Dressed Rabi Oscillation in a Crystalline Organic Radical

Free electron laser-powered pulsed electron paramagnetic resonance experiments performed at $240\mathrm{GHz}/8.56\mathrm{T}$ on the crystalline organic radical 1,3-bisdiphenylene-2-phenylallyl reveal a tip-angle dependent resonant frequency. Frequency shifts as large as 11 MHz (45 ppm) are observed during a single Rabi oscillation. We attribute the frequency shifts to a “dressing” of the nutation by spin-spin interactions. A nonlinear semiclassical model which includes a temperature- and sample-geometry-dependent demagnetizing field reproduces experimental results. Because experiments are performed without a cavity, radiation damping, the most common nonlinear interaction in magnetic resonance, is negligible in our experiments.

Figure 1

(a) Room-temperature FID signal generated by a 2 ns FEL pulse, highlighted in gray, applied to a BDPA-Bz grain. Inset: signal digitized at the intermediate frequency ($\mathrm{IF}=500\mathrm{MHz}$, shown in inset). (b) Fourier transform of the FID generated by a 2 ns pulse. The FT-EPR line shape is well described by a Lorentzian with a FWHM of $5.9\pm 0.1\mathrm{MHz}$. (c) Integrated FT-EPR intensity as a function of pulse length, demonstrating Rabi oscillations. The magnetic field was chosen so the FID generated by a 2 ns pulse is on resonance with the FEL pulse. For pulse lengths corresponding to the two maxima, the sample magnetization is rotated by $\pi /2$ (*) and by $3\pi /2$ (***), while at the minimum (**) the magnetization has been rotated by $\pi$. The minimum of the Rabi oscillation is not at zero, indicating incomplete population inversion. (d) FT-EPR absorption line shape plotted for four pulse lengths. The FID generated by a 2 ns pulse is on resonance with the FEL pulse; FIDs generated by longer pulses are not. (e) In red, the trajectory taken by the sample magnetization on the Bloch sphere. In blue, the magnetization vector projected onto the $x\text{−}y$ plane.

Figure 2

(a) Schematic representation of a BDPA-Bz crystal as an oblate spheroid, with a ratio of major to semiminor axes of $7:1$. (b) Contour plot of the FT-EPR absorption line shape, (c) integrated FID intensity, and (d) mean FID frequency, as a function of pulse length as BDPA-Bz magnetization undergoes Rabi oscillations. The FID frequency axes are referenced to the FEL frequency. The magnetic field is chosen so that the FID generated by a $\pi /2$ pulse has the same frequency as the FEL. The Rabi oscillations minimum is close to zero, indicating nearly complete population inversion is achieved with the magnetic field thus chosen.

Figure 3

Mean FID frequency as a function of pulse length as a BDPA-Bz crystal undergoes Rabi oscillations over many cycles. Simulated mean FID frequencies match experimental results over multiple oscillations.

Figure 4

Contour plots of the FT-EPR line shape at (a) 290 K, (b) 229 K, and (c) 190 K. (d) The maximum frequency shift $\mathrm{\Delta }F$ as a function of temperature.