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

Outline Unruh effect Geometric phase Geometric phase and Unruh effect Summary

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).

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

Observable?

2. Geometric phase Dynamical phase

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).

Adiabatic theorem: n=m Dynamic phase Geometric phase

Geometric phase in an open quantum system Environment D. M. Tong, E. Sjoqvist, L. C. Kwek, and C. H. Oh, PRL 93.080405 (2004).

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, 131301 (2011).

Inertial detector Accelerated detector

The phase difference as a function of the acceleration

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, 032105 (2012).

The master equation

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

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 Non-thermal Inertial Thermal The GP for an inertial atom, single period

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

Thanks! jwhu3.14@gmail.com