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:1204.1708

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

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

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, 062107 (2004). J. H. An and W. M. Zhang, Phys. Rev. A 76, 042127 (2007). K.-L. Liu and H.-S. Goan, Phys. Rev. A 76, 022312 (2007). C. H. Chou, T. Yu and B. L. Hu, Phys. Rev. E 77, 011112 (2008). W. M. Zhang, M. H. Wu, C. U. Lei, and H. N. Xiong, Opt. Express 18, 18407 (2010). C. H. Fleming and B. L. Hu, Ann. Phys. 327, 1238 (2012).

The N-cavity model  arXiv:1204.1708 where Exact Master Equation

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.

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

Example 2: Three -cavity  arXiv:1204.1708 Different boundary conditions

In OBC case 1 2 3 1 2 3 Standing Wave

Example 2: Three -cavity  arXiv:1204.1708 Different boundary conditions Red (solid): Cavity 1 Green (dashed): Cavity 2 Blue (dash-dotted): Cavity 3

Example 2: Three -cavity  arXiv:1204.1708 Entanglement transfer Environment Cavity 1 Entangled Cavity 2 Cavity 3 Red:Entanglement between 1-2 Green:2-3 Blue:1-3

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

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