scholarly journals Experimental nonlocal and surreal Bohmian trajectories

2016 ◽  
Vol 2 (2) ◽  
pp. e1501466 ◽  
Author(s):  
Dylan H. Mahler ◽  
Lee Rozema ◽  
Kent Fisher ◽  
Lydia Vermeyden ◽  
Kevin J. Resch ◽  
...  
Keyword(s):  
Bohmian Mechanics ◽  
Weak Measurement ◽  
Weak Measurements ◽  
Quantum Particles ◽  
Bohmian Trajectories

Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed “surreal” when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.

scholarly journals Relativistically invariant Bohmian trajectories of photons

2021 ◽  
Author(s):  
Joshua Foo ◽  
Estelle Asmodelle ◽  
Austin Lund ◽  
Timothy Ralph
Keyword(s):  
Bohmian Mechanics ◽  
Quantum Mechanical ◽  
Relativistic Velocity ◽  
Weak Measurements ◽  
Hidden Variable ◽  
Bohmian Trajectories ◽  
Velocity Addition ◽  
Velocity Equation ◽  
Interpretation Of Quantum Theory ◽  
Deterministic Trajectories

Abstract Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has been restricted to nonrelativistic regimes due to the widely held belief that the theory is incompatible with special relativity. Here we derive expressions for the relativistic velocity and spacetime trajectories of photons in a Michelson-Sagnac-type interferometer. The trajectories satisfy quantum-mechanical continuity, the relativistic velocity addition rule. Our new velocity equation can be operationally defined in terms of weak measurements of momentum and energy. We finally propose a modified Alcubierre metric which could give rise to these trajectories within the paradigm of general relativity.

scholarly journals Electron Trajectories in Molecular Orbitals

2020 ◽  
Author(s):  
Isaiah Sumner ◽  
Hannah Anthony
Keyword(s):  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Molecular Orbitals ◽  
Quantum Hydrodynamics ◽  
Relativistic Limit ◽  
Quantum Particles ◽  
Quantum Force ◽  
Trajectory Methods ◽  
Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

scholarly journals Beating Standard Quantum Limit with Weak Measurement

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 354
Author(s):  
Geng Chen ◽  
Peng Yin ◽  
Wen-Hao Zhang ◽  
Gong-Chu Li ◽  
Chuan-Feng Li ◽  
...  
Keyword(s):  
Weak Measurement ◽  
Point Of View ◽  
Quantum Limit ◽  
Weak Measurements ◽  
Standard Quantum ◽  
Standard Quantum Limit ◽  
Intensive Investigation ◽  
Reduced Rate ◽  
The Cost ◽  
Positive Effect

Weak measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of a reduced rate of acquiring data, which leads to an increasing uncertainty to determine the level of meter shift. From this point of view, a number of theoretical works have suggested that weak measurements cannot improve the precision, or even damage the metrology information due to the post-selection. In this review, we give a comprehensive analysis of the weak measurements to justify their positive effect on prompting measurement precision. As a further step, we introduce two modified weak measurement protocols to boost the precision beyond the standard quantum limit. Compared to previous works beating the standard quantum limit, these protocols are free of using entangled or squeezed states. The achieved precision outperforms that of the conventional method by two orders of magnitude and attains a practical Heisenberg scaling up to n=106 photons.

Observation of Bohmian Trajectories of a Single Photon Using Weak Measurements

2010 ◽  
Author(s):  
Lynden K. Shalm ◽  
Sacha Kocsis ◽  
Sylvain Ravets ◽  
Boris Braverman ◽  
Martin J. Stevens ◽  
...  
Keyword(s):  
Single Photon ◽  
Weak Measurements ◽  
Bohmian Trajectories

scholarly journals On the Weak Measurement of Velocity in Bohmian Mechanics

2009 ◽  
Vol 134 (5-6) ◽  
pp. 1023-1032 ◽  
Author(s):  
Detlef Dürr ◽  
Sheldon Goldstein ◽  
Nino Zanghì
Keyword(s):  
Bohmian Mechanics ◽  
Weak Measurement

scholarly journals Anomalous Weak Values Without Post-Selection

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 194 ◽  
Author(s):  
Alastair A. Abbott ◽  
Ralph Silva ◽  
Julian Wechs ◽  
Nicolas Brunner ◽  
Cyril Branciard
Keyword(s):  
Quantum System ◽  
Weak Measurement ◽  
Weak Values ◽  
Weak Measurements ◽  
Weak Value ◽  
Average Value ◽  
Causal Structures

A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an ``anomalous weak value'', is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.

scholarly journals Reconstruction of Bohmian trajectories via weak measurement for bipartite states

2018 ◽  
Vol 510 ◽  
pp. 518-521
Author(s):  
Agnaldo R. de Almeida ◽  
Wesley B. Cardoso ◽  
Ardiley T. Avelar ◽  
Norton G. de Almeida
Keyword(s):  
Weak Measurement ◽  
Bohmian Trajectories ◽  
Bipartite States

Electron Trajectories in Molecular Orbitals

2020 ◽  
Author(s):  
Isaiah Sumner ◽  
Hannah Anthony
Keyword(s):  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Molecular Orbitals ◽  
Quantum Hydrodynamics ◽  
Relativistic Limit ◽  
Quantum Particles ◽  
Quantum Force ◽  
Trajectory Methods ◽  
Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

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