Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer

Kocsis, Sacha; Braverman, Boris; Ravets, Sylvain; Stevens, Martin J.; Mirin, Richard P.; Shalm, Lynden K.; Steinberg, Aephraim M.

doi:10.1126/science.1202218

Cited by 640 publications

(793 citation statements)

References 24 publications

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“…It seems timely, not only for conceptual purposes but to help the development of realistic experiments, to work out further models, in particular for such quantum measurements in which the whole history of the process is used to gather information. In this context we should mention the so-called weak measurements [365] that (in a sense) minimize the back-action of the measurement device on the measured system, and -although they have certain counterintuitive features -can reveal the analogues of classical concepts in quantum mechanics; e.g., state determination with the minimal disturbance, classical causality [366,367,368,369,370,371], and even mapping out of the complete wave function [372] or of the average trajectories of single photons in a double-slit experiment [373].…”

Section: Other Types Of Measurementsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Other Types Of Measurementsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…The expression between square brackets on the right-hand side thus corresponds to the weak value associated with a (weak) measurement of the usual momentum operator,p = −i ∇, followed by a standard (strong) measurement of the position operator r (with outcome r). The combination of the two measurements eventually provides the value of the local momentum p at the position r. In particular, the quantity measured in the experiment performed by Kocsis et al [2] was the transversal component of this momentum.…”

Section: Introductionmentioning

confidence: 99%

“…This landscape started changing in 2011, with experiments showing that it is possible to reconstruct the photon wave function from direct measurements [1] and to infer how photons travel (on average) in Young's experiment [2]. This apparent breach in the above principles is possible through the experimental implementation of the concept of weak measurement [3][4][5], which does not constitute a true violation of the quantum rules, but only looking at them with different eyes.…”

Section: Introductionmentioning

confidence: 99%

“…In this regard, if the same experiment is repeated introducing some degree of incoherence, the collection of frames of the transverse momentum will give us an idea on how the corresponding mixed state evolves, even though we are aware that such a state only represents a kind of average information about the quantum system. Leaving aside the question about what such a state really represents or if it really exists, our purpose here is just to investigate which kind of trajectories can be associated with it and, therefore, what could be expected from a real experiment, which in principle could be easily tested by means of the same experimental setup used in [2], although including some minor changes related to the way how the mixedness or incoherence is treated.…”

Section: Introductionmentioning

confidence: 99%

“…Notice that in the first scenario one would expect the classical-like result of trajectories for two independently open slits, while in the second scenario trajectories evolve with the information that both slits are open. Now, under such circumstances, how does the transverse momentum (weak value) looks like if we perform measurements at different positions from the slits as in [2]? What we have noticed is that the trajectories associated with sets of measurements render in the end results that display analogous properties to those of the pure case, namely that trajectories avoid crossing through the same point at the same time even if we do not observe any interference features.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

What dynamics can be expected for mixed states in two-slit experiments?

Luis

Sanz

2015

Annals of Physics

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Weak-measurement-based experiments [Kocsis et al., Science 332 (2011) 1170 have shown that, at least for pure states, the average evolution of independent photons in Young's two-slit experiment is in compliance with the trajectories prescribed by the Bohmian formulation of quantum mechanics. But, what happens if the same experiment is repeated assuming that the wave function associated with each particle is different, i.e., in the case of mixed (incoherent) states? This question is investigated here by means of two alternative numerical simulations of Young's experiment, purposely devised to be easily implemented and tested in the laboratory. Contrary to what could be expected a priori, it is found that even for conditions of maximal mixedness or incoherence (total lack of interference fringes), experimental data will render a puzzling and challenging outcome: the average particle trajectories will still display features analogous to those for pure states, i.e., independently of how mixedness arises, the associated dynamics is influenced by both slits at the same time. Physically this simply means that weak measurements are not able to discriminate how mixedness arises in the experiment, since they only provide information about the averaged system dynamics.

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Fundamental Tests of Quantum Mechanics

Bachor

Ralph

2019

A Guide to Experiments in Quantum Optics

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Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer

Cited by 640 publications

References 24 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

What dynamics can be expected for mixed states in two-slit experiments?

Fundamental Tests of Quantum Mechanics

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