Coherence time of decoupled nuclear spins in silicon

Abstract

We report NMR experiments using high-power, RF decoupling techniques to show that a 29 Si nuclear spin qubit in a solid silicon crystal at room temperature can preserve quantum phase for 10 9 precessional periods. The coherence times we report are longer than for any other observed solid-state qubit by more than four orders of magnitude. In high quality crystals, these times are limited by residual dipolar couplings and can be further improved by isotopic depletion. In defect-heavy samples, we provide evidence for decoherence limited by 1/f noise. These results provide insight toward proposals for solid-state nuclear-spin-based quantum memories and quantum computers based on silicon.PACS numbers: 03.67. Lx, 03.67.Pp, 76.60.Lz, 82.56.Jn Quantum information processing devices outperform their classical counterparts by preserving and exploiting the correlated phases of their constituent quantum oscillators, which are usually two-state systems called "qubits." An increasing number of theoretical proposals have shown that such devices allow secure long-distance communication and improved computational power [1]. Solid-state implementations of these devices are favored for reasons of both scalability and integration with existing hardware, although previous experiments have shown limited coherence times for solid-state qubits. The development of quantum error correcting codes [2] and fault tolerant quantum computation [3] showed that largescale quantum algorithms are still theoretically possible in the presence of decoherence. However, the coherence time must be dauntingly long: approximately 10 5 times the duration of a single quantum gate, and probably longer depending on the quantum computer architecture [1]. The question of whether a scalable implementation can surpass this coherence threshold is not only important for the technological future of quantum computation, but also for fundamental understanding of the border between microscopic quantum behavior and macroscopic classical behavior.Experimentally observed coherence times (T 2 ) for various qubit implementations are shown in Table I. The atomic systems shown -trapped ions and molecular nuclei in liquid solution -have already been employed for small quantum algorithms [6,13]; not coincidentally, they show very high values of Q, the product of the qubit frequency ω 0 /2π and πT 2 . Most solid-state qubits show smaller values of Q; as we demonstrate in this Letter, however, the long coherence times we observe in solid-state 29 Si nuclei afford them a Q and ΩT 2 as high or higher than atomic systems, indicating this system's promise for solid-state quantum computing.Many promising qubits and coherence time measurements are not mentioned in Table I either because reliable experimental data are not available, or because the existing experimental data are taken under conditions not sufficiently similar to the corresponding quantum computer architecture. For example, electron spins bound to phosphorous donors in pure, isotopically depleted silicon also show prom...

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

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Storage of quantum coherences as phase-labelled local polarization in solid-state nuclear magnetic resonance

“…In all the samples mentioned already, the spin-spin decay time measured with a Hahn echo sequence (T HE 2 ) [34] was about an order of magnitude longer than the FID characteristic time (T * 2 ), evidencing the line inhomogeneity. Magnetization tails have been observed in 29 Si, C 60 and Y 2 O 3 [13,41,42], in adamantane under 1 H decoupling [57] and indirectly in 31 P in EPR experiments [20].…”

“…From the beginning, it was verified that there is no dependence on the amount of donors or acceptors in the 29 Si polycrystalline sample even when these could change the linewidths and spin-lattice relaxation time by one order of magnitude. Experiments were repeated on 29 Si single crystals and Pyrex, as well as 13 C in C 60 , yielding the same behaviour.…”

“…Notice that the spin dipolar interactions decay with the cube of the distance and that the gyromagnetic factors of 29 Si and 13 C are approximately one-fifth and one-fourth that of 1 H, rendering 29 Si- 29 Si and 13 C- 13 phase shifts with respect to the first p/2 pulse, respectively), and considering the number of phases (one or two) for the p pulses in each cycle, these sequences were named as follows:…”

Creating nuclear spin entanglement using an optical degree of freedom

“…Employing molecular systems as "quantum hardware" [6,7] offers the advantages of high reproducibility, chemically engineered system properties, and the potential for selfassembly into more complex functional units. In general, nuclear spins are widely considered to be the most promising quantum bits (qubits) for a quantum memory in solid-state systems, since they have remarkably long coherence times [8]. However, they are also hard to manipulate on a fast time scale, as nuclei are usually only weakly coupled.…”