Observing spontaneous emission in spins is challenging. Nuclear spins in 800 MHz NMR exhibit a free space spontaneous emission rate of ~1E-22 Hz, while for electron spins at a typical X-band (10 GHz) frequency this rate is ~1E-12 Hz. Spontaneous emission therefore presents a negligible contribution to the spin relaxation time, which is instead driven by a variety of other processes, such as spin-phonon interactions. When a two-level system is placed in a resonant cavity, spontaneous emission is enhanced through the Purcell effect , which has been observed for several decades for optical transitions in a variety of atomic and solid state systems . Nevertheless, for typical cavity Q-factors and mode volumes in conventional ESR, even this enhanced relaxation rate remains on the order of a year^-1 and does not compete with intrinsic spin relaxation mechanisms.
By coupling an ensemble of bismuth donor spins in silicon to a 7.3 GHz micron-scale high-Q superconducting resonator, we are able to achieve a Purcell factor of over 1E12 leading to a cavity-enhanced relaxation rate of up to 3 Hz, well in excess of the natural spin relaxation rate of this system. In this way, by controlling the cavity-spin detuning by a few MHz it is possible to tune the spin relaxation time by over three orders of magnitude. This represents an important step in the coupling of spins to microwave photons and the development of microwave-domain quantum memories.
In addition to cavity-based engineering of spin relaxation time (T1), we also show the ability to control the spin coherence time (T2) of bismuth donors in silicon, making use of so-called “clock transitions” where the first-order dependence of the electron spin resonance frequency on magnetic field goes to zero. Around such transitions, the coherence time can be tuned by two orders of magnitude, leading to T2 times as long as 3 seconds (the longest reported for electron spins in the solid state). Overall, these results show bismuth donors in silicon to be a rich and versatile spin system, with potential applications in quantum information processing and storage.
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 A. Bienfait et al., Cavity enhanced spin relaxation, Nature 531 74 (2016)
 G. Wolfowicz et al., Atomic clock transitions in silicon-based spin qubits, Nature Nano. 8 561 (2013)