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Physical Review B

Spin tunneling in the diamond color center coupled to the P1 center

Mohamed Hebbache

Published Nov 16, 2011• 8 citations
Publisher

Abstract

The spin-1 carried by the nitrogen-vacancy (NV${}^{\ensuremath{-}}$) color center of a diamond is a promising candidate as a quantum bit (qubit) for the realization of a solid-state quantum computer. The interaction with the $P1$ center, which is a single substitutional nitrogen atom with spin-$\frac{1}{2}$, converts the NV${}^{\ensuremath{-}}$ qubit to a multilevel system. The 18-level energy diagram of the NV${}^{\ensuremath{-}}$-$P1$ coupled defect pair exhibits several level anticrossings and the spin functions change sign at different values of the applied magnetic field. Beyond each resonance, the two electronic spins of the coupled triplet-doublet system flip individually or in concert, offering possibilities to implement quantum logic gates. Interlevel transitions are also possible. The transition probabilities can be predicted rigorously in the framework of the Landau-Zener theory. The spin flip occurs by quantum tunneling. It is also possible to introduce geometric phases, which can be useful for the realization of phase gates.

DOI
10.1103/physrevb.84.193204

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The spin-1 carried by the nitrogen-vacancy (NV\ensuremath−{}^{\ensuremath{-}}\ensuremath−) color center of a diamond is a promising candidate as a quantum bit (qubit) for the realization of a solid-state quantum computer. The interaction with the P1P1P1 center, which is a single substitutional nitrogen atom with spin-12\frac{1}{2}21​, converts the NV\ensuremath−{}^{\ensuremath{-}}\ensuremath− qubit to a multilevel system. The 18-level energy diagram of the NV\ensuremath−{}^{\ensuremath{-}}\ensuremath−-P1P1P1 coupled defect pair exhibits several level anticrossings and the spin functions change sign at different values of the applied magnetic field. Beyond each resonance, the two electronic spins of the coupled triplet-doublet system flip individually or in concert, offering possibilities to implement quantum logic gates. Interlevel transitions are also possible. The transition probabilities can be predicted rigorously in the framework of the Landau-Zener theory. The spin flip occurs by quantum tunneling. It is also possible to introduce geometric phases, which can be useful for the realization of phase gates.
Impurity spins in semiconductors are potential quantum bits. Entanglement and topological phases are key resources in quantum computation. We prove that the coupled electron spins carried by a diamond nitrogen-vacancy color center (NV${}^{\ensuremath{-}}$) and a single substitutional nitrogen impurity (P1 center) are entangled in the immediate vicinity of the level anticrossing that appears in the Zeeman energy diagram at about 500 G. We also determine the Aharonov-Anandan, Berry, and marginal geometric phases that can be accumulated by the state vectors of this spin system when it is magnetically transported around a closed path. At the resonance where the gap between two energy levels is minimum, the geometric phases undergo discontinuities, and the entanglement of the two electron spins is maximal.
The negatively charged nitrogen-vacancy (NV) center spin in diamond can be used to realize quantum computation and to sense magnetic fields. Its spin triplet consists of three levels labeled with its spin zzz-components of +1, 0, and \ensuremath{-}1. Without external field, the +1 and \ensuremath{-}1 states are degenerate and higher than the 0 state due to the zero-field splitting. By taking the symmetrical and antisymmetrical superpositions of the +1 and \ensuremath{-}1 states as our qubit basis, we obtain the exact evolution operator of the NV center spin under time-dependent magnetic field by mapping the three-level system on time-dependent quantum two-level systems with exact analytical solutions. With our exact evolution operator of the NV center spin including three levels, we show that arbitrary qubits can be prepared from the starting 0 state, and arbitrary rapid quantum logic gates of these qubits can be realized with magnetic fields. In addition, it is made clear that the typical quantum logic gates can be accomplished within a few nanoseconds and the fidelity can be very high because only magnetic field strength needs to be controlled in this approach. These results should be useful to realizing quantum computing with the NV center spin systems in diamond and exploring other effects and applications.
Abstract The controlled and coherent manipulation of individual quantum systems is fundamental for the development of quantum information processing. The nitrogen-vacancy (NV) color center in diamond is a promising system since its photoluminescence is perfectly stable at room temperature and its electron spin can be optically read out at the individual level. We review here the experiments currently realized in our laboratory concerning the use of a single NV color center as the single photon source and the coherent magnetic manipulation of the electron spin associated with a single NV color center. Furthermore, we demonstrate a nanoscopy experiment based on the saturation absorption effect, which allows to optically pin-point a single NV color center at sub-λ resolution. This offers the possibility to independently address two or multiple magnetically coupled single NV color centers, which is a necessary step towards the realization of a diamond-based quantum computer.
A concept combining optics and microwave pulses with the negative charge-state of the nitrogen-vacancy (NV—) center in diamond is demonstrated through experiments that are equivalent to single-qubit gates, and decoherence for this qubit is examined. The spin levels of the ground state provide the two-level system. Optical excitation provides polarization of these states. The polarized state is operated coherently by 35 GHz microwave pulses. The final state is read out through the photoluminescence intensity. Decoherence arises from different sources for different samples. For high-pressure, high-temperature synthetic diamonds, the high concentration of substitutional N limits the phase-memory to a few μs. In a single-crystal CVD diamond, the phase memory time is at least 32 μs at 100 K. 14N is tightly coupled to the electronic spin and produces modulation of the electron–spin echo decay under certain conditions. A two-qubit gate is proposed using this nuclear spin. This demonstration provides a great deal of insight into quantum devices in the solid state with some possibility for real application.
This work investigates the applicability of the nitrogen-vacancy (NV) defect center in diamond for quantum computation and metrology purposes. The NV center is a molecule like defect in the diamond lattice which is optically active and possesses an electron spin in its ground state. The spin can be used as a quantum bit and as a field sensor. The NV center has three major properties enabling individual control of single defects. Its optical properties depend on the spin state, the spin can be polarized optically and the spin state has an exceptionally long lifetime. Single NV centers can be controlled by optical and microwave radiation. Generally, the research on individually controllable quantum systems is not only motivated by quantum computation and communication. With the ongoing miniaturization nowadays electronic and electro-optic devices will soon reach the limit of single quantum building blocks. While in these applications the full complexity of single quantum systems might not be needed, small sensors based on single atoms or molecules might very well take advantage of the susceptibility of quantum coherences to environmental conditions. Major challenges for all approaches towards single quantum system control are the individual addressing, the measurement of the quantum state and the protection of quantum coherence from environmental noise. Today, there is a variety of systems (including the NV center) that allow control on the single quantum level. These are for example single photons, single ions and atoms in traps, single spins in semiconductors or single molecules in solid state systems. Rather mesoscopic examples are superconducting devices, nanomechanical oscillators or surface plasmon polaritons. Regarding the NV center it has been shown that the magnetic moment of its electron spin allows individual sensing and coupling to other surrounding electron and nuclear spins. Especially single nuclear spins were shown to be exceptional quantum memories. In this work small quantum registers of up to 5 spins have been used to test major requirements for a feasible quantum processor. Therefore, mainly artificially created high purity diamond samples with controlled spin and impurity concentration were used. The NV centers were either grown in or created via ion implantation techniques in a controlled fashion. As a first requirement for quantum computation entanglement among up to three spins has been generated and was verified by quantum state tomography. This proves the access of the full Hilbert space. Especially, entanglement among nuclear spins was very long-living. In further experiments this processor was used for first quantum algorithms like super-dense coding and the Deutsch algorithm. In addition, this work demonstrates new methods to initialize nuclear spin qubits into a desired quantum state. This is particularly important as improper initialization inhibits quantum computation. One of these methods is related to dynamic nuclear spin polarization and the other to measurement based state preparation. Nuclear spins in the diamond lattice originate mainly from the C-13 isotope. By artificially altering its content the influence on the NV center spin was investigated. The coherence times of the NV center were increasing inversely with the nuclear spin density. Even increasing nuclear spin density to offer more nuclear spin qubits to an operational quantum register was possible. As an alternative route of scaling up the quantum register pairs of closely spaced NV centers were investigated. For the first time two qubit gates among two NV centers mediated by magnetic dipolar coupling have been realized. Furthermore the sensing ability was demonstrated by measuring the relative distance of the two centers (10 nm) with sub-nm precision. Eventually, this work contains new insight into the electronically excited state of the NV center which allowed a more advanced control of the electron and nuclear spins. A comparably high magnetic field was used to decouple electron and nuclear spins. Finally, this allowed quantum nondemolition measurements on single nuclear spins which manifests in the observation of quantum jumps. The new insight was used to drastically improve the performance of quantum state readout. Summarizing, it was shown that single NV centers and proximal nuclear spins form versatile small quantum registers which can be interconnected with neighboring such NV quantum registers. Although the number of qubits used in this work is still small the experimental results propose a way of how to proceed when building a quantum computer. Regarding quantum metrology, however, the use of such a small register which can sense fields and store and process the results would already outperform a single NV electron spin by orders of magnitude.
Artificial atoms like the nitrogen vacancy (NV) centers in diamond enable the realization of fully functional qubits in a solid at room temperature. The functionalities of all the parts needed to create a quantum computer, such as quantum error correction, couplings, quantum teleportation, and a quantum repeater, have already been experimentally demonstrated. These achievements are expected to influence the industrial development of quantum information technology as well as quantum sensing. Whereas quantum sensing has been established and a large number of organizations are working on new developments in this area, a quantum computer itself remains elusive due to technical reasons and limitations of the available materials. For example, only in recent months has it become possible to electrically readout the NV spin state at the level of a single center and significantly improve the scalability of NV center production. A number of ideas have been proposed to overcome the above-mentioned limitations. This paper summarizes the status of research in the area, details the most promising concepts for development, and discusses factors limiting progress as well as the most recent developments in the field.