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

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Presentation on theme: "Dissipative dynamics of spins in quantum dots A.O. Caldeira Universidade Estadual de Campinas Campinas, BRAZIL."— Presentation transcript:

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

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

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

4 Movimento dissipativo

5 Movimento em um meio viscoso Dissipação + Flutuações O movimento Browniano

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

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

8 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.

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

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

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

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

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

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

15 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 » ?

16 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

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

18 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)

19 Dots Model Electronic confinement

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

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

22 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/

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

24 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

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

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

27 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):

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

29 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

30 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

31 Dissipation Mechanism No bath No spin-orbit interaction

32 No bath Spin-Orbit interaction Dissipation Mechanism

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

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

35 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:

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

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

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

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

40 Dissipative Mechanism weak coupling Bath resonance strong coupling

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

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

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

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

45

46 Microscopic dissipative spin dynamics

47

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

49 Driven spin dynamics Peaks:

50 Driven spin dynamics Peak:

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

52 Resonant dynamics

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

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

55 Short time dynamics Resonant dynamics

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

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

58 Resonant dynamics

59 Bulk values

60 Off-resonance dynamics Bulk values

61 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)

62 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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