Neutron Interferometric Observation of Noncyclic Phase

Wagh, Apoorva G.; Rakhecha, Veer Chand; Fischer, Peter; Ioffe, A.

doi:10.1103/physrevlett.81.1992

Cited by 84 publications

(69 citation statements)

References 26 publications

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“…Several researches have addressed this difficulty, in particular, by neutron-interferometric methods, which also can yield the open-path phase [123], though only under restricted conditions [313]. The continuous tracing method and other methods for cycling reviewed in this section can be used in several very different areas.…”

Section: Experimental Phase Probingmentioning

confidence: 99%

“…To single out some special results in the extremely broad field of interference, we point to recent observations using two-photon pulse transition [94] in which a differentiation was achieved between interferences due to temporal overlap (with finite pulse-width) and quantum interference caused by delay. The (component-specific) topological phase in wave functions has been measured, following the proposal of Berry in [9], by neutron interferometry in a number of works, e.g., [123,124] with continual improvements in the technique. The difficulties in the use of coherent neutron beams and the possibility of using conventional neutron sources for phase-sensitive neutron radiography have been noted in a recent review [125].…”

Section: Aspects Of Phase In Moleculesmentioning

confidence: 99%

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Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

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A review is given of phase properties in molecular wave functions, composed of a number of (and, at least, two) electronic states that become degenerate at some nearby values of the nuclear configuration. Apart from discussing phases and interference in classical (non-quantal) systems, including light-waves, the review looks at the constructability of complex wave functions from observable quantities ("the phase problem"), at the controversy regarding quantum mechanical phase-operators, at the modes of observability of phase and at the role of phases in some non-demolition measurements. Advances in experimental and (especially) theoretical aspects of Aharonov-Bohm and topological (Berry) phases are described, including those involving two-electron and relativistic systems. Several works in the phase control and revivals of molecular wave-packets are cited as developments and applications of complex-function theory. Further topics that this review touches on are: coherent states, semiclassical approximations and the Maslov index. The interrelation between time and the complex state is noted in the contexts of time delays in scattering, of time-reversal invariance and of the existence of a molecular time-arrow.When the stationary Born-Oppenheimer description for nearly degenerate state is regarded as "embedded" in a broader dynamic formulation, namely through solution of the time dependent Schrödinger equation, the wave function becomes necessarily complex. The analytic behavior of this function in the complex time-plane can be exploited to gain information about the connection between phases and moduli of the componentamplitudes. One form of this connection are a pair of reciprocal (Kramers-Kronig type) relations in the complex time-domain. These show that certain phase changes in a component amplitude (such as, e.g., lead to a non-zero Berry-phase) require changes in the amplitude-moduli, too, and imply degeneracies of the electronic state.The subject of conical degeneracy, or intersection, of adjacent potential surface is extended to nonlinear nuclear-electronic coupling, which can then result in multiple conical degeneracies on a nuclear coordinate plane. We treat cases of double and fourfold intersections, the latter under trigonal symmetry, and employ an analytic-graphical phase tracing method to obtain the resulting Berry phases as the system circles around some or all of the degeneracy points. These phases can take up values that are all integral multiples of π, with integers that vary with the physical situation (or with the model postulated for it).A further type of invariance, with respect to gauge transformation, is also tied to the complex form of the wave function. For a many-component state this leads to a consideration of tensorial (Yang-Mills type) fields F for molecular systems. It is shown that it is the truncation of the Born-Oppenheimer electron-nuclear superposition that generates the molecular Yang-Mills fields.The equations of motion for the nuclear degrees of freedom are derived from a Lagr...

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Section: Experimental Phase Probingmentioning

confidence: 99%

Section: Aspects Of Phase In Moleculesmentioning

confidence: 99%

Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

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“…Among them, those with a polarized incident beam served as an ideal tool to investigate properties of a spin-1/2 system [20]. For instance, starting from spinor superposition [21,22], double resonance flipper experiments [23], geometric and dynamical phase measurements [24,25], and noncyclic Pancharatnam phase measurement [26] were accomplished. Besides the interferometric method, the geometric and dynamical phases are more precisely measured with the use of a neutron polarimeter [27].…”

Section: Introductionmentioning

confidence: 99%

Observation of off-diagonal geometric phases in polarized-neutron-interferometer experiments

Hasegawa¹,

Loidl²,

Badurek³

et al. 2002

Phys. Rev. A

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Off-diagonal geometric phases acquired in the evolution of a spin-1/2 system have been investigated by means of a polarized neutron interferometer. Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off-diagonal) and in terms of the quantum erasing phenomenon.

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“…This condition can be implemented in a Mach-Zehnder interferometric setup, where the spatial state of the system prior to the last beam splitter is a coherent superposition of the two paths [17,18]. If we let | A and | B be the internal states corresponding to the output of respective paths of the interferometer, then Pancharatnam parallelity is achieved by shifting a U(1) phase in one of the paths, such that the interference intensity is maximal.…”

Section: Introductionmentioning

confidence: 99%

Correlation-induced non-Abelian quantum holonomies

Johansson

Ericsson

Singh

et al. 2011

J. Phys. A: Math. Theor.

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Abstract. In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally nonAbelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase [2004 J. Phys. A: Math. Gen. 37 1821 in the case of twoqubit systems undergoing local SU (2) evolutions.

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Neutron Interferometric Observation of Noncyclic Phase

Cited by 84 publications

References 26 publications

Complex States of Simple Molecular Systems

Complex States of Simple Molecular Systems

Observation of off-diagonal geometric phases in polarized-neutron-interferometer experiments

Correlation-induced non-Abelian quantum holonomies

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