Controlled quantum dynamics of Nitrogen vacancy centers in diamond

Color centers in diamond, and in particular the nitrogen-vacancy center (NV center), have proven promising for the emerging field of quantum technologies. In this thesis, new concepts for the manipulation and better understanding of the NV center dynamics will be addressed, along with the proposal of novel fields of application. It comprises (i) a study of the NV coupling to intrinsic acoustical phonons in nanocrystals, (ii) the proposal for the bottom-up creation of NV arrangements on the nanoscale by the ordered arrangement of nanodiamonds directed by biological scaffold structures, (iii) the interferometry with nanodiamonds in search of signatures of quantum gravity and (iv) the creation of an illustrative framework for the analysis and design of hybrid NV-nuclear spin couplings. The NV embedding in the diamond crystal lattice naturally involves the coupling to vibrational degrees of freedom. On the nanoscale, the combination of discrete mode properties with significant phonon coupling strengths has the potential for the coherent coupling of the NV center to selected distinct modes. We analyze the nanodiamond size dependence of the coupling to low-energy acoustical phonon modes, thereby focusing on its (strong) impact revealed in energy shifts on the orbitally distinct NV ground-excited state transition. In this way, the potential for coherent coupling for crystal sizes . 30 nm is shown. Moreover, for the specific example of an elastic sphere, the breathing mode is identified as promising, pairing close to homogeneous interaction with stable mode properties. Schemes for exploiting this phonon mechanism for the conditional manipulation of NV-centers are constructed. This is achieved by introducing the phonon coupling to the ground state by Raman transitions and a direct conditional coupling amongst NV centers is obtained in a dispersive regime. Moreover, several concepts for improving the speed and robustness of such conditional gates are addressed. Scaling NV-centers in a controllable coherently-interacting way remains a crucial milestone for a wide range of quantum applications. In contrast to the implantation approach in bulk crystals, we propose an inverse bottom-up approach by assembling nanodiamonds on the nanoscale in designed biological (protein) lattices. This allows for controlled distances of around ten nanometers, thus overcoming fundamental resolution limitations of implantation techniques imposed by scattering. A complete framework for the implementation of controlled quantum operations in such assembled nanodiamond networks is presented. In particular, we show that the challenging random distribution of the NV symmetry axis, combined with a magnetic field, allows for both beneficial individual addressing and a uniform Ising-type coupling. A detailed study is carried out to analyze the decoherence properties based on a diamond surface noise model; this then leads to the construction of fully decoupled gate interactions by time-addition or second order driving methods. Applications, such as cluster state computation or the simulation of Heisenberg chains are proposed and their viability in this framework is supported by numerical simulations. Interferometry with massive particles has potential in studying decoherence mechanisms, but also for testing fundamental limitations of quantum mechanics. We propose and analyze the interferometry with nanodiamonds in a Ramsey-Bordé setup in view of identifying mass enhanced quantum gravity (QG) modifications of the energy dispersion. A phase suppression mechanism associated with the thermal motion and gravitation turns out to render QG signatures inaccessible in such systems; as a remedy a revised setup based on gravitational momentum inversion is constructed. A careful analysis of the interference pattern for different particles sizes, temperatures and decoherence influences suggests typical nanodiamonds capable to shed light on the controversial discussions in the field of QG. Moreover, simple widely applicable formulas for calculating the interference phase and path contributions are derived. Last, a framework for the interpretation and customization of coherent hyperfine-couplings between a ‘pulsed decoupled’ NV-center and single nuclear spins is introduced. This is based on the filter formalism widely known from decoherence descriptions, with the filter describing the external control on the NV-center. Based on an analysis in the perturbative limit, thereby identifying the relation to semiclassical frameworks and resonance conditions for the pulse spacing, this concept is extended beyond that limitation by relying on ‘sliced evolutions’ of non-equidistant decoupling pulses. This then allows for an intuitive interpretation and design of gate interactions both in the weak and strong coupling limit, thus applicable for single spin sensing and the intended use of nuclear spins as a qubit. List of Publications Parts of this thesis are based on or have been taken from material first published in the following peer-reviewed journals: [A1] A. Albrecht, A. Retzker, F. Jelezko and M. B. Plenio, Coupling of nitrogen vacancy centres in nanodiamonds by means of phonons, New. J. Phys. 15, 083014 (2013), arXiv: 1304.2192. Copyright (2013) by IOP Publishing and Deutsche Physikalische Gesellschaft (Creative Commons Attribution Unported (CC BY 3.0)). Chapter 4. [A2] A. Albrecht, G. Koplovitz, A. Retzker, F. Jelezko, S. Yochelis, D. Porath, Y. Nevo, O. Shoseyov, Y. Paltiel and M. B. Plenio, Self-assembling hybrid diamond-biological quantum devices, New. J. Phys. 16 093002 (2014), arXiv: 1301.1871. Copyright (2014) by IOP Publishing and Deutsche Physikalische Gesellschaft (Creative Commons Attribution Unported (CC BY 3.0)). Chapter 5 and parts of Chapter 3. [A3] A. Albrecht, A. Retzker and M. B. Plenio, Testing quantum gravity by nanodiamond interferometry with nitrogen-vacancy centers, Phys. Rev. A 90 033834 (2014), arXiv: 1403.6038 (2014). Copyright (2014) by the American Physical Society (APS Journals). Chapter 6. Publications not covered in this thesis: [A4] A. Albrecht, A. Retzker, Ch. Wunderlich and M. B. Plenio, Enhancement of laser cooling by the use of magnetic gradients, New. J. Phys. 13, 033009 (2011), arXiv: 1009.2441.