We propose a method for detecting the presence of a single spin in a crystal by coupling it to a high-quality factor superconducting planar resonator. By confining the microwave field in the vicinity of a constriction of nanometric dimensions, the coupling constant can be as high as 5--10 kHz. This coupling affects the amplitude of the field reflected by the resonator and the integrated homodyne signal allows detection of a single spin with unit signal-to-noise ratio within few milliseconds. We further show that a stochastic master equation approach and a Bayesian analysis of the full time-dependent homodyne signal improves this figure by $\ensuremath{\sim}30%$ for typical parameters.
We propose a method for detecting the presence of a single spin in a crystal by coupling it to a high-quality factor superconducting planar resonator. By confining the microwave field in the vicinity of a constriction of nanometric dimensions, the coupling constant can be as high as 5--10 kHz. This coupling affects the amplitude of the field reflected by the resonator and the integrated homodyne signal allows detection of a single spin with unit signal-to-noise ratio within few milliseconds. We further show that a stochastic master equation approach and a Bayesian analysis of the full time-dependent homodyne signal improves this figure by \ensuremath∼30 for typical parameters.
We report on electron spin resonance measurements of phosphorus donors localized in a 200 μm^{2} area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design, we are able to detect around 2×10^{4} spins with a signal-to-noise ratio of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1-10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Because of the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell.
We introduce a multilayer superconducting microwave resonator with sub-Ohm impedance optimized for high coupling strength to single electron spins. The design minimizes the magnetic far-field and therefore achieves a Purcell factor FP>1015. We show several ways to fabricate this type of resonator and present resonators with an intrinsic Q-factor exceeding 2⋅104 at the single-photon level. We further characterize these resonators in magnetic fields up to 500mT. Finally, we evaluate the impact of the achievable Purcell factor on single-spin detection through photon counting and dispersive readout.
Electron spin resonance (ESR) is a powerful spectroscopy method which allows to identify and characterize paramagnetic species. It usually relies on detecting microwave radiation absorbed or emitted by the spins into a microwave resonator tuned to their Larmor precession frequency. Because of the weak spin-microwave coupling, conventional ESR spectroscopy has a low sensitivity. Recent experiments have demonstrated that superconducting quantum circuits have the potential to enhance the spin detection sensitivity to single spin detection; by namely using high quality factor small mode volume resonator. However, these demonstrations have been realized in very restrictive conditions, using well-known spin systems. To probe samples coming from chemistry or biology, quantum-circuit enabled spectrometers have to be adapted to be robust to losses. They have typically two origins: the dielectric losses introduced by the samples, mostly aqueous, and losses coming from the strong magnetic field required to tune the electronic spins to the resonator frequency. This PhD work centered on implementing a resonator that would achieve the same ESR sensitivity while being robust to dielectric losses and strong magnetic fields. Using NbTiN films deposited on sapphire, microwave resonators were shown to have quality factors above Q=105 in magnetic field, even when samples with dielectric losses above tan d > 0.05 were introduced. A study of the resonator intrinsic losses showed marked drops at multiple specific magnetic fields: a signature of coupling to spurious systems. Over the course of the PhD, mitigation nanofabrication techniques for these contaminants were developed, such as hard mask etching and annealing, to remove all but one of this contaminants. Finally, test of the spectrometer on a benchmark species (BDPA, α,γ-Bisdiphenylene-β-phenylallyl, a known ESR marker) were realized.
Strong coupling of semiconductor spin qubits to superconducting microwave resonators was recently demonstrated [X. Mi et al., Nature 555, 599 (2018); A. J. Landig et al., Nature 560, 179 (2018); N. Samkharadze et al., Science 359, 1123 (2018); T. Cubaynes et al., NPJ Quant. Inf. 5, 47 (2019)]. These breakthroughs pave the way for quantum information processing that combines the long coherence times of solid-state spin qubits with the long-distance connectivity, fast control, and fast high-fidelity quantum-non-demolition readout of existing superconducting qubit implementations. Here we theoretically analyze and optimize the dispersive readout of a single spin in a semiconductor double quantum dot (DQD) coupled to a microwave resonator via its electric dipole moment. The strong spin-photon coupling arises from the motion of the electron spin in a local magnetic field gradient. We calculate the signal-to-noise ratio (SNR) of the readout accounting for both Purcell spin relaxation and spin relaxation arising from intrinsic electric noise within the semiconductor. We express the maximum achievable SNR in terms of the cooperativity associated with these two dissipation processes. We find that while the cooperativity increases with the strength of the dipole coupling between the DQD and the resonator, it does not depend on the strength of the magnetic field gradient. We then optimize the SNR as a function of experimentally tunable DQD parameters. We identify wide regions of parameter space where the unwanted backaction of the resonator photons on the qubit is small. Moreover, we find that the coupling of the resonator to other DQD transitions can enhance the SNR by at least a factor of two, a ``straddling'' effect [J. Koch et al., Phys. Rev. A 76, 042319 (2007)] that occurs only at nonzero energy detuning of the DQD double-well potential. We estimate that with current technology, single-shot readout fidelities in the range 82--95% can be achieved within a few $\ensuremath{\mu}\mathrm{s}$ of readout time without requiring the use of Purcell filters.
Quantum emitters respond to resonant illumination by radiating electromagnetic fields. A component of these fields is phase-coherent with the driving tone, while another one is incoherent, consisting of spontaneously emitted photons and forming the fluorescence signal. Atoms and molecules are routinely detected by their fluorescence at optical frequencies, with important applications in quantum technology and microscopy. Spins, on the other hand, are usually detected by {their coherent response} at radio- or microwave frequencies, either in continuous-wave or pulsed magnetic resonance. Indeed, fluorescence detection of spins is hampered {by their low spontaneous emission rate} and by the lack of single-photon detectors in this frequency range. Here, using superconducting quantum devices, we demonstrate the detection of a small ensemble of donor spins in silicon by their fluorescence at microwave frequency and millikelvin temperatures. We enhance the spin radiative decay rate by coupling them to a high-quality-factor and small-mode-volume superconducting resonator, and we connect the device output to a newly-developed microwave single-photon counter based on a superconducting qubit. We discuss the potential of fluorescence detection as a novel method for magnetic resonance spectroscopy of small numbers of spins.
We demonstrate a planar superconducting microwave resonator intended for use in applications requiring strong magnetic fields and high quality factors. In perpendicular magnetic fields of 20 mT, the niobium resonators maintain a quality factor above 25 000 over a wide range of applied powers, down to single photon population. In parallel field, the same quality factor is observed above 160 mT, the field required for coupling to free spins at a typical operating frequency of 5 GHz. We attribute the increased performance to the current branching in the fractal design. We demonstrate that our device can be used for spectroscopy by measuring the dissipation from a pico-mole of molecular spins.