Addressing spins at the clock transitions with a frequency- and bandwidth-tunable superconducting resonator

Abstract

Solid-state spin ensembles addressed via superconducting circuits are promising candidates for quantum memory applications, offering multimodal storage capability and second-long coherence times at their clock transition. Implementing practical memory schemes requires dynamic control over both the resonator frequency and bandwidth. In this letter, we report measurements of a superconducting resonator whose frequency can be tuned by passing a DC current through the high-kinetic-inductance thin film, and whose bandwidth can be tuned by parametric coupling to a low-Q buffer resonator. Using this resonator, we address an ensemble of bismuth donors at their clock transition, measuring a Hahn-echo coherence time of 450 ms. We demonstrate RF driving of the bismuth donor hyperfine transitions, as well as dynamic bandwidth control of the resonator.

Figures (7)

• Figure 1: Device layout. (a) Schematic circuit diagram. The lumped element models of resonator A (blue) and resonator B (red) are highlighted in (c). The kinetic inductance coupler (KIC) is shown as an inductive shunt to the ground. (b) Overview micrograph of the circuit substrate before flip chip bonding. The green box outlines the footprint of the Bi-doped silicon die which is subsequently glued on top. The external polarising field $B_\mathrm{z}$ is applied parallel to the microwire of resonator A, i.e., horizontal in this image. (c) Zoom-in of the resonator region (brown box in (b)). Resonators A and B are marked with dashed boxes. The arrows point to the KIC. (d) Optical and scanning electron micrographs of the KIC nanowire. The bright areas of various shades are NbTiN films with different vortex-trapping hole densities. The darkest regions are the exposed silicon substrate.
• Figure 2: Resonator tunabilities. (a-b) Resonance frequency shift of the two modes in response to sweeping DC bias current $I_\mathrm{A}$ (a) or $I_\mathrm{B}$ (b), under different $I_\mathrm{B}$ or $I_\mathrm{A}$ offsets. Solid curves: fits to Ginzburg-Landau theory annunziata_tunable_2010. (c-d) Amplitude of the microwave reflection $S_{11}$ off port B near the resonance frequency of mode B (c) and A (d), as the RF pump frequency $f_\text{3WM}$ is swept across the frequency difference $f_\mathrm{A} -f_\mathrm{B}$. (e) Dependence of the measured mode A linewidth $\kappa_\mathrm{i}^\mathrm{A}$ (open circles) on the RF pump amplitude, under various DC bias through $I_\mathrm{B}$ while $I_\mathrm{A}$ is held neutral. (f) Ringdown suppression via dynamic control of resonator bandwidth. The green curves of varying shades represent the ringdown amplitude after a resonant microwave pulse, as the 3WM pump pulses are delayed by $0~\mu$s, $1~\mu$s, ..., $4~\mu$s. The pulse sequences are shown in insets with the varying parameters marked in red with arrows. (g) Resonance frequency $f_\mathrm{A}$ (left axis) and internal loss rate $\kappa_\mathrm{i}^\mathrm{A}$ (right axis) of mode A as functions of the magnetic field $B_\mathrm{z}$ applied in-plane, parallel to microwire A.
• Figure 3: Tracking bismuth spin transitions with a tunable resonator. (a) Calculated bismuth donor energy spectrum as a function of the polarising field $B_z$mohammady_bismuth_2010morley_initialization_2010. The arrows mark the clock transitions characterised in Fig. \ref{['fig:pESR']}, and the relevant spin states are coloured green. (b) The resonator absorption spectrometry, measured by the internal loss rate $\kappa_\mathrm{i}^\mathrm{A}$ of mode A as its resonance frequency $f$ is swept across the tuning range, and $B_\mathrm{z}$ between 0 and 65 mT. The contrast is enhanced and the field-independent background is removed for visibility. The red dashed curves indicate the calculated transition frequencies. (c) The absorption spectrum (open circles) at $2.1$ mT. The bismuth transition peaks are indicated by the gray dash lines. Inset: the extracted bismuth transition peak width $\Gamma$ versus the gyromagnetic ratio $\gamma$ in unit of the Bohr magneton $\gamma_\mathrm{e}$. The dashed line represents the homogenous linewidth corresponding to an Overhauser field $\delta B_0=4~\mu$T due to the residual 500 ppm of $^{29}$Si abe_electron_2011george_electron_2010.
• Figure 4: Clock transitions and electron nuclear double resonance (ENDOR). The open circles represents the raw data, and the solid curves Lorentzian (a, e) or exponential (b-d) fits. The pulse sequences are shown in insets with the varying parameters marked in red with arrows. (a) Hahn echo spectroscopy at $25.6$ mT. $T_1$ (b) and $T_2$ (c) measurement at 7.3382 GHz (dashed grey line in (a)). (d) Echo silencing via resonator shifting. The normalised echo magnitude decays with increasing resonance frequency detuning $\Delta f_\mathrm{A}$ of mode A during the period of echo. (e) Normalised microwave echo magnitude (open circles) as a function of the disruptive radio frequency pulse frequency $f_\text{NMR}$. The grey lines indicate the nuclear magnetic resonance (NMR)–like transitions. The ones involving $\ket{4,1}, \ket{4,0}, \ket{5, 0}$, or $\ket{5, 1}$ are highlighted with solid lines. Left inset: the extracted peak width $\Gamma$ of the NMR-like transitions versus their gyromagnetic ratio $\gamma$. The dashed line represents the homogenous linewidth corresponding to a magnetic noise $\delta B_0=4~\mu$T.
• Figure S1: Stopping and Range of Ions in Matter (SRIM) simulation of the bismuth donor concentration as a function of the distance from the surface.