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Dissipative dynamics of spins in quantum dots A.O. Caldeira Universidade Estadual de Campinas Campinas, BRAZIL

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Collaborators Harry Westfahl Jr. – LNLS – BRAZIL Frederico Borges de Brito – UNICAMP – BRAZIL Gilberto Medeiros-Ribeiro – LNLS – BRAZIL Maya Cerro – UNICAMP/LNLS – BRAZIL

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O que é dissipação quântica? Movimento dissipativo + Mecânica quântica Uma breve preparação

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Movimento dissipativo

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Movimento em um meio viscoso Dissipação + Flutuações O movimento Browniano

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A Mecânica Quântica através de alguns exemplos O tunelamento de uma partícula quântica

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A Mecânica Quântica através de alguns exemplos O tunelamento coerente de uma partícula quântica

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Mecânica Quântica X Dissipação A mecânica quântica se aplica a sistemas nas escalas atômicas e sub-atômicas: sistemas isolados ou sujeitos a interações externas controladas. A dissipação ocorre em sistemas macroscópicos sujeitos à influência (incontrolável) do ambiente onde estão inseridos.

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Onde os dois efeitos podem ser simultaneamente observados? ? Quântico (microscópico) Clássico (macroscópico)

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Sistemas meso e nanoscópicos Superconducting Quantum Interference Devices (SQUIDs): O paradigma H

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Sistemas magnéticos Partículas magnéticas Tunelamento coerente de partículas magnéticas ( spins por partícula)

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Sistemas de dois níveis Vários sistemas aqui apresentados envolvem sobreposições de duas configurações

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Dispositivos e qubits Dissipação destrói a coerência necessária para o funcionamento do processador quântico: descoerência

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Spin eletrônico em pontos quânticos Um possível candidato a qubit NANO ???

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Introduction Main goal –Study of the possibility of implementation of solid state qubits: spins in self assembled quantum dots Candidates and drawbacks –Photons » non-interacting entities –Optical Cavity » weak atom-field coupling –ion traps » short phonon lifetime –NMR » low signal –Superconducting devices » decoherence –Spins in quantum dots » ?

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Quantum bits (DiVincenzo '01) Well defined two level system –Single electron spin Quantum dots: Coulomb blockade + Pauli exclusion Addressing –Well defined energy splittings g-factor (Landé) engineering Reset –Energy splitting » kT Electronic Zeeman frequency Gates –Resonant EM Field Microcavity Long decoherence times –Isolated from dissipative channels Strong electronic confinement

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Quantum bits (DiVincenzo '01) Well defined two level system –Single electron spin Quantum dots: Coulomb blockade + Pauli exclusion

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Self Assembled Quantum Dots STM scans of self-assembled island formation through epitaxial growth of Ge on a Si substrate. Left scans: 50nm x 50nm. Right scan: 35nm x 35nm (Courtesy of G. Medeiros-Ribeiro)

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Dots Model Electronic confinement

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Coulomb Blockade 1e 2e 5e 3e 4e 6e s-shellp-shell by G. Medeiros-Ribeiro

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Quantum bits (DiVincenzo '01) Addressing –Well defined energy splittings g-factor (Landé) engineering Reset –Energy splitting » kT Electronic Zeeman frequency

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Addressing and resetting SRL- strain reducing layer gAgA gAgA gAgA gAgA gBgB gCgC samples A, D sample C g-factor engineering G. Medeiros-Ribeiro, E. Ribeiro, H. W. Jr., Appl. Phys. A, 2003; cond-mat/

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Quantum bits (DiVincenzo '01) Gates –Resonant EM Field Microcavity Long decoherence times –Isolate from dissipative channels Strong electronic confinement

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Magnetic moment (red vector) in a magnetic field (brown vector) : the conservative dynamics –Precession of the moment around the external field direction Dissipative spin dynamics

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Relaxation dynamics –Landau-Lifshits damping (yellow arrow) drives the system towards a collinear state

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Noise – Fluctuating terms (green arrow) to our equations of motion Dissipative spin dynamics

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Microscopic dissipative spin dynamics Quantum noise and dissipation –Damping and Noise from microscopic interaction with lattice phonons Static Field: Noise+Fluctuations: Phonons Oscillating Field (microcavity):

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Microscopic dissipative spin dynamics Quantum dissipation formulation: x z y Noise and dissipation

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Bloch-Redfield equations –Linear differential equations of motion (quantum average of components) Determined by noise time correlation function x z y Microscopic dissipative spin dynamics

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Fluctuating magnetic field (noise) Electrons: Phonons: Spin-Orbit Interaction: Orbital degrees of freedom: 2D Harmonic Oscillator states Optical Acoustic e-Ph interaction: Piezoelectric Deformation Potential Magneto- elastic Rashba Dresselhaus Fluctuating magnetic fields

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Dissipation Mechanism No bath No spin-orbit interaction

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No bath Spin-Orbit interaction Dissipation Mechanism

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Orbital contact with the phonon bath Non-interacting spin and orbit

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Dissipation Mechanism Orbital contact with the phonon bath Spin-orbit interaction –Indirect spin entanglement with the bath

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Lateral – - LQD (Hanson et al 03) – - VQD (Fujisawa et al 02) – - SAQD (Medeiros-Ribeiro et al 99) Vertical (frozen): Electronic Confinement Spin-Orbit Hamiltonian: parameters:

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Acoustic Phonon Bath orbital bath spectral function piezoelectric – deformation potential GaAs InAs Approximate form of the Hamiltonian

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Effective Bath of Oscillators Equivalent Hamiltonian: Laplace transform of the equations of motion for the spin: allows us to define an effective spectral function

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Spin Orbit Phonon bath –B is the generalized incomplete beta function As seen by the spins... where

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Bath resonance Behaviour of the effective bath spectral function Piezoelectric coupling: H. W. Jr. et al. Phys. Rev B. 70 (2004)

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Dissipative Mechanism weak coupling Bath resonance strong coupling

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Effective spectral function Low frequency limit ( and ) Always super-ohmic – See also (Khaetskii & Nazarov '01) – Can be ohmic! High frequency limit ( )

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Microscopic dissipative spin dynamics x z y General expression for the microscopic spin dynamics: The Bloch-Redfield equation

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Microscopic dissipative spin dynamics General expression for the coefficients is the free spin time evolution operator

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Microscopic dissipative spin dynamics Long time asymptotic behavior –(No driving) Damped precession around the static field direction

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Microscopic dissipative spin dynamics

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Driven spin dynamics Transverse external field Useful parameters for the model detuning effective field amplitude dephasing

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Driven spin dynamics Peaks:

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Driven spin dynamics Peak:

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Two distinct time regimes Driven spin dynamics Short time dynamics Long time dynamics

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Resonant dynamics

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Very long decoherence (relaxation) times –Good for keeping quantum information –Bad for reseting

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Very long decoherence (relaxation) times –Good for keeping quantum information –Bad for reseting Resonant dynamics

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Short time dynamics Resonant dynamics

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Very long decoherence (relaxation) times –Good for keeping quantum information –Bad for reseting Resonant dynamics

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Very long decoherence (relaxation) times –Good for keeping quantum information –Bad for reseting Resonant dynamics Resonance dominated

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Resonant dynamics

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Bulk values

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Off-resonance dynamics Bulk values

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Bath assisted cooling – A high degree of polarization can be achieved in short times with a sequence of (ns) short pulses A. E. Allahverdyan et al., Phys. Rev. Lett. 93 (2004) Reset pulses –Use the large dissipation mechanism (cooling) –Reset times O(ns)

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Summary Indirect dissipation mechanism: Spin Orbit Phonon Non-perturbative approach reveals a new resonance and new regimes of dissipation Perturbative regime only valid for large confinement energies (SAQD) Solution of the Bloch-Redfield equations reveals two dynamical regimes Short time dynamics dominated by the bath resonance Thanks: HP-Brazil, FAPESP, CNPq

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