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Scaling of entanglement and Berry phase in the Dicke model

Scaling of entanglement and Berry phase in the Dicke model. F. Plastina, G. Liberti, R. Zaffino, F. Piperno (UNICAL) A. Carollo (IQOQI). Refs: G. Liberti, R. Zaffino, F. Piperno, F. P., Phys. Rev. A 73 032346 (2006) G. Liberti, F. P., F. Piperno, Phys. Rev. A 74 022324 (2006)

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Scaling of entanglement and Berry phase in the Dicke model

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  1. Scaling of entanglement and Berry phase in the Dicke model F. Plastina, G. Liberti, R. Zaffino, F. Piperno (UNICAL) A. Carollo (IQOQI) Refs:G. Liberti, R. Zaffino, F. Piperno, F. P., Phys. Rev. A 73 032346 (2006) G. Liberti, F. P., F. Piperno, Phys. Rev. A 74 022324 (2006) F. P., G. Liberti, A. Carollo, Europhys. Lett. 76, 182 (2006)

  2. Aim: • To describe the critical properties of entanglement and Berry phase near the super-radiant QPT; • To characterize the finite size scaling and obtain the critical exponents for both quantities. Outline: • Dicke model and its solution in the Born-Oppenheimer approach; • The thermodynamic limit and QPT; • Finite size scaling; • Entanglement and its scaling properties; • Berry phase and the scaling of its topological character.

  3. Dicke model Collective coupling of N qubits to a boson mode Quantum Phase Transition: • Super-radiant phase: • Macroscopic mode occupation • Macroscopic magnetization

  4. Adiabatic Limit: Born-Oppenheimer (in 5 steps) Adiabatic qubit Hamiltonian 1) Write the state in the form slow component fast component 2) Adiabatic qubit equation for a fixed value of the slow variable Q

  5. 3) The qubit eigenvalue gives an effective potential 4) Find the oscillator wave function

  6. 5) Observables: spin components Thermodynamic limit

  7. Finite size scaling (Symanzik) Perturbation theory Critical exponent

  8. Entanglement - a - Once the oscillator is traced out, the qubit state is completely separable - b – Entanglement of each qubit with the rest of the system Critical exponent

  9. c – Entanglement of the oscillator • with the entire qubit register Thermodynamic limit Finite size system

  10. Berry Phase Q-parametrized connection Thermodynamic limit Finite size

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