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**Dissipative dynamics of spins in quantum dots**

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

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**Movimento dissipativo**

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**Movimento dissipativo**

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? Clássico**

(macroscópico) Quântico (microscópico)

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**Superconducting Quantum Interference Devices (SQUIDs):**

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

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**Tunelamento coerente de partículas magnéticas**

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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**NANO ??? Um possível candidato a qubit**

Spin eletrônico em pontos quânticos

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**Introduction Main goal Candidates and drawbacks**

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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**Electronic confinement**

Dots Model

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**Electronic confinement**

Coulomb Blockade 1e 2e 5e 3e 4e 6e s-shell p-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**

g-factor engineering samples A, D sample C gB gC gA gA gA gA SRL- strain reducing layer 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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**Dissipative spin dynamics**

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

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**Dissipative spin dynamics**

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

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**Dissipative spin dynamics**

Noise Fluctuating terms (green arrow) to our equations of motion

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**Microscopic dissipative spin dynamics**

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

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**Microscopic dissipative spin dynamics**

Quantum dissipation formulation: Noise and dissipation x z y

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**Microscopic dissipative spin dynamics**

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

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**Electrons: Fluctuating magnetic field (noise)**

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

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**Dissipation Mechanism**

No bath No spin-orbit interaction

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**Dissipation Mechanism**

No bath Spin-Orbit interaction

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**Dissipation Mechanism**

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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**Electronic Confinement**

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

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**Acoustic Phonon Bath Approximate form of the Hamiltonian GaAs**

“orbital” bath spectral function InAs piezoelectric deformation potential

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**Effective Bath of Oscillators**

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

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**Spin Orbit Phonon bath As seen by the spins... where**

B is the generalized incomplete beta function

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**Bath resonance Behaviour of the effective bath spectral function**

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

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**Dissipative Mechanism**

Bath resonance Dissipative Mechanism weak coupling strong coupling

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**Effective spectral function**

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

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**Microscopic dissipative spin dynamics**

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

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

Short time dynamics

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Resonant dynamics Long time dynamics

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**Resonant dynamics Very long decoherence (relaxation) times**

Good for keeping quantum information Bad for reseting

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**Resonant dynamics Very long decoherence (relaxation) times**

Good for keeping quantum information Bad for reseting

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Resonant dynamics Short time dynamics

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**Resonant dynamics Very long decoherence (relaxation) times**

Good for keeping quantum information Bad for reseting

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**Resonant dynamics Very long decoherence (relaxation) times**

Good for keeping quantum information Bad for reseting Resonance dominated

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Resonant dynamics

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Resonant dynamics Bulk values

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**Off-resonance dynamics**

Bulk values

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**Bath assisted cooling Reset pulses**

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

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**Summary Thanks: HP-Brazil, FAPESP, CNPq**

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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