1. Dissipative dynamics of spins in quantum dots
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. Uma breve preparação
O que é dissipação quântica?
Movimento dissipativo +
Mecânica quântica

4. Movimento dissipativo

5. Movimento dissipativo
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? Clássico
(macroscópico)
Quântico (microscópico)

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

11. Tunelamento coerente de partículas magnéticas
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. NANO ??? Um possível candidato a qubit
Spin eletrônico em pontos quânticos

15. 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 » ?

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. Electronic confinement
Dots
Model

20. Electronic confinement
Coulomb Blockade 1e 2e 5e 3e 4e 6e
s-shell
p-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
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/

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

24. 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

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

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

27. 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

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

29. 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

30. 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

31. Dissipation Mechanism
No bath
No spin-orbit interaction

32. Dissipation Mechanism
No bath
Spin-Orbit interaction

33. Dissipation Mechanism
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. 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:

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

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

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

39. 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:

40. Dissipative Mechanism
Bath resonance
Dissipative Mechanism
weak coupling
strong coupling

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

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

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

46. Microscopic dissipative spin dynamics

47. Microscopic dissipative spin dynamics

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

52. Resonant dynamics
Long time dynamics

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

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

55. Resonant dynamics
Short time dynamics

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

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

58. Resonant dynamics

59. Resonant dynamics
Bulk values

60. Off-resonance dynamics
Bulk values

61. 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

62. 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