Observing Quantum Oscillation of Ground States in Single Molecular Magnet

Single molecular magnets (SMMs) are among the potential systems for quantum memory and quantum information processing. Quantum coherence and oscillation are critical for these applications. The ground-state quantum coherence and Rabi oscillations of the SMM ${\mathrm{V}}_{15}$ ($[{\mathrm{V}}_{15}^{\mathrm{IV}}{\mathrm{As}}_6^{\mathrm{III}}{\mathrm{O}}_{42}({\mathrm{H}}_2\mathrm{O}){]}^{6-}$) have been studied in this context. We have affirmatively measured at 2.4 K the Rabi quantum oscillations and coherence time $T_2$ for the ground states of the ${\mathrm{V}}_{15}$ ion of collective spin $S=1/2$, in addition to confirming the previously reported results for the $S=3/2$ excited states. The oscillations of $S=3/2$ and $S=1/2$ states are of different frequencies, and so can be separately selected for purposive manipulations. $T_2$ of $188\pm 4\mathrm{ns}$ ($S=3/2$) and $149\pm 10\mathrm{ns}$ ($S=1/2$) are much less than $T_1\sim 12\mu \mathrm{s}$ and are further extendible via various approaches for qubit implementations.

Figure 1

(a) Ball-and-stick diagram of molecular structure of ${\mathrm{V}}_{15}$ gaining from the result of single crystal XRD at room temperature (red, V; black, As; silver, O). (b) Cw spectrum of ${\mathrm{V}}_{15}$ single crystal at 100 K. Experimental settings: microwave frequency, 9.7 GHz; microwave power, 0.002 mW; modulation frequency, 100 kHz. (c) The energy diagram of ${\mathrm{V}}_{15}$ low-lying states with the magnetic field parallel to the ${\mathrm{C}}_3$ axis [8]. The two lower red arrows denote the transitions in the ground doublet states and the three upper black arrows denote those in the first excited states. The energy gap between the excited states and the ground states is about 3.67 K (see text).

Figure 2

The time evolution of the average spin $⟨S_z⟩$ after a spin-echo sequence of $S=1/2$ states (lower curve), corresponding to the transitions labeled with red arrows in Fig. 1c, and the $S=3/2$ states (upper curve), corresponding to the transitions labeled with black arrows in Fig. 1c. Inset: the $T_2$ decay curves for $S=3/2$ (upper curve) and $S=1/2$ (lower curve) measured with Hahn echo sequences. The experiment parameter settings: The temperature was 2.4 K. For $S=1/2$ states, $B_0$ was set to be 3552 G, microwave power attenuation was 1 dB, pulse duration $t_{\pi }=20\mathrm{ns}$ and 20 scans. For $S=3/2$ states, $B_0$ was set to be 3550 G, microwave power attenuation was 1 dB, pulse duration $t_{\pi }=10\mathrm{ns}$ and 2 scans.

Figure 3

(a) Dependence of the Rabi oscillations of both $S=3/2$ and $S=1/2$ states on the driving field strengths, $B_1$. Pulses settings were the same as described in Fig. 2. Temperature was 2.4 K. (b) Corresponding dependence of Rabi frequencies on $B_1$ field. The $B_1$ field was calibrated by using the Rabi frequency of a standard $S=1/2$ sample (P doped in Si). The dashed lines are the theoretical calculations for $S=3/2$ and $S=1/2$ as described in the main text.

Figure 4

(a) The detected Rabi oscillation of $S=1/2$ (lower curve) and cavity background (upper curve) observed with the same experimental parameter settings. (b) The FSED of detected $S=1/2$ (upper curve) and background (lower curve). (c) The FFT results of $S=1/2$ (lower curve) and $S=3/2$ (upper curve). The corresponding Rabi frequencies are 23.4 MHz and 46.9 MHz, respectively. (d) The FSED of $S=1/2$ (lower curve) and $S=3/2$ (upper curve). The signal of $S=1/2$ is gained by the detected signal subtract the signal of background (see text).

Figure 5

(a) Dependence of Rabi oscillation with different temperatures of $S=1/2$ states with the same setting described in legend of Fig. 2 but at different temperatures. (b) Corresponding FFT of (a). The main peak of spectra detected at 4.2 K (with the highlighted color of blue around 40 MHz) is originated from $S=3/2$. And the smaller peak shown at the left of the main peak in the spectrum (with the highlighted color of yellow around 20 MHz) is originated from $S=1/2$ and it grows larger with lower temperature (see text).