Optical manipulation of the Berry phase in a solid-state spin qubit

Phase relations between quantum states represent a resource for storing and processing quantum information. Although quantum phases are commonly controlled dynamically by tuning energetic interactions, the use of geometric phases that accumulate during cyclic evolution may offer superior robustness to noise. To date, demonstrations of geometric phase in solid-state systems employ microwave fields that have limited spatial resolution. Here, we demonstrate an all-optical method to accumulate a geometric phase, the Berry phase, in an individual nitrogen–vacancy centre in diamond. Using stimulated Raman adiabatic passage controlled by diffraction-limited laser light, we loop the nitrogen–vacancy centre's spin around the Bloch sphere to enclose an arbitrary Berry phase. We investigate the limits of this control due to the loss of adiabaticity and decoherence, as well as its robustness to noise introduced into the experimental control parameters. These techniques set the foundation for optical geometric manipulation in photonic networks of solid-state qubits linked and controlled by light. An all-optical manipulation of the Berry phase based on stimulated Raman adiabatic passage is demonstrated in an individual nitrogen–vacancy centre in diamond. The adiabatic control is 100 times faster than that demonstrated before in atomic systems.

[1]  Roman Kolesov,et al.  Coherent population trapping in a crystalline solid at room temperature , 2005, physics/0505051.

[2]  U. Gaubatz,et al.  Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laser fields. A new concept and experimental results , 1990 .

[3]  D. Leibfried,et al.  Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate , 2003, Nature.

[4]  Klaus Molmer,et al.  Geometric phase gates based on stimulated Raman adiabatic passage in tripod systems , 2007 .

[5]  S. Pancharatnam,et al.  Generalized theory of interference, and its applications , 1956 .

[6]  M. Lončar,et al.  Quantum photonic networks in diamond , 2013 .

[7]  Thomas Schenkel,et al.  Chip-scale nanofabrication of single spins and spin arrays in diamond. , 2010, Nano letters.

[8]  F. Jelezko,et al.  Low temperature studies of the excited-state structure of negatively charged nitrogen-vacancy color centers in diamond. , 2009, Physical review letters.

[9]  S. Gsell,et al.  Deterministic coupling of a single silicon-vacancy color center to a photonic crystal cavity in diamond. , 2014, Nano letters.

[10]  J. Wrachtrup,et al.  All-Optical Preparation of Coherent Dark States of a Single Rare Earth Ion Spin in a Crystal. , 2015, Physical review letters.

[11]  Lee C. Bassett,et al.  Spin-Light Coherence for Single-Spin Measurement and Control in Diamond , 2010, Science.

[12]  S. Berger,et al.  Experimental realization of non-Abelian non-adiabatic geometric gates , 2013, Nature.

[13]  Christian Hepp,et al.  All-optical formation of coherent dark states of silicon-vacancy spins in diamond. , 2014, Physical review letters.

[14]  C. Zu,et al.  Experimental realization of universal geometric quantum gates with solid-state spins , 2014, Nature.

[15]  A single-molecule approach to ZnO defect studies: Single photons and single defects , 2014, 1402.1773.

[16]  Jeeva Anandan,et al.  Non-adiabatic non-abelian geometric phase , 1988 .

[17]  Philip Hemmer,et al.  All-optical initialization, readout, and coherent preparation of single silicon-vacancy spins in diamond. , 2014, Physical review letters.

[18]  Jonathan A. Jones,et al.  Geometric quantum computation using nuclear magnetic resonance , 2000, Nature.

[19]  G. Castagnoli,et al.  Geometric quantum computation with NMR , 1999, quant-ph/9910052.

[20]  S. Berger,et al.  Exploring the effect of noise on the Berry phase , 2013, 1302.3305.

[21]  Stefan W. Hell,et al.  Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin , 2014, Nature Communications.

[22]  Philip Hemmer,et al.  Coherent population trapping of single spins in diamond under optical excitation. , 2006, Physical review letters.

[23]  J I Cirac,et al.  Geometric Manipulation of Trapped Ions for Quantum Computation , 2001, Science.

[24]  D. Golter,et al.  Optically driven Rabi oscillations and adiabatic passage of single electron spins in diamond. , 2014, Physical review letters.

[25]  Takeshi Ohshima,et al.  Isolated electron spins in silicon carbide with millisecond coherence times. , 2014, Nature materials.

[26]  S. Urabe,et al.  Realization of holonomic single-qubit operations , 2013, 1304.6215.

[27]  R. J. Schoelkopf,et al.  Observation of Berry's Phase in a Solid-State Qubit , 2007, Science.

[28]  Gabriele De Chiara,et al.  Berry phase for a spin 1/2 particle in a classical fluctuating field. , 2003, Physical review letters.

[29]  Hayato Goto,et al.  Population transfer via stimulated Raman adiabatic passage in a solid , 2006 .

[30]  M. Markham,et al.  Heralded entanglement between solid-state qubits separated by three metres , 2012, Nature.

[31]  L. Jiang,et al.  Quantum entanglement between an optical photon and a solid-state spin qubit , 2010, Nature.

[32]  Neil B. Manson,et al.  The nitrogen-vacancy colour centre in diamond , 2013, 1302.3288.

[33]  Cefe López,et al.  Materials Aspects of Photonic Crystals , 2003 .

[34]  Hannes Bernien,et al.  Coherent manipulation, measurement and entanglement of individual solid-state spins using optical fields , 2015, Nature Photonics.

[35]  S. Pancharatnam Generalized theory of interference, and its applications , 2013 .

[36]  D. Awschalom,et al.  Ultrafast optical control of orbital and spin dynamics in a solid-state defect , 2014, Science.

[37]  B. Shore,et al.  Coherent population transfer among quantum states of atoms and molecules , 1998 .

[38]  R. N. Schouten,et al.  Unconditional quantum teleportation between distant solid-state quantum bits , 2014, Science.

[39]  Nan Zhao,et al.  Coherent control of single spins in silicon carbide at room temperature. , 2014, Nature Materials.

[40]  Hideo Kosaka,et al.  Entangled absorption of a single photon with a single spin in diamond. , 2015, Physical review letters.

[41]  M. Berry Quantal phase factors accompanying adiabatic changes , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[42]  Environment-assisted quantum control of a solid-state spin via coherent dark states , 2014, 1408.1272.

[43]  Z. Kis,et al.  Qubit rotation by stimulated Raman adiabatic passage , 2002, quant-ph/0307208.

[44]  B. Hensen,et al.  High-fidelity projective read-out of a solid-state spin quantum register , 2011, Nature.

[45]  Bob B. Buckley,et al.  All-optical control of a solid-state spin using coherent dark states , 2013, Proceedings of the National Academy of Sciences.

[46]  Paolo Zanardi,et al.  Holonomic quantum computation , 1999 .