A double-slit `which-way' experiment on the complementarity--uncertainty debate

Abstract

A which-way measurement in Young's double-slit will destroy the interference pattern. Bohr claimed this complementarity between wave- and particle behaviour is enforced by Heisenberg's uncertainty principle: distinguishing two positions a distance s apart transfers a random momentum q \sim \hbar/s to the particle. This claim has been subject to debate: Scully et al. asserted that in some situations interference can be destroyed with no momentum transfer, while Storey et al. asserted that Bohr's stance is always valid. We address this issue using the experimental technique of weak measurement. We measure a distribution for q that spreads well beyond [-\hbar/s, \hbar/s], but nevertheless has a variance consistent with zero. This weakvalued momentum-transfer distribution P_{wv}(q) thus reflects both sides of the debate.

13 pages, 4 figures

References in corpus (12)

• Quantum weak values
• How much time does a tunneling particle spend in the barrier region?
• Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values
• Experimental Realization of the Quantum Box Problem
• Weak Values, Quantum Trajectories, and the Stony-Brook Cavity QED experiment
• Grounding Bohmian Mechanics in Weak Values and Bayesianism
• Fast light, slow light, and phase singularities: a connection to generalized weak values
• Optical telecom networks as weak quantum measurements with post- selection
• Cherenkov radiation and superluminal particles
• Directly Observing Momentum Transfer in Twin-Slit "Which-Way" Experiments
• Counterfactual Statements and Weak Measurements: an Experimental Proposal
• The Uncertainty Relation in "Which-Way" Experiments: How to Observe Directly the Momentum Transfer using Weak Values

Cited by in corpus (72)

• Direct Measurement of the Quantum Wavefunction
• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Measuring small longitudinal phase shifts: weak measurements or standard interferometry?
• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Nonperturbative theory of weak pre- and post-selected measurements
• Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
• Direct measurement of general quantum states using weak measurement
• Soundness and completeness of quantum root-mean-square errors
• Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin-measurements
• Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
• Precision metrology using weak measurements
• The significance of the imaginary part of the weak value
• Observing Dirac's classical phase space analog to the quantum state
• Photon trajectories, anomalous velocities, and weak measurements: A classical interpretation
• Violation of Heisenberg's error-disturbance uncertainty relation in neutron spin measurements
• Weak Measurements Beyond the Aharonov-Albert-Vaidman Formalism
• State tomography via weak measurements
• Measuring measurement--disturbance relationships with weak values
• Measuring incompatible observables of a single photon
• Complex joint probabilities as expressions of determinism in quantum mechanics
• Super Quantum Discord with Weak Measurements
• Measuring Non-Hermitian Operators via Weak Values
• Quantum interference experiments, modular variables and weak measurements
• Complete characterization of post-selected quantum statistics using weak measurement tomography
• Illustration of quantum complementarity using single photons interfering on a grating
• Contextual-value approach to the generalized measurement of observables
• Uncertainty limits for quantum metrology obtained from the statistics of weak measurements
• On the role of complex phases in the quantum statistics of weak measurements
• Weak measurements with a qubit meter
• Using weak values to experimentally determine "negative probabilities" in a two-photon state with Bell correlations
• Products of weak values: uncertainty relations, complementarity and incompatibility
• Observation of a classical cheshire cat in an optical interferometer
• Classical Field Approach to Quantum Weak Measurements
• Observation of the quantum paradox of separation of a single photon from one of its properties
• Sequential measurements of non-commuting observables with quantum controlled interactions
• Quantum optical reconstruction scheme using weak values
• Measuring Which-Path Information with Coupled Electronic Mach-Zehnder Interferometers
• Fock-state view of weak-value measurements and implementation with photons and atomic ensembles
• Feasible optical weak measurements of complementary observables via a single Hamiltonian
• Control of quantum interference in the quantum eraser
• Observing momentum disturbance in double-slit "which-way" measurements
• Unifying theory of quantum state estimation using past and future information
• Experimental simultaneous read out of the real and imaginary parts of the weak value
• Non-zero total correlation means non-zero quantum correlation
• Sufficient conditions for uniqueness of the weak value
• How to simulate a quantum computer using negative probabilities
• Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies
• What dynamics can be expected for mixed states in two-slit experiments?
• Estimating Pre- and Post-Selected Ensembles
• Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance
• Complementarity and uncertainty relations for matter wave interferometry
• Characterization of measurement uncertainties using the correlations between local outcomes obtained from maximally entangled pairs
• Complex counterpart of variance in quantum measurements for pre- and post-selected systems
• Obtaining a Single-Photon Weak Value from Experiments using a Strong (Many-Photon) Coherent State
• An x-ray quantum eraser setup for time-energy complementarity
• An investigation of the transfer dynamics of quantum teleportation by weak measurement statistics
• Dual to the anomalous weak value effect of photon-polarisation separation
• Robustness of interferometric complementarity under Decoherence
• Time-reversed Young's experiment: Deterministic, diffractionless second-order interference effect
• Which-Way Measurement and Momentum Kicks
• Field extension of real values of physical observables in classical theory can help attain quantum results
• Extraction of Product and Higher Moment Weak Values: Applications in Quantum State Reconstruction and Entanglement Detection
• Amplification of mechanical quadratures using weak values
• Dynamics, locality and weak measurements: trajectories and which-way information in the case of a simplified double-slit setup
• Stronger sum uncertainty relations for non-Hermitian operators
• Momentum Kicks in Imperfect Which-Way Measurement
• Linear and angular momenta of photons in the context of "which path" experiments of quantum mechanics
• State distinguishability under weak measurement and post-selection: A unified system and device perspective
• Quantum Properties of a Which-Way Detector
• Quantum erasure in the presence of a thermal bath: the effects of system-environment microscopic correlations
• Maximizing complementary quantities by projective measurements
• Macroscopic Violation of Duality Generated on a Laser Beam