Geometric phase and the Unruh effect

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

jwhu3.14@gmail.com