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arXiv:2205.00589 · Quantum Science and Technology

Electron spin coherence on a solid neon surface

Qianfan Chen, Ivar Martin, Liang Jiang, Dafei Jin

Published Jul 20, 2022• 13 citations

Abstract

Abstract A single electron floating on the surface of a condensed noble-gas liquid or solid can act as a spin qubit with ultralong coherence time, thanks to the extraordinary purity of such systems. Previous studies suggest that the electron spin coherence time on a superfluid helium (He) surface can exceed 100 s. In this paper, we present theoretical studies of the electron spin coherence on a solid neon (Ne) surface, motivated by our recent experimental realization of single-electron charge qubit on solid Ne. The major spin decoherence mechanisms investigated include the fluctuating Ne diamagnetic susceptibility due to thermal phonons, the fluctuating thermal current in normal metal electrodes, and the quasi-statically fluctuating nuclear spins of the 21 Ne ensemble. We find that at a typical experimental temperature about 10 mK in a fully superconducting device, the electron spin decoherence is dominated by the third mechanism via electron–nuclear spin–spin interaction. For natural Ne with 2700 ppm abundance of 21 Ne, the estimated inhomogeneous dephasing time T 2 * is around 0.16 ms, already better than most semiconductor quantum-dot spin qubits. For commercially available, isotopically purified Ne with 1 ppm of 21 Ne, T 2 * can be 0.43 s. Under the application of Hahn echoes, the coherence time T 2 can be improved to 30 ms for natural Ne and 81 s for purified Ne. Therefore, the single-electron spin qubits on solid Ne can serve as promising new spin qubits.

DOI: 10.1088/2058-9565/ac82c3

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Abstract A single electron floating on the surface of a condensed noble-gas liquid or solid can act as a spin qubit with ultralong coherence time, thanks to the extraordinary purity of such systems. Previous studies suggest that the electron spin coherence time on a superfluid helium (He) surface can exceed 100 s. In this paper, we present theoretical studies of the electron spin coherence on a solid neon (Ne) surface, motivated by our recent experimental realization of single-electron charge qubit on solid Ne. The major spin decoherence mechanisms investigated include the fluctuating Ne diamagnetic susceptibility due to thermal phonons, the fluctuating thermal current in normal metal electrodes, and the quasi-statically fluctuating nuclear spins of the 21 Ne ensemble. We find that at a typical experimental temperature about 10 mK in a fully superconducting device, the electron spin decoherence is dominated by the third mechanism via electron–nuclear spin–spin interaction. For natural Ne with 2700 ppm abundance of 21 Ne, the estimated inhomogeneous dephasing time T 2 * is around 0.16 ms, already better than most semiconductor quantum-dot spin qubits. For commercially available, isotopically purified Ne with 1 ppm of 21 Ne, T 2 * can be 0.43 s. Under the application of Hahn echoes, the coherence time T 2 can be improved to 30 ms for natural Ne and 81 s for purified Ne. Therefore, the single-electron spin qubits on solid Ne can serve as promising new spin qubits.

Abstract Recent experiments show ∼0.1 ms coherence time for a single electron charge qubit on a solid neon surface. This remarkably long coherence time is believed to result from the intrinsic purity of solid neon as a qubit host. In this paper, we present theoretical studies on the decoherence mechanisms of an electron’s charge (lateral motional) states on solid neon. At the typical experimental temperature of ∼10 mK, the two main decoherence mechanisms are the phonon-induced displacement of neon surface and phonon-induced modulation of neon permittivity (dielectric constant). With a qubit frequency increasing from 1 GHz to 10 GHz, the charge coherence time decreases from about 366 s to 7 ms and from about 864 s to 24 ms, respectively, limited by the two mechanisms above. The calculated coherence times are at least one order longer than the observed ones at ∼6.4 GHz qubit frequency, suggesting plenty of room for experimental improvement.

Electrons floating in vacuum provide a clean platform for quantum information processing owing to their isolation from material defects. In particular, electrons on solid neon have emerged as a promising qubit platform because of their potentially long coherence times. Here, toward spin-qubit realization, we couple a single electron on solid neon to a magnetic-field-compatible superconducting NbTiN nanowire resonator. We realize a charge qubit and demonstrate microwave readout and coherent control, with Rabi frequencies up to 76 MHz, an order of magnitude larger than in previous studies. Under strong driving, we observe a qubit frequency shift from nonlinear interactions with the intense microwave field. Deterministic electron trapping at an intended position remains challenging due to solid neon surface roughness; we characterize the electron's position from its differential coupling to distinct electrodes. Although not trapped at an intended position, our estimates indicate that spin-qubit demonstrations remain feasible.

Electrons floating on condensed noble-gas substrates form a remarkably clean material system that is minimally influenced by the underlying host material, and recent experiments have explored their potential as a qubit platform. In particular, single electrons floating on solid neon thin films have attracted significant interest because they exhibit long coherence times when probed with superconducting circuits at frequencies around 6 GHz. Surprisingly, however, the energy spectrum of these qubits resembles that of a two-level-system defect more than the spectrum expected from the Coulomb potential defined by the bias electrodes. In this thesis, I first review floating-electron systems and the experimental methods used to probe their quantum states. I then show that electron-on-neon qubits with transition frequencies of a few GHz are observed only on neon films deposited on silicon surfaces, and not on neon films deposited on sapphire. Motivated by this observation, I propose a model in which a floating electron on the neon surface interacts with fixed positive charge defects in the native oxide at the silicon surface. Using realistic parameters, this model reproduces the observed voltage-dependent transition frequency and coupling strength of electron-on-neon qubits.

Electrons trapped above cryogenic substrates such as liquid helium and solid neon form exceptionally clean physical systems, since they reside in vacuum and are largely isolated from environmental noise. A recent breakthrough has been the realization of charge qubits using electrons on solid neon surfaces, with coherence times reaching T2 = 2T1 ≈ 100 µs. In this article, we describe in detail the preparation of cryogenic substrates, electron deposition and the measurement of electron mobility. We further discuss the differences in surface morphology between helium and neon, their impact on mobility and qubit performance, and emphasize the necessity of systematic surface characterization as a means to optimize cryogenic substrate preparation and electron deposition.

The promise of quantum computing has driven a persistent quest for new qubit platforms with long coherence, fast operation, and large scalability. Electrons, ubiquitous elementary particles of nonzero charge, spin, and mass, have commonly been perceived as paradigmatic local quantum information carriers. Despite superior controllability and configurability, their practical performance as qubits via either motional or spin states depends critically on their material environment. Here we report our experimental realization of a new qubit platform based upon isolated single electrons trapped on an ultraclean solid neon surface in vacuum. By integrating an electron trap in a circuit quantum electrodynamics architecture, we achieve strong coupling between the motional states of a single electron and microwave photons in an on-chip superconducting resonator. Qubit gate operations and dispersive readout are used to measure the energy relaxation time

T_1

of

15~\mu

s and phase coherence time

T_2

over 200 ns, indicating that the electron-on-solid-neon qubit already performs near the state of the art as a charge qubit.

Levitating electron qubit on the surface of solid neon has recently emerged as a promising and intrinsically noise-resilient platform for quantum information processing. Their ultra-clean, inert environment suppresses conventional decoherence pathways associated with lattice disorder, charge traps, and nuclear-spin baths that limit coherence in semiconductor qubits. Yet, uncontrolled surface features such as bumps, valleys, and electrode-defined gaps can bind electrons unintentionally, contributing charge noise and inducing spin-orbit coupling mediated decoherence. To address this challenge, we propose an engineered interface in which a dielectric layer is deposited beneath the solid neon to provide an atomically smooth template, eliminating surface-roughness induced trapping. By selectively etching this dielectric layer at desired qubit locations, deterministic potential minima can be engineered to reliably capture electrons while suppressing unwanted surface bound states. We perform large-scale Schrodinger and Poisson simulation to compare the existing and proposed strategies of electron trapping on neon, obtaining good agreement with recent experimental measurements.