine in ${\mathrm{CDCl}}_3$. The time evolution of pyridine’s spin polarizations was monitored for each of the molecule’s three chemically inequivalent sites, in a point-by-point fashion. The transfer pattern under a free evolution driven by ${\widehat{H}}_J$ was recreated using pulse sequences capable of efficiently suppressing chemical shift differences, including DIPSI-3 and MLEV-8 [6, 11].Reuse & Permissions

Figure 2

(a) Polarization transfer sequence emulating projective measurements interspersed with segments of isotropic ${\widehat{H}}_J$ evolution. The sequence begins with a $t_{\mathrm{sel}}$ pulse, that excites or depletes a single spin polarization. It continues with a looped evolution incorporating an isotropic ${\widehat{H}}_J$ action of length $\tau$, and an emulated projective measurement. This projection consists of a chirped $\pi$ pulse acting in combination with a gradient $G_{\mathrm{chirp}}$ for dephasing the zero-quantum off-diagonal elements in the spin density matrix [12], followed by a spoil gradient $G_s$ charged with erasing all remaining higher coherence orders [6]. Commonly used parameters were $M=20–40$, $t_{\mathrm{sel}}=5–10\mathrm{ms}$, $\tau =1–60\mathrm{ms}$, $t_p=25–30\mathrm{ms}$, $G_s=20\mathrm{G}/\mathrm{cm}$, $G_{\mathrm{chirp}}=0.5–1\mathrm{G}/\mathrm{cm}$ and a sweep range of the chirped $\pi$ pulses of $\Delta \omega =20\mathrm{kHz}$. (b) Transfer characteristics expected during the course of this sequence for the two-spin zero- and double-quantum spin operators (off-diagonal terms of the density matrix). Notice the predicted suppressions of off-diagonal elements of the density matrix over the full sample volume: $G_s$ is predominantly responsible for eliminating single- and double-quantum coherences, whereas $G_{\mathrm{chirp}}$ erases off-diagonal zero-quantum terms. The amplitudes of all these gradients were varied in a random fashion throughout each loop in order to avoid fortuitous revivals (echoes) of the coherences [4, 7]. (c) The destruction of the correlations between the spins and their surroundings steers the $⟨{\widehat{I}}_{ix}⟩$ single-quantum elements corresponding to populations in terms of the initial density matrix, towards the desired monotonic evolution.Reuse & Permissions

Figure 3

Experimental single-spin polarizations, obtained from a sequence of the kind illustrated in Fig. 2a for pyridine. (a),(b) Transfer characteristics resulting from a “projected” ${\widehat{H}}_J$ evolution, following selective single-spin state preparations of ${\widehat{I}}_1$ (a) and ${\widehat{I}}_2$ (b) for $\tau =63.5\mathrm{ms}$ (filled symbols) and $\tau =12.5\mathrm{ms}$ (empty symbols). (c) Time evolution for an analogous repolarization experiment performed after a selective demagnetization of spin ${\widehat{I}}_1$ for $\tau =50.45\mathrm{ms}$ (filled symbols) and $\tau =12.61\mathrm{ms}$ (empty symbols). The main discrepancies between the experimental data and the simulated expectation (black dashed line) arise from the fact that the asymptotic polarization distributions are reached at a lower signal amplitude ($\sim 0.35$) than ideally expected as determined by the quasi-Boltzmann equilibrium [$\sim 0.35$ vs $\frac{2}{5}=0.4$ for Figs. 3a, 3b; $\sim 0.5$ vs $\frac{3}{5}=0.6$ for Fig. 3c]. Radio-frequency pulse inaccuracies and/or relaxation-derived losses are probably responsible for this.Reuse & Permissions