Quantum Computation with Spins and Excitons in Semiconductor Quantum Dots (Part III)

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Department of Physics and Astronomy Michigan State University, East

1 Quantum Computation with Spins and Excitons in Semiconductor Quantum Dots (Part III) Carlo Piermarocchi Condensed Matter Theory Group Department of Physics and Astronomy Michigan State University, East Lansing, Michigan Dipartimento di Fisica, Pisa, Italy July 11 th,14 th, 15 th 2008

Where is Michigan State University? www.msu.

2 Where is Michigan State University? East Lansing 46K Students 10K Graduates 36K Undergraduates

3 Research Groups Astronomy / Astrophysics (10 faculty) Condensed Matter Physics (17) Nuclear Physics (16) Particle Physics (18)

4 Astronomy / Astrophysics

5 Condensed Matter Physics Nano-Science Spintronics Biophysics Institute for Quantum Science W.M.Keck Microfabrication Facility

6 Nuclear Physics National Superconducting Cyclotron Laboratory Research: basic nuclear physics Supported by NSF (~M$15/year) Faculty: Physics (16), Chemistry (2) Ph.D. program ranked #2 in USA

7 Particle Physics Experimental group working on detectors (D0 and CDF) at Fermilab and ATLAS (CERN);D0 collaboration spokesperson Theory Group

8 Cavity Polaritons Polaritons and spin coupling in quantum computing architectures q Bragg polaritons in quantum dot lattices

9 Planar Microcavities Spacer Mirrors Fabry-Pérot resonator Quantization of the em field in the z direction L c K z ω c = ncav K 2 = Nπ L c SEMICONDUCTOR MICROCAVITIES

10 Polaritons: Half-light half-matter particles Semiconductor Cavity QED C. Weisbuch et al. (1992) Upper Polariton Reflectivity Photon Exciton Lower Polariton

11 Photons in a cavity have a mass π k E = c k + E0 + L 2M γ M γ π = 5 M γ 10 me cl Polariton-mixing is k-dependent (J.J. Hopfield, 56) Polaritons have a photon-like mass

Sept 28 2006 Bose Einstein Condensation of Polaritons J.

00001 x m 0 T ~ 100 K t ~ 1-10 ps BEC ATOMS 100,000 x m 0 T

12 Sept Bose Einstein Condensation of Polaritons J. Kasprzak et al. (2006) Mass T Lifetime POLARITONS x m 0 T ~ 100 K t ~ 1-10 ps BEC ATOMS 100,000 x m 0 T ~ 10 nk t ~ 1 s Bottleneck-effect F. Tassone, C. Piermarocchi at al. (1997)

13 Can polaritons in planar microcavities be useful for Quantum Computing?

14 The Range Problem in Quantum Computing Architectures Qubits B. Kane Science (1995) Common problem to many semiconductor spin-qubit architectures ~ 10 nm Polaritons can induce a very Long Range Spin-Qubit Coupling

15 Optical RKKY: Itinerant excitons mediate a spin interaction QW Charged QD (donors) as spin qubits C. Piermarocchi, P.Chen, L.J.Sham, G.D.Steel, PRL (2002) Conduction band J s eff s 1 2 Jeff κ = e 2M X R / κ δ Valence band δ = ω E X p

16 Optical spin coupling with polaritons π k E = c k + E0 + L 2M γ Polariton-mixing is k-dependent cavity upper polariton lower polariton Polaritons have a photon-like mass exciton M γ π = 5 M γ cl 10 me QW Spin qubits Mirrors Light polariton mass Long range spin coupling

17 Polariton-mediated Ising component has a very long range J e f R y * D J X J P p s D B * D ( ) = eff X x x y y P z z H J s s s s J s s G. Quinteiro Rosen, J Fernández-Rossier, and C Piermarocchi, PRL (2006)

18 Polariton splitting causes spin anisotropy e: J z =±1/2 h: J z =±3/2 J z =±2 J z =±1 QW Ω R QW+Cavity Upper Polariton J z =±1 Dark states J z =±2 Lower Polariton J z =±1 A spin flip necessarily implies polariton-dark states mixing

19 Dimensionality mismatch in light-matter coupling Quantum Well Mirrors Quantum Dot Exciton couples to single Photon Exciton couples to a Photon Continuum Photon Exciton Photon Exciton

20 Quantum Dot Rabi Splitting 0D cavity Photon+0D quantum dot exciton Nature 432 p. 197 p.200 (2004)

21 2D photons coupled to 2D array of Quantum Dots Mirror L Photon a Exciton Quantum Dots q q+g Exciton couples to discrete photon modes differing by reciprocal lattice vectors G

22 Hamiltonian: exciton in QD lattice and 2D photons i e N q i i R q i i = 1 ( ) q BZ H hq = ( ) = RL G q G q G q G q G q q q x c h A g A A G q q h.. ) ( ) ( σ ω σ ω σ Fourier transform of the localized states Lattice momentum q is in the first Brillouin Zone (BZ) of the dot lattice Umklapp excitonphoton coupling Γ X W q q G BZ Normal coupling

23 The reduced Zone Scheme Consider the Photon q+g as quasiparticle labelled by a quantum number G and with momentum q (restricted to 1 st BZ) Umklapp-Photon G has energy dispersion ω ( q) = ω( q G) G G = G = G = 0 1 G = q x First BZ 0 G = 0

24 Bragg Polaritons Idea: Create polaritons in the neighborhood of a Bragg plane! QW-like polaritons 2 Bragg polaritons Have small momentum q~ q x 1 st BZ Have large momentum q at the edge of the BZ BZ BZ BZ BZ E. M. Kessler, M. Grochol, C. Piermarocchi, Phys. Rev. B

25 Square lattice: X-Point Bragg Polaritons a=150 nm, dot size= 40 nm, GaAs BZ X-direction The UP has a local minimum Y-direction e V D ~2 mev e V D q The LP has a saddlepoint q X-Bragg polaritons have strong in-plane asymmetry

The upper polariton (UP) mode Valley-like dispersion The excitonic component 0.1 qy @2pêaD 0-0.1 0.4 0.5 0.

26 The upper polariton (UP) mode Valley-like dispersion The excitonic component q half matterhalf light Photon-like mass in y-direction (~10-5 m 0 ) Even smaller in x-direction (~10-8 m 0 )

27 π-polaritons in micro-cavities 1D Periodic Modulation C. W. Lai et al. Nature (2007)

28 Dirac Polaritons The UP has a local minimum The LP has a local maximum Three photon branches are intersecting Isotropic mass

29 Dirac Polaritons on Square Lattices e V D ~2 mev q The UP has a local minimum The LP has a local maximum Four photon modes are intersecting BZ The dot size and lattice spacing can be optimized to maximize the Rabi splitting as at zone boundary

30 The Upper Polariton and Lower Polariton at M UP LP q q Isotropic extremely small mass for UP and LP One central polariton mode is slow photon mode, photon mass increase ~L/a

31 QW Can polariton effects be useful for Quantum Computing? Charged QD (donors) Mirrors Quantum Well Polaritons Long range spin coupling Continuous-discrete mismatch Dirac polaritons Quantum Dot Lattice Quantum memory

32 Lu Sham UC San Diego Guillermo Quinteiro Rosen, Univ. Buenos Aires, Argentina Joaquin Fernandez Rossier Alicante, Spain Po Chung Chen Tsing-Hua Taipei Eric Kessler, MPI Garching, Germany Allan MacDonald U Texas Austin

33 Disorder Energy disorder Oscillator strength disorder Positional disorder E E E Quantum dots Impurities

34 Absorption spectra M-point Oscillator strength Energy Positional s w ~ g s q ~ 0.5g s R ~ 0.5a Polaritonic effects the most sensitive to energy disorder. M. Grochol and C. Piermarocchi, arxiv: (Accepted in Phys Rev B)

35 Multi-spin coupling Dot energy levels Coupling exciton Effective Hamiltonian

36 CNOT-gate error Ideal one-qubit operation No decoherence Detuning 3 High fidelity gate operation in short time (t G << T 2 ) possible. M. Grochol and C. Piermarocchi, arxiv:

Microcavity Exciton-Polariton

Microcavity Exciton-Polariton Neil Na ( 那允中 ) Institute of Photonics Technologies National Tsing-Hua University 5/3/2012 Outline Microcavity Exciton-polariton QW excitons Microcavity photons Strong coupling