1. Dynamics of coupled cavity arrays embedded in a non-Markovian bath
EDC2012 presentation
Dynamics of coupled cavity arrays embedded in a non-Markovian bath
Xinyu Zhao
Jun Jing
J. Q. You
Ting Yu
Department of Physics
Stevens Institute of Technology
 arXiv:

2. Outline 5 Background: Quantum open system, QSD approach Motivation
N-cavity model
Model and exact solution 5
Two-cavity example: cat-state transfer
Three-cavity example: boundary condition
Summary

3. Open System, Bosonic QSD approach
Markovian—Lindblad MEQ
Non-Markovian,
Quantum State Diffussion (QSD)
Interaction
Gaussian noise
Correlation function
Bosonic bath
W. Strunz, L. Diosi, N. Gisin,
e.g., see RPA 58, 1699; PRL 82, 1801
From the QSD equation, one can derive the exact master equation

4. Why CV system? Why large system?
In the past two years, our research mainly focus on this QSD approach, many models have been solved exactly. (3-level, 2-qubit, N-level)
However, all of them are discrete system. A natural question is:
What about a large (N-partite),
Continuous variable (CV) system?
Some examples of references on CV system:
B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D 45, 2843 (1992).
T. Yu, Phys. Rev. A 69, (2004).
J. H. An and W. M. Zhang, Phys. Rev. A 76, (2007).
K.-L. Liu and H.-S. Goan, Phys. Rev. A 76, (2007).
C. H. Chou, T. Yu and B. L. Hu, Phys. Rev. E 77, (2008).
W. M. Zhang, M. H. Wu, C. U. Lei, and H. N. Xiong, Opt. Express 18, (2010).
C. H. Fleming and B. L. Hu, Ann. Phys. 327, 1238 (2012).

5. The N-cavity model
 arXiv:
where
Exact Master Equation

6. Example 1: Two-cavity case
Cat state transfer
Cat-like
Superposition
state
Cavity 1
Cavity 2
No direct coupling between two cavities!!
Non-Markovian Environment
This cat-state transfer is induced by memory effect, and can be only observed in highly non-Markovian environment.

7. Two types of boundary conditions
In the case of 3-cavity, we have two boundary conditions.
Open Boundary Condition (OBC) 1 2 3
Periodical Boundary Condition (PBC) 2 1 3

8. Example 2: Three -cavity
 arXiv:
Different boundary conditions

9. In OBC case 1 2 3 1 2 3
Standing Wave

10. Example 2: Three -cavity
 arXiv:
Different boundary conditions
Red (solid):
Cavity 1
Green (dashed):
Cavity 2
Blue (dash-dotted):
Cavity 3

11. Example 2: Three -cavity
 arXiv:
Entanglement transfer
Environment
Cavity 1
Entangled
Cavity 2
Cavity 3
Red:Entanglement between Green:2-3 Blue:1-3

12. Thanks Summary Solving N-cavity model by QSD approach
Exact solution to N-cavity model (for the first time)
Solving N-cavity model by QSD approach
Applying QSD approach to large (N-partite),CV system
Memory-effect assisted cat-state transfer
Effect of boundary conditions
Entanglement transfer
Thanks

13. Exact solution at finite temperature
QSD Eq. at finite T
O operators
Exact
Solutions
Exact Master Equation