Signatures of discrete time crystalline order in dissipative spin ensembles

Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, an exotic new phase of matter. We present observations characteristic of discrete time crystalline order in a driven system of paramagnetic P-donor impurities in isotopically enriched 28Si cooled below 10 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of discrete time crystalline order. This signal has a finite lifetime of ∼ 100 Floquet periods, but this effect is long-lived relative to coherent spin–spin interaction timescales, lasting ∼ 104 times longer.We present simulations of the system based on the paradigmatic central spin model and show good agreement with experiment. We investigate the role of dissipation and interactions within this model, and show that both are capable of giving rise to discrete time crystal-like behaviour

Nuclear spin decoherence of neutral P-31 donors in silicon: Effect of environmental Si-29 nuclei

Spectral diffusion arising from Si29 nuclear spin flip-flops, known to be a primary source of electron spin decoherence in silicon, is also predicted to limit the coherence times of neutral donor nuclear spins in silicon. Here, the impact of this mechanism on P31 nuclear spin coherence is measured as a function of Si29 concentration using X-band pulsed electron nuclear double resonance. The P31 nuclear spin echo decays show that decoherence is controlled by Si29 flip-flops resulting in both fast (exponential) and slow (nonexponential) spectral diffusion processes. The decay times span a range from 100 ms in crystals containing 50% Si29 to 3 s in crystals containing 1% Si29. These nuclear spin echo decay times for neutral donors are orders of magnitude longer than those reported for ionized donors in natural silicon. The electron spin of the neutral donors “protects” the donor nuclear spins by suppressing Si29 flip-flops within a “frozen core,” as a result of the detuning of the Si29 spins caused by their hyperfine coupling to the electron spin

Line Broadening and Decoherence of Electron Spins in Phosphorus-Doped Silicon Due to Environmental 29^Si Nuclear Spins

Phosphorus-doped silicon single crystals with 0.19 % <= f <= 99.2 %, where f is the concentration of 29^Si isotopes, are measured at 8 K using a pulsed electron spin resonance technique, thereby the effect of environmental 29^Si nuclear spins on the donor electron spin is systematically studied. The linewidth as a function of f shows a good agreement with theoretical analysis. We also report the phase memory time T_M of the donor electron spin dependent on both f and the crystal axis relative to the external magnetic field.Comment: 5 pages, 4 figure

Si-29 nuclear spins as a resource for donor spin qubits in silicon

Nuclear spin registers in the vicinity of electron spins in solid state systems offer a powerful resource to address the challenge of scalability in quantum architectures. We investigate here the properties of 29Si nuclear spins surrounding donor atoms in silicon, and consider the use of such spins, combined with the donor nuclear spin, as a quantum register coupled to the donor electron spin. We find the coherence of the nearby 29Si nuclear spins is effectively protected by the presence of the donor electron spin, leading to coherence times in the second timescale—over two orders of magnitude greater than the coherence times in bulk silicon. We theoretically investigate the use of such a register for quantum error correction (QEC), including methods to protect nuclear spins from the ionisation/neutralisation of the donor, which is necessary for the re-initialisation of the ancillae qubits. This provides a route for multi-round QEC using donors in silicon

Electron Spin Resonance of P Donors in Isotopically Purified Si Detected by Contactless Photoconductivity

Coherence times of electron spins bound to phosphorus donors have been measured, using a standard Hahn echo technique, to be up to 20 ms in isotopically pure silicon with [P]=1014cm-3 and at temperatures ≤4K. Although such times are exceptionally long for electron spins in the solid state, they are nevertheless limited by donor electron spin-spin interactions. Suppressing such interactions requires even lower donor concentrations, which lie below the detection limit for typical ESR spectrometers. Here we describe an alternative method for phosphorus donor ESR detection, exploiting the spin-to-charge conversion provided by the optical donor-bound-exciton transition. We characterize the method and its dependence on laser power and use it to measure a coherence time of T2=130ms for one of the purest silicon samples grown to date ([P]=5×1011cm-3). We then benchmark this result using an alternative application of the donor-bound-exciton transition: optically polarizing the donor spins before using conventional ESR detection at 1.7 K for a sample with [P]=4×1012cm-3, and measuring in this case a T2 of 350 ms. In both cases, T2 is obtained after accounting for the effects of magnetic field noise, and the use of more stable (e.g., permanent) magnets could yield even longer coherence times

Competition between homogeneous and inhomogeneous broadening of orbital transitions in Si:Bi

Contains fulltext : 180733.pdf (publisher's version ) (Open Access

Optical pumping and readout of bismuth hyperfine states in silicon for atomic clock applications

The push for a semiconductor-based quantum information technology has renewed interest in the spin states and optical transitions of shallow donors in silicon, including the donor bound exciton transitions in the near-infrared and the Rydberg, or hydrogenic, transitions in the mid-infrared. The deepest group V donor in silicon, bismuth, has a large zero-field ground state hyperfine splitting, comparable to that of rubidium, upon which the now-ubiquitous rubidium atomic clock time standard is based. Here we show that the ground state hyperfine populations of bismuth can be read out using the mid-infrared Rydberg transitions, analogous to the optical readout of the rubidium ground state populations upon which rubidium clock technology is based. We further use these transitions to demonstrate strong population pumping by resonant excitation of the bound exciton transitions, suggesting several possible approaches to a solid-state atomic clock using bismuth in silicon, or eventually in enriched 28Si