Quantum Geometric Phase between Orthogonal States

Wong, Hon Man; Cheng, Kai Ming; Chu, M.-C.

doi:10.1103/physrevlett.94.070406

Cited by 18 publications

(5 citation statements)

References 18 publications

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“…[34][35][36], gaugeinvariant quantities do exist that are associated with transitions. They are known as off-diagonal geometric phases [39][40][41][42][43]. The set of all geometric phases-diagonal and off-diagonal-gives all of the geometric information about neutrino oscillations.…”

Section: Off-diagonal Geometric Phasesmentioning

confidence: 99%

Geometric and Majorana phases in neutrino oscillations

Johns

2021

Preprint

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Geometric (Aharonov-Anandan) phases in neutrino oscillations have been claimed [Phys. Lett. B 780 (2018) 216] to be sensitive to the Majorana phases in neutrino mixing. More recently, however, it has been pointed out [Phys. Lett. B 818 (2021) 136376] that the proposed phases are not gauge invariant. Using both kinematic and geometric approaches, we show that all gaugeinvariant Aharonov-Anandan phases (including the off-diagonal geometric phases associated with flavor transitions) are independent of the Majorana phases. This finding, which generalizes the wellknown fact that conventional oscillation experiments cannot discern the Dirac or Majorana nature of the neutrino, implies that a hypothetical interference experiment cannot distinguish between the two either.

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Section: Off-diagonal Geometric Phasesmentioning

confidence: 99%

Geometric and Majorana phases in neutrino oscillations

Johns

2021

Preprint

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“…On the Bloch sphere, thus, they are positioned precisely at an antipodal position, which results in this case in an ill-defined expression for the geometric phase (see, however, Ref. [53]). We therefore devote this section to the study of this special limit using several techniques.…”

Section: Massless Dirac Cones With Opposite Chirality and Diagonmentioning

confidence: 99%

Geometric phase in Stückelberg interferometry

2015

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We study the time evolution of a two-dimensional quantum particle exhibiting a two-band energy spectrum with two Dirac cones as, for example, in the honeycomb lattice, A force is applied such that the particle experiences two Landau-Zener transitions in succession in the vicinity of the Dirac cones. The adiabatic evolution between the two transitions leads to Stiickelberg interferences, due to two possible trajectories in energy-momentum space. In addition to well-known dynamical and Stokes phases, the interference pattern reveals a geometric phase which depends on the chirality (winding number) and the mass sign associated with each Dirac cone, as well as on the type of trajectory (parallel or diagonal with respect to the two cones) in parameter space. This geometric phase reveals the coupling between the bands encoded in the structure of the wave functions. Stiickelberg interferometry therefore appears as a way to access both intra-and interband geometric information.

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“…[4]) and Pancharatnam phase (e.g. [5,6]). One especially fertile area of application of PPS theory is the time symmetric reformulation of quantum mechanics developed by Aharonov et al [7] and the closely related notion of the weak value of a quantum mechanical observable (e.g.…”

Section: Introductionmentioning

confidence: 99%

Exact pointer theories for von Neumann projector measurements of pre- and postselected and preselected-only quantum systems: statistical mixtures and weak value persistence

2014

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Exact expressions for the mean pointer position, the mean pointer momentum and their variances are obtained for projection operator measurements performed upon ensembles of pre-and postselected (PPS) and preselected-only (PSO) quantum systems. These expressions are valid for any interaction strength which couples a measurement pointer to a quantum system, and consequently should be of general interest to both experimentalists and theoreticians. To account for the 'collapse' of PPS states to PSO states that occurs as interaction strength increases and to introduce the concept of 'weak value persistence', the exact PPS and PSO pointer theories are combined to provide a pointer theory for statistical mixtures. For the purpose of illustrating 'weak value persistence', mixture weights defined in terms of the Bhattacharyya coefficient are used and the statistical mixture theory is applied to mean pointer position data associated with weak value projector measurements obtained from a recent dynamical quantum non-locality detection experiment.

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Quantum Geometric Phase between Orthogonal States

Cited by 18 publications

References 18 publications

Geometric and Majorana phases in neutrino oscillations

Geometric and Majorana phases in neutrino oscillations

Geometric phase in Stückelberg interferometry

Exact pointer theories for von Neumann projector measurements of pre- and postselected and preselected-only quantum systems: statistical mixtures and weak value persistence

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