High-Cooperativity Coupling of Electron-Spin Ensembles to Superconducting Cavities

Abstract

Electron spins in solids are promising candidates for quantum memories for superconducting qubits because they can have long coherence times, large collective couplings, and many quantum bits can be encoded into the spin-waves of a single ensemble. We demonstrate the coupling of electron spin ensembles to a superconducting transmission-line resonator at coupling strengths greatly exceeding the cavity decay rate and comparable to spin linewidth. We also use the enhanced coupling afforded by the small cross-section of the transmission line to perform broadband spectroscopy of ruby at millikelvin temperatures at low powers. In addition, we observe hyperfine structure in diamond P1 centers and time domain saturation-relaxation of the spins.An eventual quantum computer, like its classical analog, will make use of a variety of physical systems specialized for different tasks. Just as a classical computer uses charge-based transistors for fast processing and magnetic hard drives for long term information storage, a quantum computer might use superconducting qubits for processing [1] and ensembles of electron spins as quantum memories [2,3], linked by single microwave photons. Although other microscopic systems have been proposed for use in a hybrid architecture [4][5][6][7], electron spins complement superconducting qubits particularly well. They feature similar transition frequencies, do not require trapping, and can be packed densely. Furthermore, a single ensemble could be used to store many qubits using holographic encoding techniques [3] demonstrated classically for nuclear [8] and electron [9] spins.In this Letter, we demonstrate the first step toward realizing a solid-state quantum memory: coupling an electron spin ensemble to an on-chip superconducting cavity at powers corresponding to a single cavity photon. We observe megahertz spin-photon interaction strengths in both ruby Cr 3+ spins and N substitution (P1) centers in diamond. A parallel effort by Kubo, et. al.[? ] sees similar coupling to nitrogen vacancy (NV) centers in diamond. In doing so we develop a platform for the study of electron spin resonance (ESR) physics in picoliter mode volumes, millikelvin temperatures, and attowatt powers. Finally, we perform time-resolved saturation/relaxation measurements of the P1 centers, a precursor to full pulsed control of the system. ESR studies the microwave response of electron spins at their resonant frequency in a magnetic field. Samples are conventionally placed inside a 3D high quality-factor (Q) cavity which enhances the sensitivity by confining photons with the spins and extending the interaction time [10]. In this work, several 1D cavities are capacitively coupled to a common feedline on a sapphire chip. We place the spins within the mode volume by fabricating the device on doped sapphire (ruby - Fig. 1a), attaching a substrate on top of an existing device (diamond - Fig. 1b), or simply spin-coating the surface (DPPHnot shown). The single spin-photon coupling is given by g s /2π = m 0 (µ 0 ω/2hV c ) 1/2 ,...

Microwave transitions as a signature of coherent parity mixing effects in the Majorana-transmon qubit

“…The first (second) set of wave functions is periodic (antiperiodic) under a change of j by 2p. The Cooper-pair tunnelling operator modifies the eigenvalue ofn by ±1, hence only couples states internally within the two subspaces (9) and (10). In contrast, the single-electron tunnelling operator intermixes the two subspaces.…”

“…In addition, the phase-dependent part of the electron tunnelling operator ensures that the eigenvalue ofn changes by ±1/2. Hence, states of the form (9) can only couple to states of the form (10).…”

“…The properties of solid-state qubits and resonators and coupling to photons can be engineered to some degree by design and this enables the combination of several different subsystems to form hybrid devices that take advantage of their relative strengths 9,10 . In turn, this leads to new methods of probing physical systems and, where highly quantum coherent subsystems are involved, to establishing control over their quantum variables.…”

Magnetic field resilient superconducting fractal resonators for coupling to free spins

“…[1][2][3] Recently, an ensemble of spins embedded in a crystal has become a subject of quantum manipulation by interaction with a superconducting resonator. 4,5 Spin systems are very promising quantum objects since their coherence times can be very long. However, the magnetic field required to bring free-electron spins into resonance with microwave field exceeds many times the field a standard coplanar waveguide (CPW) resonator can withstand.…”

Coherent Rabi Dynamics of a Superradiant Spin Ensemble in a Microwave Cavity

“…2(b)]. This technique has been demonstrated for spin ensembles coupled to both 3D volume resonators [31] and 2D superconducting microresonators [32]. The spin transition frequency (ω s ) is varied through resonance with the cavity (ω c ) by changing the Zeeman splitting with a magnetic field (B 0 ), which results in an avoided crossing with a clear splitting showing that the system is in the strong-coupling regime.…”