geometric phase and the unruh effect
DESCRIPTION
Geometric phase and the Unruh effect. Speaker: Jiawei Hu, Hunnu Supervisor: Prof. Hongwei Yu. Outline. Unruh effect Geometric phase Geometric phase and Unruh effect Summary. 1. Unruh effect. particle. observer. In the Minkowski vacuum inertial observers: nothing - PowerPoint PPT PresentationTRANSCRIPT
Geometric phase and the Unruh effect
Speaker: Jiawei Hu, HunnuSupervisor: Prof. Hongwei Yu
23/4/21
Outline
• Unruh effect
• Geometric phase
• Geometric phase and Unruh effect
• Summary
1. Unruh effect
S.A. Fulling, PRD 7, 2850 (1973). P.C.W. Davies, JPA 8, 609 (1975).W.G. Unruh, PRD 14, 870 (1976).
particle observer
In the Minkowski vacuum
inertial observers: nothing
accelerating observers:
a thermal bath of Rindler particles at the Unruh temperature a/2π
Minkowski vacuum
No particles
T=a/2πRindler particles
Observable?
2. Geometric phase
• Dynamical 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
Geometric phase
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).
Adiabatic theorem: n=m
Dynamic phase
Geometric phase
EnvironmentSystem
D. M. Tong, E. Sjoqvist, L. C. Kwek, and C. H. Oh, PRL 93.080405 (2004).
Geometric phase in an open quantum system
3. Geometric phase and the Unruh effect
E. Martin-Martinez, I. Fuentes, R. B. Mann, PRL 107, 131301 (2011).
The detector: harmonic oscillator
The field: single-mode scalar field
The Hamiltonian
The model : a detector coupled to a massless scalar field in the vacuum state in a flat 1+1 D space-time.
Inertial detector
Accelerated detector
The phase difference as a function of the acceleration
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:
GP for an accelerated open two-level atom and the Unruh effect
J. Hu and H. Yu, PRA 85, 032105 (2012).
The master equation
The evolution of the reduced density matrix
The initial state of the atom
The trajectory of the atom
The field correlation function
The coefficients of the dissipator
The GP for an open system
The GP for an accelerated atom, single period
The GP for an inertial atom, single period
Non-thermal ThermalInertial
The GP purely due to acceleration
Numerical estimation
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
