1. Geometric phase and the Unruh effect
Speaker: Jiawei Hu, Hunnu
Supervisor: Prof. Hongwei Yu
2019/5/23

2. Outline Unruh effect Geometric phase Geometric phase and Unruh effect
Summary

3. 1. Unruh effect particle observer In the Minkowski vacuum
inertial observers: nothing
accelerating observers:
a thermal bath of Rindler particles at the Unruh temperature a/2π
S.A. Fulling, PRD 7, 2850 (1973).
P.C.W. Davies, JPA 8, 609 (1975).
W.G. Unruh, PRD 14, 870 (1976).

4. Minkowski vacuum
No particles
T=a/2π
Rindler particles

5. Observable?

6. 2. Geometric phase
Dynamical phase

7. Geometric phase The Hamiltonian H(R) depends on a set of parameters R
The external parameters are time dependent, R(T)= R(0)
Adiabatic approximation holds
The system will sit in the nth instantaneous eigenket of H(R(t)) at a time t if it started out in the nth eigenket of H(R(0)).
M. Berry, Proc. Roy. Soc. A 392, 45 (1984).

8. Adiabatic theorem: n=m
Dynamic phase
Geometric phase

9. Geometric phase in an open quantum system
Environment
D. M. Tong, E. Sjoqvist, L. C. Kwek, and C. H. Oh, PRL (2004).

10. 3. Geometric phase and the Unruh effect
The model : a detector coupled to a massless scalar field in the vacuum state in a flat 1+1 D space-time.
The detector: harmonic oscillator
The field: single-mode scalar field
The Hamiltonian
E. Martin-Martinez, I. Fuentes, R. B. Mann, PRL 107, (2011).

11. Inertial detector
Accelerated detector

12. The phase difference as a function of the acceleration

13. GP for an accelerated open two-level atom and the Unruh effect
Our model:
a uniformly accelerated two-level atom coupled to a bath of fluctuating electromagnetic fields in vacuum in 3+1 D space-time
Hamiltonian:
J. Hu and H. Yu, PRA 85, (2012).

14. The master equation

15. The initial state of the atom
The evolution of the reduced density matrix

16. The trajectory of the atom
The field correlation function
The coefficients of the dissipator

17. The GP for an open system
The GP for an accelerated atom, single period
Non-thermal
Inertial
Thermal
The GP for an inertial atom, single period

18. The GP purely due to acceleration
Numerical estimation

19. Summary The environment has an effect on the GP of the open system
The phase corrections are different for the inertial and accelerated case due to the Unruh effect
This may provide a feasible way for the detection of the Unruh effect

20. Thanks!