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Meeting of FIRST QIP Project/Quantum Cybanetics Kyoto, Dec. 15, 2011 |↑> θ α |↓> Manipulation and detection of electron charge/spin qubits Agenda • • • • • Coherent control of spins Measurement of spins New gear : spin-orbit interaction Unpleasant neighbors : nuclear spins Topics Yasuhiro Tokura NTT Basic Research Laboratories FIRST Project, theory subtheme Quantum Cybanetics, semiconductor nano-system FIRST research theme Theory of physical qubits In collaboration with experimental groups spin qubit system, quantum interface • Entanglement of two spin qubits (Tarucha, U. Tokyo) • Interference circuits to initialize and analyze flying spin qubits (Aharony, Ben Gurion U.) • Back-action of charge detector (Kubo, poster Thu-3) • Coherent coupling of flux-qubit and NV ensemble (Semba NTT, Nemoto NII) • Quantum computing with coherent photon conversion (Munro) Build/predict long-term research directions through own/integrated theoretical activities in collaboration with experimental groups. 2005.8.18 那覇平和通り Q cybanetics research theme Control, detection, and transfer of quantum states in semiconductor nanostructure Spin manipulation, detection S. Tarucha, U. Tokyo T. Ota, NTT BRL • Control of spin-orbit interaction in QD (Oiwa, Tarucha, U. Tokyo) • Transport in QD with g-tensor modulation (Ono, Riken) • Improved spin detection scheme with field gradient • Quantitative analysis of dynamical nuclear spin pumping (Nazarov, TUD, Ono, Amaha, Riken) • Quantum capacitance of a few electrons in coupled QD (Ota, NTT) 2005.8.18 那覇平和通り Coherent control of spins Measurement of spins New gear : spin-orbit interaction Unpleasant neighbors : nuclear spins Topics Two qubits system with split micro-magnets Dumping of the Rabi oscillation is originating from nuclear spin fluctuations Rabi frequency is order of 1MHz – need to be faster R. Brunner et al., Phys. Rev. Lett. 107, 146801 (2011). 5 Manipulation of two spin states J. Petta et al. Science (05) cf T. Hatano et al. Science (05). SWAP operation One spin manipulation (Hadamard) + two spin SWAP operations L-ESR 3π/2 |↑� + |↓� √ |↑, ↑� → ⊗ |↑� → 2 Charge moves � (SWAP + L-ESR π2 ) (SWAP2 + L-ESR π2 ) → → 1 2 {|↑, ↑� |↑, ↑� − |↓, ↓� − √ 2S0 } No charge move → Distinguish this change by QPC charge detector 6 Demonstration of partial SWAP and entanglement Solid lines: theory with being averaged over the nuclear spin random distribution Estimation of concurrence: no effect of nuclear spin fluctuation is taken into account. 7 Two-qubit Hamiltonian with Zeeman offset H = 1 1 J⊥ (σ̂1+ σ̂2− + σ̂1− σ̂2+ ) + Jz σ̂1z σ̂2z 2 4 1 1 + EZ (σ̂1z + σ̂2z ) + δ(σ̂1z − σ̂2z ), 2 4 EZ |↑, ↓� ω δ ≡ ≡ 1 (E1Z + E2Z ), 2 E1Z − E2Z θ Bloch vector obeys precession frequency x |↑, ↓� + i |↓, ↑� √ 2 y |↑, ↓� + |↓, ↑� √ 2 1 ω≡ 2� � 2 δ 2 + J⊥ around the axis determined by δ 2 δ 2 + J⊥ cos θ = � |↓, ↑� Bloch sphere spanned with two electron Sz=0 basis 8 SWAP cannot be accomplished by controlling J once Two spin state dynamics is determined by the evolution operator: Û (t) = |↑, ↑� i 1 ( 2 Jz +EZ )t −� e 0 0 0 |↑, ↓� 0 cos ωt − i cos θ sin ωt −i sin θ sin ωt 0 |↑, ↓� θ |↑, ↓� + i |↓, ↑� √ 2 ω |↓, ↑� 0 −i sin θ sin ωt cos ωt + i cos θ sin ωt 0 |↓, ↓� i 1 0 0 0 e− � ( 2 Jz −EZ )t |Ψ(t)� = Û (t)|Ψ(0)� x |↑, ↓� + |↓, ↑� √ 2 y |↓, ↑� 9 . SWAP by three π pulses SWAP operation is realized with a combination of three π pulses for a given fixed δ. z π/4 2θ1 − θ2 = π/2 π/4 < θ1 < π/2 θ2 π/2-θ2 θ1 θ1 TSW AP = = = 2T1π + T2π π π + 2 2ω1 2ω2 π� δ δ � {2 � + } 2 2 2 2 δ δ + J⊥1 δ + J⊥2 This scheme cannot realize √SWAP. x π/4-θ2/2 10 SWAP by two exchanges and one zero-J pulses Alternative SWAP operation realized with a combination of three pulses for a given fixed δ, allowing a √SWAP. We assume: J > Time evolution operator: Usw U√sw = = U (t, J ) ≡ i −� Hex t e U (T, J ) · U (τ, J = 0) · U (T, J ) τ τ U ( , J = 0) · U (T, J ) · U ( , J = 0) 2 2 |↑, ↓� Operation times are determined by τ T = = δ δ 2 (π − arcsin √ ) 2 2 δ √ J −δ 2 √ sin−1 δ2 + J 2 δ2 + J 2 √ 2J ω θ |↑, ↓� + i |↓, ↑� √ 2 y |↓, ↑� x |↑, ↓� + |↓, ↑� √ 2 11 Coherent control of spins Measurement of spins New gear : spin-orbit interaction Unpleasant neighbors : nuclear spins Topics Spin-charge conversion/charge detection N N-1 N+1 J. M. Elzerman, et al., Nature 430, 431 (2004). Spin-to-charge conversion Level separation EZ >> kBT Destructive measurement A high sensitive charge sensor is realized by a quantum point contact, but how to detect spin ?` Signal Idot IQPC QPC electrometer Signal only discriminates spin singlet/triplet or just spin flip! K. Ono, et al., Science 297, 1313 (2002). New spin detection scheme Non-destructive both spin readout with micro-magnet and microwave Y. –S. Shin, et al., Phys. Rev. Lett. 104, 046802 (2010). Backaction dephasing by a quantum dot detector Environment The quantum dot detector (QDD) couples to the reservoir with a large number of degrees of freedom. Thermal noise, Charge noise, Current noise,… Backaction by coupling with an environment • Capacitive coupling to neighboring QDs in multi-qubit systems • Spin-charge conversion in spin qubits Origin of backaction dephasing γd1: Charge noise γd2: Nonequilibrium current noise related charge noise Visibility of AB oscillations in linear conductance T. Kubo, Poster TODAY Coherent control of spins Measurement of spins New gear : spin-orbit interaction Unpleasant neighbors : nuclear spins Topics SOI in a parabolic quantum dot External uniform magnetic field Rashba spin-orbit interaction (SOI) Hamiltonian HSOI = � × p� · �σ λR E Effective field is assumed to normal to plane • Self-organized InAs quantum dot on GaAs contacted laterally • Large (anisotropic) g-factor ~ 5 • Quasi-two dimensional anisotropic confinement potential S. Takahashi, et al., Phys. Rev. Lett. 104, 246801 (2010). Control of SOI by a side gate Anti-crossing of two two-electron levels • SOI and g-factor can be controlled with side gate Y. Kanai, et al., Nature Nanotechnology 6 511, (2011). R. Deacon et al., Phys. Rev. B 84, 041302(R) (2011). Fig. The strength of SOI, Δ, controlled by a side gate. Inset shows the InAs quantum dot (red) sandwiched with electrodes. Aharonov-Bohm-Casher interferometer Controlled spin-orbit interaction and magnetic flux in a diamond-like loop - works as an emitter, rotator, and detector of flying spin qubits Magnetic flux φ Effective field from Rashba spin-orbit interaction, α Coupled diamonds offer more flexible, and ideal realization of Datta-Das spin transistor A. Aharony, Y. Tokura, Guy Z. Cohen, O. Entin-Wohlman, and S. Katsumoto, Phys. Rev. B 84, 035323 (2011). Perfect spin filter β=.05π β=.15π β=.25π β =.27π β =.25π β =.23π Coherent control of spins Measurement of spins New gear : spin-orbit interaction Unpleasant neighbors : nuclear spins Topics Nuclear Spin Bath Problem Contact interaction to nuclei: 69 Ga, 71Ga, 75As (I=3/2) in GaAs QD Flip-flop 50 nm 2 ⎛ I + S − + I − S + ( ) H HF = A ø x ⎜ ⎝ e Bext N=105 to 106 nuclei in GaAs QD 2 ⎞ + I Z S Z ⎟ ⎠ Nuclear spins are dynamically polarized Btot because of the long lifetime (~min.). Bext Overhauser shift (ΔEZeeman) …Shift of ESR condition µ Inhomogeneous broadening of ESR condition Phase fluctuation (or dephasing) in the ensemble measurement T2*=10 to 30 ns Bnuc Decoherence mechanism by electron spin mediated spin diffusion T ~> 1µs L. Cywinski, et al., Phys. Rev. B 79, 245314 (2009). 2 W. A. Coish, et al., Phys. Rev. B 81, 165316 (2010). Coherence time of spin qubits • Hyperfine coupling with the nuclear spins is the dominant factor R. Brunner, et al., to be submitted. Dynamical nuclear spin pumping: DNP Instead of conventional Fermi’s golden rule, we calculate DNP rate using new scheme by electron spin response and correlation function. Danon and Nazarov, Phys. Rev. B 83, 245306 (2011). E- Hysteresis loops of nuclear spin polarization :stable fixed point Energy ε ε=2 ε=4 ε=6 <Kz> EZ ε=-6 ε=-4 ε=-2 -EZ Magnetic field sweep d<Kz>/dt = P±peak �K z � − 1 + [C± (K0± − �K z �)]2 τN E+ <Kz> d�K z � dt Spontaneous symmetry breaking We found the condition when the difference of the nuclear spin polarizations between the two QDs becomes finite. Note: • The physical origin of τN: diffusion • Statistical fluctuation about the average value • Limit cycle around unstable fixed point • Quantum entanglement, interaction with the environment Coherent control of spins Measurement of spins New gear : spin-orbit interaction Unpleasant neighbors : nuclear spins Topics LETTER doi:10.1038/nature10463 Efficient quantum computing using coherent photon Nature 478, 360 (2011) conversion N. K. Langford1,2,3, S. Ramelow1,2, R. Prevedel1,4, W. J. Munro5,6, G. J. Milburn7,1 & A. Zeilinger1,2 Single photons quantum information carriers: they The storyaresoexcellent far ... have suggested that they cannot in fact produce phase shifts large enough were used in the earliest demonstrations of entanglement1 and in for NLOQC because of spectral correlations created between the interthe production of the highest-quality entanglement reported so acting fields20. Other work, however, shows that these difficulties can be • 2,3. Efficient linear optics Knill,processing Laflamme Milburn, Nature 409, 46 (2001) However, current schemes for QC: preparing, and &circumvented far in the related case of strong, second-order nonlinear (x(2)) measuring them are inefficient. For example, down-conversion pro- interactions by carefully engineering the phase-matching conditions21. linear vides randomly timed,QC: single Nielsen, photons4, and • heralded, Opticalbutcluster-state PRL 93, 040503 (2004) Coherent photon conversion is an alternative nonlinear approach 5 optics gates are inherently probabilistic . Here we introduce a deter- that uses coherent oscillations between different multi-excitation • …process—coherent photon conversion (CPC)—that pro- states. The underlying process is a nonlinear interaction between m ministic vides a new way to generate and process complex, multiquanta bosonic modes that coherently converts single excitations in some of states for photonic quantum information applications. The tech- the modes (depending on the precise form of the interaction) into nique uses classically pumped nonlinearities to induce coherent single excitations in the remaining modes. A key principle of CPC is oscillations between orthogonal states of multiple quantum excita- that this basic nonlinearity can in turn be generated by pumping some One example of CPC, on a pumped four-wave-mixing • tions.One process tobased provide a whole toolbox ofmodes components fornonlinearity QCMC of a higher-order with applications strong classical fields. This interaction, is shown to yield a single, versatile process that provides induces an effective coupling between the quantum modes that can be e.g. ⇒ addresses all DiVincenzo Criteria a full set of photonic quantum processing tools. This set satisfies the tuned and enhanced by the classical pumps, even to the point where DiVincenzo criteria for a scalable quantum computing architecture6, the effective ⇒ high-quality, heralded single-photon sources interaction is stronger than naturally occurring couplings including deterministic multiqubit entanglement gates (based on a of the same form. A similar effect is achieved in photon-pair sources Fock-state filter high-quality heralded based on four-wave mixing in photonic crystal fibres. Such systems novel form of⇒ photon–photon interaction), single- and multiphoton states free from higher-order imperfec- have produced some of the highest-brightness photon-pair sources tions, and robust, high-efficiency detection. It can also be used to with very low pump powers7, and precise dispersion engineering produce heralded multiphoton entanglement, create optically and fibre-structuring technologies have allowed optimization of these switchable quantum circuits and implement an improved form of sources to produce ultrabright, high-purity, heralded single photons4. down-conversion with reduced higher-order effects. Such tools are To illustrate the potential of CPC, here we focus on a novel case that valuable building blocks for many quantum-enabled technologies. has very interesting properties for quantum optics applications and Finally, using photonic crystal fibres we experimentally demonstrate which is based on the following standard four-wave-mixing interquantum correlations arising from a four-colour nonlinear process action involving four distinct frequency modes (a, b, c and d): suitable for CPC and use these measurements to study the feasibility 4,7 of reaching the deterministic regime with current technology . Our H~cab{ c{ dzc! a{ bcd{ ð1Þ What we have now… Parametric Processes Standard Spontaneous Parametric Down-conversion (SPDC) (non-depleted pump) photon pairs higher-order terms Stronger χ(2) nonlinearities via pumped χ(3) (4-wave mixing) processes • χ(3) nonlinearities < χ(2) • nonlinearity can be enhanced (and tuned) by a pump laser • near-degenerate frequencies possible (e.g., all in telecom band) • all materials possess χ(3) nonlinearity Applications Solving the DiVincenzo Criteria - scaleable photon QC with CPC initialised multiphoton sources high-efficiency measurement Other Applications • two-qubit entangling (CZ) gates • • • • • • heralded entangled states (Bell pairs, GHZ states) error correction protocols single-photon sources n-photon Fock filters better down-conversion switchable gates for QC circuits … Very early results • • • ΓL ~ 10-4 for 1W 532nm ΓL ~ π/2 for 100% χ(3) (chalcogenide) ~ 103 χ(3) (silica) ⇒ 103 improvement • Measured efficiency with off-the-shelf components shows we re within reach of deterministic regime with PCFs (using chalcogenides) ΓL ~ 10-5 ~ 29 ± 1 counts / sec Future work • experiment with chalcogenide PCFs Future directions Spin measurement Non-demolition measurement and characterize the back-action Amicable relationship to nuclei Quantum nature of ensemble nuclear spins through DNP Explore to suppress the fluctuation of nuclear spins Small scale quantum circuits Propose faster operation scheme and evaluate its fidelity New directions Explore possible quantum interfaces: local spin/flying qubits (Q-bus)