Isoelectronic centers as building blocks for quantum - PDF document

Isoelectronic ¡centers ¡as ¡building ¡blocks ¡ for ¡quantum ¡information ¡processing Recent ¡progress ¡on ¡isoelectronic ¡centers ¡ and ¡their ¡applications Sébastien ¡Francoeur Polytechnique ¡de ¡Montréal �1 Qubit initialization and control, two qubit gates, and read out. | 0 i | 0 i | 0 i | 0 i | 1 i | 1 i | 1 i | 1 i | 0 i | 0 i | 0 i | 0 i | 1 i | 1 i | 1 i | 1 i | 0 i | 0 i | 0 i | 0 i | 1 i | 1 i | 1 i | 1 i Scalable any two-qubit gates requires 1) uniforme and predictable qubits, 2) and the large dipole moment. �2

Well-known families of nanostructure Quantum ¡dots Epitaxial ¡QD Electrostatic ¡QD Colloidal ¡QD Atomic ¡defects Si: ¡P Diamond: ¡NV N P V �3 Isoelectronic centers � Atomic or Molecular-sized optically-active defects in semiconductors �4

What impurities make Isoelectronic traps? Crystal GaAs:N' + Isovalent impurity �5 Exciton binding mechanism to isoelectronic traps 1) ¡Primary ¡charge ¡capture 2) ¡Exciton ¡formation ~ a 0 �6

Isoelectronic centers Single( Dyad( impurity( Triad( Tetrad( �7 Isoelectronic centers �8

Uniformity and predictability of atomic defects Dyads ¡of ¡various ¡interatomic ¡separations Triads Nearest anionic neighbor Infinite separation 250 meV Exciton ¡ emission ¡ 10 ¡mev 150 meV energy A-Line Intensity (a.u.) NN 4 NN 6 NN 1 NN 4 NN 3 A-Line A-Line + 2 TO/LO + TO/LO + TO/LO Tetrads 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 Energy (eV) �9 Optical dipole moment Optical dipole moment (Debye) Monolayer fluctuations (D=0.021 e nm) 100 InAs QDots 10 NV centers Si:P 1 0.1 �10

Optical dipole moment Optical dipole moment (Debye) Monolayer fluctuations (D=0.021 e nm) GaAs:NN 100 InAs QDots 10 NV centers Si:P 1 0.1 �11 Sample growth and instrumentation � Some experimental details �12

Samples Molecular beam epitaxy Thanks ¡to ¡our ¡collaborators: ¡ ¡ ¡ ¡ J.F. ¡Klem ¡ ¡ ¡ Sandia ¡National ¡Lab ¡, ¡USA Institut ¡Néel, ¡France ¡ ¡ ¡ R. ¡André ¡ ¡ ¡ U. ¡de ¡Montréal ¡ ¡ ¡ S. ¡Roorda ¡ ¡ ¡ École ¡Polytechnique ¡ ¡ ¡ R. ¡Masut ¡ ¡ ¡ ¡ ¡ Y. ¡Sakuma ¡ ¡ Nat. ¡Inst. ¡for ¡materials ¡science, ¡Japan �13 Cryogenic confocal microscope �14

Single isoelectronic center luminescence Nitrogen ¡dyad ¡of ¡C 2v ¡symmetry ¡in ¡GaAs . Energy= ¡1.50812 ¡eV 500 nm 5 µ m �15 Excitonic fine structure � Spin and symmetry �16

Excitonic states in systems of reduced symmetry �17 Experimental spectra of a nitrogen molecule Emisson ¡[001] Polarization angle �18 Energy

Coherent optical control of an exciton � Rabi oscillations of an exciton qubit. �19 The Bloch sphere … is used to represent the superposition states of two eigenstates, e.g. a qubit. ✓ θ ◆ ✓ θ ◆ | ψ i = cos | 0 i + (cos φ + i sin φ ) sin | 1 i 2 2 | 0 i θ 1 1 p 2 ( | 0 i � | 1 i ) p 2 ( | 0 i � i | 1 i ) φ 1 1 y = ˆ p 2 ( | 0 i + i | 1 i ) x = ˆ p 2 ( | 0 i + | 1 i ) | 1 i �20

Rotations on the Bloch sphere (at resonance) In a rotating frame, an optical pulse rotates the qubit state counterclock-wise around the x -axis. Ω t = π Ω t = π 2 | 0 i | 0 i 1 1 1 1 p 2 ( | 0 i � | 1 i ) p 2 ( | 0 i � | 1 i ) p 2 ( | 0 i � i | 1 i ) p 2 ( | 0 i � i | 1 i ) R x R x 1 1 1 1 p p 2 ( | 0 i + | 1 i ) 2 ( | 0 i + | 1 i ) p 2 ( | 0 i + i | 1 i ) p 2 ( | 0 i + i | 1 i ) | 1 i | 1 i �21 Experimental difficulty: rejecting the control excitation pulse Control pulse rejection through ∆ E L Laser Linear polarization angle (degrees) 150 µeV 1) detection of a witness state of orthogonal 240 polarization and 210 2) time-selection using an gated ultrafast APD. 180 Y 150 c 120 Measured y Y 90 τ xy X z 60 x X 350 µeV Laser ~15 ps dark 30 0 x PL intensity Gating 1507.6 1508.0 1508.4 1508.8 z window Energy (meV) dark y PL ~ 6.2 ns Ω R Rabi 1 ns flopping Time Measured PL 0 �22

Rabi oscillations For a gaussian pulse of duration 𝞾 p , repetition frequency f r , and area A , the rotation angle is ✓ 2 ⇡ ◆ 1 4 r ✓ = µ 1 ⌧ p √ P ~ ln 2 f r Acn ✏ 0 Excitation power (W) K: pulse characteristics Dipole moment (Cm) and physical constants ✓ µK ◆ √ I P L ∝ | c 1 | 2 = sin 2 After the control pulse, the PL intensity is P 2 Pulse area ( π ) a The oscillation period is related to the dipole moment. | µ | = e | h 0 | x | 1 i | = 55 D I II III b �23 Excitation induced dephasing Raby oscillations in But not in a Pulse area ( π ) quantum dots are isoelectronic strongly damped. centers III II I PRB 72, 35306 (2005) b Exciton + acoustic phonon hamiltonian X ω k b † k b k + | X i h X | [ g k b † H = ω 0 | X i h X | + Ω ( t ) cos( ω l t ) [ | 0 i h X | + | X i h 0 | ] + k + g ∗ k b k ] k Two Coherent Exciton-phonon Phonon bath levels interaction term. interaction system. Deformation potential Γ 2 ( t ) = KT Ω 2 ( t ) = ( D e − D h ) 2 g q = q D e − D h k B T Ω 2 ( t ) p 2 ρ ~ ω q V 4 π ~ 2 ρ c 5 s �24

Coherent optical control of an exciton � Ramsey interferometry �25 Ramsey interference with two π /2 pulses A sequence of two pulses is necessary to achieve full control of the all possible qubit states. θ 1 = π θ 2 = π 2 2 φ = ω 1 τ f 3) The second pulse has a phase 2) During time 𝞾 f , the wavefunction is 1) The first pulse creates the difference of φ with the wavefunction. superposition state. free to evolve. In the rotating frame, This imply that the rotation axis is the Bloch vector is stationary, since along δ =0. R = (cos φ , sin φ , 0) | 0 i | 0 i | 0 i z z z y y y R x x x x R | 1 i | 1 i | 1 i �26

Full qubit manipulation of bound excitons θ 1 = π θ 2 = π 2 2 φ = ω 1 τ f 3 π 5 π π 7 π 0 2 π 3 π 4 π 2 π 2 2 2 PL intensity (a.u.) Fringe amplitude τ c = 50 ps 0 1 2 3 4 5 6 τ f (fs) �27 Exciton decoherence θ 1 = π θ 2 = π 2 2 φ = ω 1 τ f As the time separation between the two pulses increases, the exciton wavefunction loses coherence. The initial pure state transform into a mixed state and the fringe amplitude decreases. | 0 i | 1 i Ramsey interference at large delays allows determining the coherence time of the exciton. �28

Coherence time T 2 * of 115 ps a b PL intensity (a.u.) τ c = 50 ps 0 1 2 3 4 5 6 τ f (fs) c Laser Exciton τ c (ps) �29 Charged exciton Charge ¡exciton Exciton �30

Negatively charged exciton Charged ¡exciton γ X * = 5.3 µ eV T -2 Exciton ¡(not ¡shown) γ X = 2.0 µ eV T -2 Electron Hole E X* X XX �31 Summary A semiconductor atomic defect with high optical dipole moment. | 0 i Control over the whole Bloch PL intensity (a.u.) sphere θ φ τ c = 50 ps | 1 i 0 1 2 3 4 5 6 τ f (fs) Charged excitons for single electron qubits �32 Acknowledgements: Gabriel Éthier-Majcher , P. St-Jean, Alaric Bergeron

Negatively charged exciton Electrons Hole Sum m s1 m s2 m j m s1 +m j ¡ m s2 +m j 3/2 Forbidden σ + Heavy-­‑hole ¡X -­‑3/2 Forbidden σ − 1/2 -­‑ ¡1/2 1/2 σ + π Light-­‑hole ¡X -­‑1/2 σ − π Singlet, ¡S= 0 �33 Molecules of various symmetries Dyads One ¡impurity Anion T d C 2v D 2d C 3v �34

Why explore other types of nanostructures? � Large-scale quantum computing is a formidable challenge. �35 Experimental spectra of a nitrogen molecule z x 0 x z 0 y 2 + µ B g e σ z B z + K J z B z + L J z 3 B z + C B z 2 ∑ ∑ H = − a i σ i J i + F i J i i = x , y , z i = x , y , z Exchange) )Zeeman)0)) Zeeman)0)) Diamagnetic) Crystal(field( interaction) electron) hole) shift) �36

Localization of the electron wavefunction V] 60 Diamagnetic Shift [ µ e 1.99 ± 0.06 B 2 40 20 0 − 6 − 4 − 2 0 2 4 6 Magnetic field [T] $ ' 2 〉 2 〉 C h = 1.27 µ eV C = C e + C h = 〈 r e + 〈 r h 2 〉 = 1.62 nm 〈 r e & ) & ) T 2 m e m h % ( �37