Geometric phase for mixed states: a differential geometric approach

A new definition and interpretation of the geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected principal fiber bundles, and the well-known Kostant-Kirillov-Souriau symplectic structure on (co-) adjoint orbits associated with Lie groups. It is shown that this framework generalizes in a natural and simple manner to the mixed state case. For simplicity, only the case of rank two mixed state density matrices is considered in detail. The extensions of the ideas of null phase curves and Pancharatnam lifts from pure to mixed states are also presented.     

Geometric phase with nonunitary evolution in the presence of a quantum critical bath

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications, the quantum geometric phase was generalized to open systems. The definition takes a kinematical approach, with an initial state that is evolved cyclically but coupled to an environment--leading to a correction of the geometric phase with respect to the uncoupled case. We obtain this correction by measuring the nonunitary evolution of the reduced density matrix of a spin one-half coupled to an environment. In particular we are interested in baths near a quantum phase transition, which are known to induce strong decoherence. The experiments are done with a NMR quantum simulator, where we emulate qualitatively the influence of a critical environment using a simple one-qubit model.     

Off-diagonal geometric phase for mixed states

We extend the off-diagonal geometric phase [Phys. Rev. Lett. 85, 3067 (2000)]] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. 85, 2845 (2000)]]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed.     

Atomic approach to the mixed configuration ground state

A variational wave function proposed by Kaplan et al. is used to exhibit the mixed valence phenomena through f-d mixing interaction. The model is applied to the mixed valence samarium monochalcogenides and explains the pressure-induced phase transition.     

Transfer of quantum correlations in nonunitary evolution

A generalized Lindblad equation has been derived for describing the evolution of two dynamical systems interacting with a bath formed by two broadband modes of squeezed light in an entangled state. The transfer of quantum correlations, in particular, entanglement between the bath and dynamic systems, which are taken in the form of two electromagnetic field modes separated by two high-Q cavities, two atoms, and an atom and a mode, has been analyzed. It has been found that the entanglement of the bath is transferred both to two modes and to two atoms, which can form an almost perfect Einstein-Podolsky-Rosen pair. It has been shown that the interaction of the bath with the system consisting of an atom and a mode for which collective boson operators are introduced leads to the appearance of coherent and squeezed states.     

Application of the nonunitary model operator approach to the16O nucleus

The nonunitary model operator approach, which has been previously described, is applied to the¹⁶O nucleus. Approximate expressions are given for the ground-state energy of this nucleus, by using both variational methods with the separation condition, developed in our previous work. Simple hardand softcore potentials are employed in the computations and the results obtained with the two methods are discussed.     

绝热演化中一般量子态的几何相位

在绝热演化中的几何相位（即Berry相位）被推广到包括非本征态的一般量子态.这个新的几何相位同时适用于线性量子系统和非线性量子系统.它对于后者尤其重要因为非线性量子系统的绝热演化不能通过本征态的线性叠加来描述.在线性量子系统中,新定义的几何相位是各个本征态Berry相位的权重平均.     

Order of phase transition between the Meissner state and the mixed state

The critical value of the Ginzburg-Landau parameter which separates type-II/1 from type-II/2 superconductors is computed by means of the boson formulation of superconductivity. By taking into account the tail effect of the function c(k), which describes the electrodynamics of the superconducting state, it is shown that the attractive part of the interaction energy between two flux lines indeed vanishes for a critical value of κ. The dependence on Λ = VN(O) is also discussed.     

A geometric mixed norm approach to shallow water acoustic channel estimation and tracking

The shallow water acoustic channel is challenging to estimate and track due to rapid temporal fluctuations of its large delay spread. However, the impulse response and representations of its time-variability often exhibit a sparse structure that can be exploited to improve estimator performance. We propose a sparse reconstruction of the shallow water acoustic channel that employs a novel optimization metric combining the complex square root of the channel coefficients and a non-convex complex function based on the $L_2$ estimation error. Our mixed norm formulation is mathematically equivalent to conventional $L_2$ constrained $L_1$ minimization, but fundamentally different in the non-convex topology we employ to solve for and track the optimal coefficients in real time directly over the complex field. Our estimation and tracking algorithm is designed for robustness with respect to the ill-conditioned nature of the data matrix, can smoothly handle different levels of sparsity, and is modeled to include delays due to multi-path and the Doppler spread induced by the channel. We present numerical evidence over simulated as well as field data to compare the performance of our method to conventional sparse reconstruction techniques.     

三能级混合态的量子几何相位

把三能级开放系统的密度矩阵按照Gellmann矩阵展开,然后将展开系数和Bloch球中的方位角对应, 从而获得了Poincaré球内部点和复三维Hilbert空间的非单位矢量即波函数的映射.进一步建议用该非单位矢量来定义混合态的量子几何相位.结果显示该几何相位仅仅与复Hilbert投影空间的几何结构有关, 与开放系统具体的演化路径无关;并且该混合态的几何相位依赖于开放系统的反转粒子数,也是描述开放系统混合度的单值光滑曲线,这个结果意味着混合态的演化的确按照几何相位保持其运动记忆.此外,在纯态的限制下,Berry相位是本文定义的几何相位极限情况.     

Measurement of geometric phase for mixed states using single photon interferometry

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.     

A state space approach in phase shifting interferometry

The paper proposes a state space approach for the determination of phase distribution in an interferogram in the presence of a non-sinusoidal waveform, random noise, and the miscalibration of the piezoelectric device. In this approach we first estimate the phase step imparted to the piezoelectric transducer (PZT) before determining the phase distribution. A denoising procedure is applied with the knowledge of the state-feedback matrix prior to the extraction of the phase step. This step ensures a good estimation of the phase distribution even at low signal-to-noise ratios. The other salient features of the proposed concept lie in its ability to compensate the detector non-linearity and in the use of non-collimated beams. The comparison of the proposed method with other bench-marking algorithms shows that our approach is efficient and robust. The experimental results show the feasibility of the proposed approach.     

Effect of measurement on the geometric phase during evolution of a quantum system

The effect of measurement on the development of the geometric phase is discussed during the evolution of a quantum system, for the model of measurement considered. It is shown that the development of the geometric phase is inhibited in the limit of high frequency of measurement, thereby erasing the memory of the quantum system.     

Unusual magnetic-field-induced phase transition in the mixed state of superconducting NbSe2

The thermal conductivity kappa in the basal plane of single-crystalline hexagonal NbSe2 has been measured as a function of magnetic field H, oriented both along and perpendicular to the c axis, at several temperatures below T(c). With the magnetic field in the basal plane and oriented parallel to the heat flux we observed, in fields well below H(c2), an unexpected hysteretic behavior of kappa(H) with all the generic features of a first order phase transition. The transition is not manifest in the kappa(H) curves, if H is still in the basal plane but oriented perpendicularly to the heat-flux direction. The origin of the transition is not yet understood.     

A geometric approach to direct minimization

The approach presented, geometric direct minimization (GDM), is derived from purely geometrical arguments, and is designed to minimize a function of a set of orthonormal orbitals. The optimization steps consist of sequential unitary transformations of the orbitals, and convergence is accelerated using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach in the iterative subspace, together with a diagonal approximation to the Hessian for the remaining degrees of freedom. The approach is tested by implementing the solution of the self-consistent field (SCF) equations and comparing results with the standard direct inversion in the iterative subspace (DIIS) method. It is found that GDM is very robust and converges in every system studied, including several cases in which DIIS fails to find a solution. For main group compounds, GDM convergence is nearly as rapid as DIIS, whereas for transition metal-containing systems we find that GDM is significantly slower than DIIS. A hybrid procedure where DIIS is used for the first several iterations and GDM is used thereafter is found to provide a robust solution for transition metal-containing systems.     

液相及固/液混合相区金属物态方程Grover模型存在的问题及修正

借助无序熵的概念, 直接推导出了液相金属的物态方程. 再利用固/液混合相区的熔化分数与其中固相、液相比体积之间的一般性关系, 替代了传统Grover模型中采用的熔化分数与温度成正比的近似条件, 得出更准确的固/液混合相区状态方程的表述形式. 修正后的物态方程解决了传统Grover模型中的固线、液线以及熔化线在P-T图上不一致的问题, 得到了更为符合物理事实的结果.