Off-diagonal geometric phase in a neutron interferometer experiment

Off-diagonal geometric phases acquired by an evolution of a 1/2-spin system have been observed by means of a polarized neutron interferometer. We have successfully measured the off-diagonal phase for noncyclic evolutions even when the diagonal geometric phase is undefined. Our data confirm theoretical predictions and the results illustrate the significance of the off-diagonal phase.     

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.     

Off-diagonal geometric phases

We investigate the adiabatic evolution of a set of nondegenerate eigenstates of a parametrized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for which off-diagonal phases can be determined from published data.     

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.     

Geometric phase for mixed states

We present a kinematic approach for obtaining the geometric phase of a mixed state under nonunitary evolution. This phase is gauge-invariant and measurable and leads to well-known results for unitary evolution.     

Quantum geometric phase between orthogonal states

We show that the geometric phase between any two states, including orthogonal states, can be extracted and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase change in an infinitesimal loop near an orthogonal state. Also, the Pancharatnam phase change during the passage through an orthogonal state is shown to be either pi or zero (mod 2pi). All the off-diagonal geometric phases can be obtained from the projective geometric phase calculated with our generalized connection.     

Observation of geometric phases for mixed states using NMR interferometry

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.     

非线性系统的非对角Berry相

研究了非线性系统中非对角情况的Berry相位, 给出了非线性非对角Berry相位的计算公式. 结果表明, 在非线性非对角情况下, 总相位包含有动力学相位, 通常意义的Berry相位, 以及非线性引起的附加相位. 此外, 还包含有非对角情况时所特有的新的附加项. 这新的一项表示, 当系统哈密顿慢变时产生的Bogoliubov涨落, 与另一个瞬时本征态之间的交叉效应, 进而对总的Berry相位产生影响. 作为应用, 对二能级玻色爱因斯坦凝聚体系, 具体计算了非线性非对角的Berry相位. 关键词： Berry 相位 非对角 绝热演化 玻色爱因斯坦凝聚     

Kinematic approach to the mixed state geometric phase in nonunitary evolution

A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the evolution is unitary.     

Coherent states and geometric quantization

Based on the concept of generalized coherent states, a theory of mechanical systems is formulated in a way which naturally exhibits the mutual relation of classical and quantum aspects of physical phenomena.This work was supported in part by The Swedish Institute     

Coherent states in geometric quantization

In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to collect some recent results. We begin by recalling the basic constructions of geometric quantization in both the Kähler and non-Kähler cases. We then study the reproducing kernels associated to the quantum Hilbert spaces and use them to define symplectic coherent states. The rest of the paper is dedicated to the properties of symplectic coherent states and the corresponding Berezin–Toeplitz quantization. Specifically, we study overcompleteness, symplectic analogues of the basic properties of Bargmann’s weighted analytic function spaces, and the ‘maximally classical’ behavior of symplectic coherent states. We also find explicit formulas for symplectic coherent states on compact Riemann surfaces.     

Generation of multi-atom cluster states via an unconventional geometric phase shift in cavity QED

This paper proposes two schemes to generate the multi-atom cluster states. The first scheme is based on the interaction of atoms with a highly detuned cavity mode and a classical field, the second scheme is based on the interaction of atoms with a cavity mode, strongly driven by a resonant classical field.     

On quantum holonomy for mixed states

There is a natural connection and parallel transport on the Hilbert tensor product (or, equivalently, the space of Hilbert-Schmidt operators), the elements of which represent density matrices in up to unitary operators. We postulate a time evolution equation, which leads to this connection after extracting a proper dynamical unitary phase. As an example, we compute the holonomy of a loop of temperature states for the spin in a rotating magnetic field.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P5588.     

Difficulties for the evolution of pure states into mixed states

Motivated by Hawking's proposal that the quantum-mechanical density matrix ? obeys an equation more general than the Schrödinger equation, we study the general properties of evolution equations for ?. We argue that any more general equation for ? violates either locality or energy-momentum conservation.     

Catalysis of entanglement manipulation for mixed states

We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.     

Optimal entanglement criterion for mixed quantum states

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N > or = 4. It is shown that Phi detects many entangled states with a positive partial transposition (PPT) and that it leads to a class of optimal entanglement witnesses. This implies that there are no other witnesses which can detect more entangled PPT states. The map Phi yields a systematic method for the explicit construction of high-dimensional manifolds of bound entangled states.     

Estimation of concurrence for multipartite mixed states

We investigate the lower bound of concurrence for multipartite quantum mixed states. Analytical lower bounds are derived for some multipartite systems, by establishing functional relations between concurrence and the generalized partial transpositions.