Quantum phase and quantum phase operators: some physics and some history

Nieto, Michael Martin

doi:10.1088/0031-8949/1993/t48/001

Cited by 49 publications

(33 citation statements)

References 58 publications

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“…introduced, as a matter of fact, by F London at the dawn of quantum mechanics [24], although their systematic use began only after the paper by Susskind and Glogower [25] (for the history see [26]). The commutator of E − and E + is the vacuum state projector,…”

Section: Quantum Counting Processes With Exponential Phase Operamentioning

confidence: 99%

A consistent quantum model for continuous photodetection processes

Oliveira

Mizrahi

Dodonov

2003

J. Opt. B: Quantum Semiclass. Opt.

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We are modifying some aspects of the continuous photodetection theory, proposed by Srinivas and Davies [Optica Acta 1981 28 981], which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the 'annihilation' and 'creation' operators that enter in the photocount superoperators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to Srinivas and Davies precepts, but also avoids some weird result appearing when previous definitions are used.pacs: 03.67. 03.65.Bz,

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Section: Quantum Counting Processes With Exponential Phase Operamentioning

confidence: 99%

A consistent quantum model for continuous photodetection processes

Oliveira

Mizrahi

Dodonov

2003

J. Opt. B: Quantum Semiclass. Opt.

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“…This is not the case and, in fact, no exact, well behaved Hermitean phase operator conjugate to the number is known to exist. [An article by Nieto [27] describes the early history of the phase operator question, and gives a feeling of the problematics of the field. An alternative discussion, primarily related to phases in the electromagnetic field, is available in [28]].…”

Section: Introduction and Preview Of The Chaptermentioning

confidence: 99%

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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“…By this we mean to consider the phase of the order parameter as a quantum operator conjugate to particle number. In spite of the difficulties involving the definition of a hermitian phase operator [27], a semi-classical treatment is possible in Josephson nanosystems and the gap closing effect we have found may disappear due to such a contribution [23]. However, in a setup where superconductivity is induced via proximity effect, the simple description in terms of the Kitaev model may apply, and the new aspects we have discussed here is likely to be remain robust .…”

Section: Resultsmentioning

confidence: 95%

Strong-coupling topological Josephson effect in quantum wires

Nogueira

Eremin²

2012

J. Phys.: Condens. Matter

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Abstract. We investigate the Josephson effect for a setup with two lattice quantum wires featuring Majorana zero energy boundary modes at the tunnel junction. In the weak-coupling, the exact solution reproduces the perturbative result for the energy containing a contribution ∼ ± cos(φ/2) relative to the tunneling of paired Majorana fermions. As the tunnel amplitude g grows relative to the hopping amplitude w, the gap between the energy levels gradually diminishes until it closes completely at the critical value g c = √ 2w. At this point the Josephson energies have the principal values E mσ = 2σ √ 2w cos[φ/6 + 2π(m − 1)/3], where m = −1, 0, 1 and σ = ±1, a result not following from perturbation theory. It represents a transparent regime where three Bogoliubov states merge, leading to additional degeneracies of the topologically nontrivial ground state with odd number of Majorana fermions at the end of each wire. We also obtain the exact tunnel currents for a fixed parity of the eigenstates. The Josephson current shows the characteristic 4π periodicity expected for a topological Josephson effect. We discuss the additional features of the current associated with a closure of the energy gap between the energy levels.arXiv:1102.3000v3 [cond-mat.mes-hall]

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Quantum phase and quantum phase operators: some physics and some history

Cited by 49 publications

References 58 publications

A consistent quantum model for continuous photodetection processes

A consistent quantum model for continuous photodetection processes

Complex States of Simple Molecular Systems

Strong-coupling topological Josephson effect in quantum wires

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