Realizing on-demand all-to-all selective interactions between distant spin ensembles

Abstract

Achieving all-to-all coherent networks is critical for the advancement of large-scale coherent computing and communication protocols. By exploiting the resonant dipole-dipole interaction between distant spin ensembles coupled to a one-dimensional coplanar waveguide (CPW) terminated by a mirror, we successfully demonstrate an on-demand all-to-all selective coherent network between four spin ensembles. Furthermore, by repositioning the spin ensembles along the CPW, we achieve collective coupling, and demonstrate coherent energy exchange between multiple spin ensembles in the time domain. These results strongly indicate the potential of this device as a medium-scale all-to-all network structure, which is poised to advance the exploration of many-body physics and enhance coherent information processing capabilities.

Figures (3)

• Figure 1: Sketch of the system. (a) Two spin ensembles positioned in front of a mirror interact via a continuum of microwaves (curves in different colors) in one dimension. (b) The experimental configuration consists of a $\unit[44]{cm}$ long CPW, with its left end shorted to ground, acting as a magnetic antinode mirror. Four YIG spheres (black spheres; an enlarged photograph of one YIG sphere is shown as an inset) are strategically placed along the CPW, with their Kittel mode (KM) transition frequencies independently tunable via corresponding local magnetic fields ($\vec{H_i}, i = 1, 2, 3, 4$), which are set by an applied current $I$. The black dashed sinusoidal curve indicates that at a specific transition frequency, all YIG spheres are positioned at the magnetic nodes of the microwave, except for the one at the mirror, which consistently resides at the magnetic antinode. The dashed red box shows the part of the system sketched in more detail in panel (a). The downscaling and scalability of this device are discussed in Sec. S9 of the Supplementary Material SupMat.
• Figure 2: All-to-all selective interaction between distant YIG-sphere pairs. (a) Schematic diagram of the setup. Four YIG spheres are placed equidistantly in front of a mirror along the CPW, with a spacing of $\unit[10]{cm}$ between them, labeled sequentially as A, B, C, and D. Green dashed curves with arrows below the YIG spheres indicate the interacting pairs. The blue text denotes the coherent interaction $\Delta / 2\pi$ between corresponding YIG spheres, while the red text represents the designed resonance frequency $\omega_r / 2\pi$. (b)--(g) Amplitude reflection coefficient $|r|$ for a weak probe as a function of the probe frequency $\omega_p$ and the current $I$ controlling the KM frequency of one YIG sphere in a pair. The six panels correspond to the pairs A&B, A&C, A&D, B&C, B&D, and C&D, respectively. In each panel, the KM frequency of the YIG sphere at the node is fixed (highlighted in red font), while the KM frequency of the other YIG sphere is tuned through resonance with this frequency. Each panel shows a clear avoided level crossing, demonstrating interactions between the selected pairs of YIG spheres. (h) Line cuts of the data [dashed lines in panels (b)--(g)] at the point where the corresponding selected YIG pair is on resonance. Here, $\delta_p = \omega_p - \omega_r$ is the detuning between the probe and resonance frequencies. The simulation results corresponding to panels (b)--(h) are shown in Fig. S2 SupMat.
• Figure 3: Time-resolved energy oscillations between YIG sphere A and joint spin ensemble. (a) Sketch of the setup. Four YIG spheres are positioned in front of a mirror along the CPW, with distances from the mirror set at $x_{\rm A} = 0$, $x_{\rm B} = \unit[10]{cm}$, $x_{\rm C} = \unit[22]{cm}$, and $x_{\rm D} = \unit[30]{cm}$. The black dashed sinusoidal curve indicates that when $\omega_p / 2\pi = \unit[2.325]{GHz}$, YIG A is at an antinode, while B, C, and D are at nodes. (b) Time evolution of the system for configurations with two (blue), three (green), and four (red) YIG spheres, each tuned on resonance at $\omega_r / 2\pi = \unit[2.325]{GHz}$, following the termination of a long ($\sim \unit[1]{\mu s}$) resonant rectangular microwave pulse. The time traces correspond to line cuts of more extensive data [dashed lines in panel (c) and Fig. S5(a)--(b) SupMat]. To enhance visibility of the oscillations, $\mleft| V_{\rm out} \mright|$ is converted to reflected power in dBm. We observe that the oscillation period decreases with an increasing number of YIG spheres. The corresponding simulation results are shown in Fig. S5(f) SupMat. (c) Time evolution of the reflected signal $\mleft| V_{\rm out} \mright|$ for the configuration involving four YIG spheres. The plot consists of two distinct regions: from 0 to $\unit[1]{\mu s}$, during which the pulse is applied, and the remaining duration when the pulse is off. Shortly after the pulse is activated and deactivated, energy oscillations can be observed. When the pulse is applied for a long time, the system reaches a steady state, revealing mode splitting, consistent with the frequency-domain measurement in Fig. S3(b) SupMat. The corresponding time-domain simulation results are shown in Fig. S5(e) SupMat. (d) Based on the oscillation periods in panel (b), $\Delta$ as a function of the number of YIG spheres located at the nodes ($N-1$). Here, $\Delta^{(0)}$ is the coherent interaction for the case of two YIG spheres (A-D). The agreement between the experimental data and the prediction ($\sqrt{N-1}$) is good.