几何相位与量子相变

Subir Sachdev的《量子相变》第一章中 我们可以知道，所谓量子相变，一般对应于量子多体系统基态能量在参数空间中的某些不可解析的点，比如基态与第一激发态的能量在参数空间中出现了交叉，或者 出现了回避交叉的现象。另外一种更加直观的理解是，零温下，外部参量的微小变化引起了物理系统宏观性质根本性的改变[3]。Berry相位，又称为几何相位，是系统的哈密顿绝热的沿着闭合的参数回路周期性的变化时，在波函数上引入的附加相位。几何相位与系统的Hilbert空间的几何性质有关，有可能反应出量子相变的一些特性。正是基于这个想法，文献[1]才以XY模型为例，首次讨论了几何相位与量子相变的联系。他们讨论的哈密顿如下：

$H=-\sum_{l=-M}^M\Big(\frac{1+\gamma}{2}\sigma_l^x\sigma_{l+1}^x+\frac{1-\gamma}{2} \sigma_l^y\sigma_{l+1}^y+\lambda\sigma_l^z \Big)$,

[1] A. C. M. Carllo and J. K. Pachos, Phys. Rev. Lett. 95, 157203 (2005).
[2] Shi-liang Zhu, Phys. Rev. Lett. 96, 077206 (2006).
[3] Alioscia Hamma, quant-ph/0602091.

又要忙一阵子了

20号更新：今天看到了两篇论文。一篇是Plenio组的最新工作，把他们上一个工作改进了一下。我浏览了一下，发现改进非常微小，实际上就是把上一个工作中的某个近似条件的要求给放松了，物理模型没有变化，最后得到的非线性项强度增加了一个数量级，而耗散强度没变。做完一个工作后，从物理出发在想想，也许就能够再得到更好的结果。我自己的有一个工作也应该可以做类似的改进，不过确认这个想法需要做不少的工作。能够让它更加易于实验实现，再做点工作也是必要的。另外一篇文献我觉得非常牛：把STM技术用于光学晶格中，能够对单个原子进行测量。而STM的针尖呢，就是束缚在阱中的离子或者原子。这样的测量精确度可以达到10nm的量级，足以对光晶格中的单个原子进行测量了。对这个工作更详细的报道，可以看看PhysicsWeb。我们做工作眼界一定要宽广，类比和借鉴是非常重要的，也是新思想的一个源泉。

我为什么成为Physicist

(首发格志：http://gezhi.org/node/513)

New paper

New paper is available now, arXiv:0704.0482

Implementation of holonomic quantum computation through engineering and manipulating environment

Zhang-qi Yin, Fu-li Li and Peng Peng

We consider an atom-field coupled system, in which two multilevel atoms are respectively trapped in two distant cavities which are connected by an optical fiber and are shined by a broadband squeezed light. We show that a two-qubit geometric CPHASE gate between the two atoms can be implemented through adiabatically manipulating the squeezed reservoir along a closed loop. The scheme has two remarkable features. First, no matter how small but nonzero the squeezing amplitude is, a CPHASE gate with arbitrary phase shift can always be implemented. Second, in contrast to previous quantum computation schemes, the larger the effective coupling strength between the environment and the atoms is, the more reliable the realized CPHASE gate is.

In this work, we investigate the possiblility of realizing quantum computation via steering environment, other than controlling Hamiltonian of the quantum systems themselves or choosing measurement strategy. Let me briefly explain our motivation on doing this work.

When building future quantum computer, we must investigate practical systems which could be divided into three subsystems, which are quantum systems, quantum environments and detectors. Up to now, to our knowledge, there are two different types of schemes, controlling the Hamiltonian of quantum systems themselves (see Cirac and Zoller’s paper in 1995) and choosing measurement strategy (such as one-way quantum computer). So it would be interesting to investigate whether it is possible to realize quantum logic gate, such as a two-qubit CPHASE gate, via manipulating quantum environment. Our work reveals this possibility. Therefore, combining our resualts with previous works, we get following insights: Hamiltonians of the quantum systems, environment where quantum systems place and detectors which measure quantum systems, each of them could be manipulated to realize quantum compution.

I believe this work makes our understanding on realizing quantum computation and quantum control more deeply. In doing this work, we got valueable suggestions from Xiao Yun-feng (USTC). I also thank Star Forum where I got valueable suggestions.