1. Donor Impurities in Semiconductors as Qubits Cameron Johnson Oct. 26, 2015 Phys 485 Image: https://sharepoint.washington.edu/phys/research/optospinlab/Pages/Project-Page-III-V-QI.aspx

2. Sources D. P. DiVicenzo, Physical implementation of quantum computation, Fortschr. Phys. 48, 9-11, 771- 783 (2000) B. E. Kane, A silicon-based nuclear spin quantum computer, Nature 393, 133-137 (1998) P. M. Koenraad, M. E. Flatte, Single dopants in semiconductors, Nature Materials 10, 91-100 (2011) KM. Fu, W. Yeo, S. Clark, C. Santori, C. Stanley, M. Holland, Y. Yamamoto, Millisecond spin-flip times of donor-bound electrons in GaAs, Phys. Rev. B. 74, 21304(R) (2006) D. Press, K. DeGreve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Hofling, A. Forchel, Y. Yamamoto, Ultrafast optical spin echo in a single quantum dot, Nature Photonics 4, 367-370 (2010) J. Tribollet, Theory of the electron and nuclear spin coherence times of shallow donor spin qubits in isotopically and chemically purified zinc oxide, Eur. Phys. J. B 72, 531-540 (2009) E. S. Kumar, I. P. Anderson, Z. Deng, F. Mohammadbeigi, T. Wintschel, D. Huang & S. P. Watkins, Effect of group-III donors on high-resolution photoluminescence and morphology of ZnO nanowires grown by metalorganic vapour phase epitaxy, Semicond. Sci. Technol. 28, 045014 (2013)

3. Motivations Quantum computing could be faster and more efficient than classical computation Kane quantum computer proposed 1998 using donor impurities as qubits Donor impurities can have high photon-spin transfer efficiencies and would be an easily scalable system Donors are abundant and naturally occurring in semiconductors Have yet to find a fully scalable system with sufficient coherence times from any qubit candidate Gives a physical understanding of these novel quantum systems Image: https://en.wikipedia.org/wiki/Kane_quantum_computer

4. What is a qubit Quantum bit, analogous to classical bit smallest quanta of information either (0) or (1) Difference, qubit is superposition of │0 〉 and │1 〉 Many physical objects can act as qubits: photons, trapped ions, quantum dots, superconductors, nanowire core-shell, semiconductor impurities Image: https://commons.wikimedia.org/wiki/File:Sphere_bloch.jpg

5. Requirements of systems of qubits Scalable system Donor impurities are perhaps the most reasonable candidate in terms of scalability with the extensive work done in semiconductor devices and technologies Coherence time >> gate time Must be able to keep quantum information stored while gate operations are being performed Donors do not have the largest coherence time to gate time ratio but it is enough to keep them in the running Qubit specific measurability Biggest hurdle for donors Experimentally difficult to isolate single impurities in lattice structures

6. What is a donor impurity N-type impurity Neutral donor D 0 ground state: impurity and bound electron Donor bound exciton D 0 X excited state: D 0, bound electron and hole Use the bound electron spin state of D 0 as qubit D+ e- h+ D0D0 D0XD0X

7. Why donor impurities They are like naturally occurring quantum dots Very accessible systems Can be optically manipulated No need for traps or complicated external structures; impurities are permanently part of a crystal lattice structure Promising coherence times reported as high as a few milliseconds and ultrafast optical manipulation gate times can be on the order of picoseconds Relatively easy on chip device integration Image: http://www.minsocam.org/msa/collectors_corner/arc/color.htm

8. The downsides Work best in extreme conditions Magnetic fields as high as 3-10 Tesla Temperatures as low as a few Kelvin Decoherence processes not always understood spin orbit coupling/phonons Perturbation hamiltonians can depend on impurity concentration, symmetry of lattice structure Need high purity samples with low impurity concentrations to limit spin interaction with the environment

9. Different structures Bulk Generally want low laying impurities Hard to isolate single impurities Nanowires Can lithographically isolate nanowires With low impurity concentrations can potentially isolate single impurities Nanostructures can degrade optical properties of defects Images: E. S. Kumar, I. P. Anderson, Z. Deng, F. Mohammadbeigi, T. Wintschel, D. Huang & S. P. Watkins, Effect of group-III donors on high-resolution photoluminescence and morphology of ZnO nanowires grown by metalorganic vapour phase epitaxy, Semicond. Sci. Technol. 28, 045014 (2013)

10. Structures (cont.) Epitaxial Layers/Heterostructures Can be designed to control strain, electric and magnetic fields, and impurity concentration and depth Bandgap can be controlled with layer thickness and order Single impurities could be spatially resolved Layers are applied applied by molecular beam epitaxy Images: http://www.scielo.org.co/scielo.php?pid=S0120-56092011000100015&script=sci_arttext&tlng=en & P. M. Koenraad, M. E. Flatte, Single dopants in semiconductors, Nature Materials 10, 91-100 (2011)http://www.scielo.org.co/scielo.php?pid=S0120-56092011000100015&script=sci_arttext&tlng=en

11. Relaxation times T 1 and T 2 T 1 (spin flip) is the time it takes for spins precessing about external magnetic field to return to the equilibrium position Much easier to measure and serves as upper limit to T 2, usually measured first T 2 (coherence) is the time it takes for spins to dephase from each other while precessing about an external magnetic field Bloch Equations:

12. Measuring T 1 (spin flip time) Ground state splits in magnetic field Optical pumping Resonantly excite │1 〉 Pumps spin states into │0 〉 Probe/collect After sufficient wait time (T 1 ) spins return to equilibrium Plotting collection intensity against t wait times gives exponential decay governed by T 1 │1 〉 │0 〉 D0XD0X D0D0 Pump Collect Pump/ Probe Sequence Wait Probe Collection Intensity t wait  e h=g e  B B

13. Measuring T 2 (coherence time) Use spin echo technique Optically pumped into │0 〉 state Spins precess about magnetic field at larmor freq.  e Circular polarized  /2 pulse coherently rotates spin at effective Rabi freq.  eff creating a superposition of│0 〉 state │1 〉 state Circular polarized  pulse reverses dephasing direction Second circular polarized  /2 pulse On second pump donor emits photon if spin was flipped back to │1 〉 state during rotation sequence │1 〉 │0 〉 D0XD0X D0D0 Pump Pump/ Pulse Sequence Pump   /2  eff  /2 Pulse  Pulse Collect Pump  e h=g e  B B

14. T 2 (cont.) Collection intensity plotted against pulse separation 2* , shows Ramsey interference fringes Amplitude of Ramsey fringes plotted against pulse sequence offset time 2*T gives decaying exponential governed by T 2 T  Collection Signal Intensity (Constant T) 22 Intensity Amplitude 2T Intensity Amplitude Pump/ Pulse Sequence Pump   /2 Collect Pump

15. Conclusion Donor impurities are candidates for qubits that can be optically controlled Structures are being created that can extend coherence times and spatially isolate single impurities Donor impurities have many attractive qualities that researchers can exploit Pump-probe method is used to measure T 1 Pump-  /2-  -  /2-pump sequence is used to measure T 2