Hybrid Quantum Systems: Coupling Single-Molecule Magnet Qudits with Industrial Silicon Spin Qubits

Abstract

Molecular spin qudits offer an attractive platform for quantum memory, combining long coherence times with rich multi-level spin structures. Terbium bis(phthalocyaninato) (TbPc$_2$) exemplifies such systems, with demonstrated quantum control and chemical reproducibility. In hybrid quantum architectures, TbPc$_2$ can act as the primary memory element, with semiconductor qubits providing scalable readout and coupling. Here we present a step toward such a hybrid system: using an industrially manufactured silicon metal-oxide-semiconductor (SiMOS) spin qubit to detect electronic spin transitions of an ensemble of TbPc$_2$ molecules. The readout is based on a compact and robust protocol that applies a microwave pulse while all gate voltages defining the qubit are held at a fixed operating point. This protocol, which combines simultaneous Rapid adiabatic Passage and Spin- Selective tunneling (RPSS), enables high-contrast resonance detection and avoids repeated $π$-pulse recalibration common in decoupling schemes. By demonstrating ensemble detection, we establish a foundation for integrating molecular quantum memories with industrial qubit platforms and mark an important step toward single-molecule hybrid quantum technologies.

Figures (11)

• Figure 1: Hybrid system combining a single-molecule magnet and a silicon spin qubit. A single [TbPc$_2$]$^{-}$ molecule is placed above a silicon quantum-dot device and is magnetically coupled to the qubit via its dipolar field. The Tb$^{3+}$ ion is depicted in red with its magnetic moment aligned with the molecular easy axis and indicated by a red arrow. The quantum-dot electron (blue) resides in isotopically enriched $^{28}$Si within a lateral confinement potential (black) defined by the metallic gate stack (brown), which is separated from the silicon by an SiO$_x$ layer. The gate stack and oxide together set the vertical separation between the molecular spin and the semiconductor qubit. Schematic not to scale; the quantum dot is an order of magnitude larger than the SMM
• Figure 2: Distance dependence of dipolar coupling in the hybrid device. The two axes show how the vertical separation $r$ between a single [TbPc$_2]^{-}$ molecule and a silicon spin qubit maps onto the corresponding qubit frequency shift $\Delta f$. In the current industrial device, the gate stack and passivation layer set a separation of $r \approx 250\,\mathrm{nm}$ (red region), leading to a corresponding frequency shift $\Delta f \approx 60\,\mathrm{Hz}$. This is below the typical detection limit of dynamical decoupling techniques (orange region, assuming $T_{2} \sim 100\,\upmu\mathrm{s}$). To amplify the signal, a dilute ensemble of molecules is used, increasing the magnetic field by several orders of magnitude and shifting the qubit response into the sensitive regime of the simultaneous rapid adiabatic passage and spin-selective tunneling (RPSS) protocol (blue region).
• Figure 3: Spin resonance detection via RPSS protocol.a A frequency-chirped microwave pulse drives the spin-up transition, triggering spin-dependent tunneling into the reservoir for charge detection. b Resonance visibility (black) and background (blue) as a function of applied microwave power at a chirp speed of $0.2\,\mathrm{GHz/s}$. The solid line is a fit to the Landau-Zener model (Appendix \ref{['sec:appendix_RPSS']}) for power levels below 5 dBm, yielding a maximum visibility of $89 \pm 1\%$. At higher powers, thermally activated background events reduce the observed visibility. c Time-resolved data from 200 single-shot traces during a 150 ms chirp over 30 MHz at 8 dBm drive power. Tunneling events appear as discrete “blips” in the sensor current. The frequency axis is offset by 18.57 GHz. d Histogram of blip onset times extracted from c, showing a pronounced resonance peak corresponding to the qubit’s Larmor frequency.
• Figure 4: Silicon spin qubit-based magnetometry of a [TbPc$_2]^{-}$ ensemble. Qubit resonance frequency (offset by 18.435 GHz) as a function of the magnetic field component along the [TbPc$_2]^{-}$ easy axis ($z$-axis), measured during angular sweeps of the external field in the $xz$-plane at 48 mK (a) and 210 mK (b). Each data point represents 50 single-shot measurements and a 1 MHz bin width. A $g$-factor of 2 Fogarty2018 is used to convert the qubit frequency to the corresponding magnetic field, up to a constant offset. Forward and backward sweeps reveal pronounced magnetic hysteresis associated with a full spin-state reversal of the [TbPc$_2]^{-}$ ensemble ($J = \pm6$). Artifacts from the 3D vector magnet appear at the sweep reversal points ($\pm$0.280 T). c Polar plot of the resonance frequency at 48 mK during angular sweeps in the $yz$-plane (radial axis spans $0.00\, \mathrm{T}$ to $0.15\,\mathrm{T}$; sweep direction from center outward). A sharp frequency transition along the $z$-axis confirms alignment with the [TbPc$_2]^{-}$ easy axis. d Time-resolved relaxation of the [TbPc$_2]^{-}$ ensemble after saturating at $-0.280$ T. The field is rapidly swept to the setpoint labeled $z_0$ in a, after which the qubit’s resonance frequency is monitored over time. A small drift of the applied vector field during the sequence shifted the effective $z_0$, reducing the frequency visibility and slightly changing its absolute value. Each data point is the average of 100 acquisitions (30 s per point) taken with a chirp rate of 0.267 GHz/s and a frequency binning of 0.1 MHz. The data are fitted with stretched exponentials (see main text), yielding relaxation times $\tau=(107\pm2)\,\mathrm{min}$ and $\tau=(0.8\pm0.3)\,\mathrm{min}$ at 48 mK and 140 mK, respectively.
• Figure 5: Device architecture. False-color scanning electron micrograph of the silicon quantum dot device prior to fabrication of the ESR antenna. The quantum dot, electron reservoir, and single electron transistor are formed in black shaded regions. The three poly-silicon gate layers are shown in blue (top), brown (middle), and red (bottom), respectively.