Delayed choice experiment

The delayed-choice experiment (Engl .; dt. About Delayed quantum choice ) shows the wave-particle duality of quantum physics , according to which on a quantum object the typical characteristics of both shafts as can be observed also in the particles. Both modes of description are mutually exclusive and can never be determined simultaneously in the details of a physical process ( principle of complementarity ). In the delayed choice experiment it is shown in particular that at the end of a process it depends on the type of observation carried out, with which of the two properties the object appears, even if the observation method is only selected after the process has been completed. In this way, the wave-particle dualism is specified in such a way that the choice between the two possibilities of the appearance is not made during an interaction process, but only at the end of an irreversible quantum mechanical measurement . In the context of the Copenhagen interpretation , this phenomenon is explained by the fact that the wave function of the quantum object contains a component for each of the possibilities and only collapses to a single really realized component during the act of measurement ( state reduction ).

The basic idea of delayed quantum choice was first worked out in 1931 by CF von Weizsäcker . In another thought experiment in 1984, JA Wheeler applied it to the observation of an interaction dating back billions of years. In recent times, real experiments have been carried out that clearly substantiate the theoretical predictions. Delayed quantum choice was also successfully demonstrated in connection with the quantum eraser .

Heisenberg microscope (from Weizsäcker)

Heisenberg gave the first physical justification for the uncertainty principle named after him in the form of a thought experiment : The location of an electron is to be determined with a microscope by means of a single photon scattered by the electron into the microscope . His then 18-year-old student C. F. von Weizsäcker described the quantum mechanical process in more detail and noticed that the same apparatus can also be used to determine the momentum of the electron instead. All you have to do is attach the photo plate on which the detected photon causes a blackened point in the microscope, not in the image plane, but in the focal plane of the objective. You have to choose between the two measurement options, because they are mutually exclusive because a (low-energy) photon can only cause blackening once. However, the selection (in the thought experiment) only needs to be made when the photon has already passed through the lens, i.e. clearly after the act of interaction with the electron. This choice between exclusive alternatives is an expression of the wave-particle dualism and thus the principle of complementarity , because the electron can only have a certain location due to its particle character, while its momentum in quantum mechanics is a property of the associated matter wave, i.e. it presupposes the wave character.

Two images of the same galaxy: interference or overlay? (Wheeler)

In 1983, J. A. Wheeler proposed another thought experiment to illustrate in a particularly drastic way the freedom that long after its interaction, one can determine whether one or the other of its complementary properties can be determined on the quantum object by choosing the type of observation. The act of interaction was here billions of years ago and billions of light years away from us. It is about the curvature of the light path caused by gravity, through which one observes two adjacent images of some distant galaxies because another galaxy is close to the direct line of sight and about halfway. “Close by” here means something like 50,000 light years. The photons can then reach us in two different ways, the direct route and the curved route around the other galaxy. Since the photons now arrive from slightly different directions, they create two closely spaced images of the original galaxy in a telescope. The two bundles of light that produce the two separate images in the image plane must first have superimposed behind the lens. If the transit time of the light waves coincided on both paths within the coherence length of natural light, i.e. in the order of magnitude of 10 ⁻⁸ s (although this has not yet been observed), their superposition would be coherent. As in a double slit experiment, one would have to expect interference fringes there, from which it would emerge that every photon must have taken both paths at the same time, i.e. it has propagated like a wave. Further back, in the image plane, one would have the two separate images of the same source, which correspond to the separate paths of the photons when they move like particles. With the free decision of the observer, where to collect the photons, he determines their wave or particle character. Obviously, this choice cannot have had any retroactive influence on your behavior during the flyby of the distracting galaxy, at a time when the earth might not even exist.

Experimental realization

Reduced to the size of a physical laboratory, Wheeler's thought experiment was actually carried out almost identically in a Mach-Zehnder interferometer . The light from a source, which only ever emits one photon at a time, is divided by a beam splitter into two different paths A and B , which cross each other at right angles after the same distance and coherently superimpose this crossing area. After passing the overlay area, the light paths separate again and at the end of each path an image of the source is created. Two photon detectors installed there register the same number of photons, but never at the same time, because one photon cannot trigger two clicks. Individual photons must have taken either one way or the other. If, however, a semi-transparent mirror is attached at the intersection at 45 °, then both light paths are split into two branches each, so that half of the A light flies together with half of the B light in the same direction, and at right angles to it also together the other two halves. In one direction, the A and B waves are 180 ° out of phase and cancel each other out completely. The detector positioned there never clicks. In the other direction, the waves are in phase (because of the additional reflection in the first beam splitter) and intensify accordingly. All photons flying into the apparatus arrive here. By moving the last mirror slightly, you can vary the length of the two paths A and B up to the intersection and then get a perfect interference pattern. The result in a nutshell: Without the last semi-transparent mirror in the light path, photons behave like particles, which as such can only fly on one of the two paths; but with the mirror every photon came as a wave on both paths. The idea is that this choice should have been made when passing the first beam splitter. Because of the small dimensions of the apparatus and the short periods of time involved in the process, one could fundamentally ask whether the presence or absence of the mirror could have influenced the photons in such a way that they choose the wave or particle option at the first beam splitter. In the delayed choice version of the experiment, this possibility is excluded (although there is no physical explanation for it anyway). Of course, the mirror couldn't be installed and removed quickly enough. But you can replace it with a fast electro-optical component that, depending on the voltage applied, acts like the desired mirror or allows light to pass unhindered from both directions. Finally, it is ensured that each photon flies individually through the apparatus, whereby the choice of the mode of action of the electro-optical component is decided by a random number, which is only obtained from the shot noise of an ordinary light source when the photon has already reached the first beam splitter happened. More precisely, these processes are spatially separated from one another, i. H. only by signals with faster than light speed could one have influenced the other at all. The result expected according to quantum mechanics, but surprising to the mind trained in everyday phenomena, is that the type of observation always decides whether the wave or particle character is shown in the manner described, regardless of when the observation takes place and when about yours Kind was decided.

interpretation

The experiments show sustained quantum choice not that the quantum object therebetween selected depending on the type of observation, "a wave or a particle to be ". They show that the object with regard to the observed physical quantity - and only this - produces the same measurement results that in classical physics could only be caused either by a wave or by a particle.

In the context of the Copenhagen interpretation of quantum mechanics, a normalized state vector is assigned to a single quantum object at any point in time (often referred to as a wave function). This contains a component with a certain amplitude for every possible measured value of a physical quantity. From the amplitudes, the probability distribution of the possible measurement results can be calculated for every possible measurement of this variable on the system. However, how the concrete measurement result emerges from this probability distribution of possibilities on an individual object, which has become the only reality through the measurement, has not been clarified. This process is described by the state reduction (also known as the collapse of the wave function), which instantaneously irretrievably deletes the components of all other possible measurement results, without it being possible to justify which the surviving component is beyond the specification of the probability. These problems of interpreting the quantum mechanical measurement process are serious, but beyond that the delayed quantum selection does not present any further difficulties. ${\ displaystyle | \ Psi \ rangle}$

A wave-like behavior of the quantum object is usually read from the observation of a location-dependent interference pattern. This arises in the areas to which the quantum object came in two different ways, in which there is a difference in the quantum mechanical phase depending on the location . Both paths are contained as components in the state vector , generally in the form ${\ displaystyle | \ Psi \ rangle}$ ${\ displaystyle | \ Phi _ {1} \ rangle, \; | \ Phi _ {2} \ rangle}$

{\ displaystyle | \ Psi \ rangle = a | \ Phi _ {1} \ rangle + b | \ Phi _ {2} \ rangle}

with the complex amplitudes or . The square of the magnitude of the associated wave function then gives the probability density (or intensity ) to find the object at the location . It is ${\ displaystyle a}$ ${\ displaystyle b}$ ${\ displaystyle \ Psi ({\ vec {r}})}$ ${\ displaystyle {\ vec {r}}}$

{\ displaystyle | \ Psi ({\ vec {r}}) | ^ {2} = | a | ^ {2} \, | \ Phi _ {1} ({\ vec {r}}) | ^ {2 } + | b | ^ {2} \, | \ Phi _ {2} ({\ vec {r}}) | ^ {2} +2 \ operatorname {Re} [ab ^ {*} \ Phi _ {1 } ({\ vec {r}}) \ Phi _ {2} ({\ vec {r}}) ^ {*}]}

The partial sum of the first two summands is the incoherent sum of the two intensities, because each summand gives the respective intensity if either only one or only the other way would be possible for each quantum object, so that only one of the two components exists. In the event that both paths are possible, but the partial waves do not interfere, the incoherent sum correctly reflects the measurement result. With this value the total intensity of the quantum objects could be observed if they were particles. The last summand is called the interference term. It depends on the quantum mechanical phases, can be positive or negative and z. B. lead to the complete extinction of the intensity. All three summands together form the coherent sum that shows the wave character of the object. ${\ displaystyle | \ Phi _ {1} \ rangle, \; | \ Phi _ {2} \ rangle}$ ${\ displaystyle | \ Phi _ {1} \ rangle, \; | \ Phi _ {2} \ rangle}$

Particle-like behavior is therefore not only evident in real particles, but also occurs in waves in areas where the interference term disappears. There can be several reasons for this:

One of the components here has a vanishing wave function. This is e.g. B. the case with crossed wave bundles, as in Wheeler's thought experiment, when they separate again behind the area where they overlap.

The individual quantum objects that are observed one after the other arrive in states in which the phase differences fluctuate in an uncontrolled manner. The coherent sum then applies to each individual object, but on average over many, the interference terms have the value zero. This usually also occurs with light when the light source is not emitting coherent radiation . It is the basis of the long-established ray optics , in which the light is viewed as if it were propagating like particles along trajectories. ${\ displaystyle | \ Psi \ rangle}$

The quantum object has an inner degree of freedom that has a different value on the two paths. Then the two components are orthogonal and cannot interfere. This occurs z. B. one if the quantum object is a photon and only orthogonal polarization directions are allowed through on the two paths. If the marking with the which-path information is reversed or made ineffective before the measurement causes the state reduction, the interference reappears (see quantum eraser ). ${\ displaystyle | \ Phi _ {1} \ rangle, \; | \ Phi _ {2} \ rangle}$

Individual evidence

↑ Delayed Choice Experiment. In: Lexicon of Physics. Spektrum der Wissenschaft Verlagsgesellschaft, 1998, accessed on February 21, 2019 .
↑ ^a ^b Determination of the position of an electron through a microscope . In: Journal of Physics . tape 70 , 1931, pp. 114-130 . See p. 128
↑ John A. Wheeler: Law without law . In: John A. Wheeler, Woijciech H. Zurek (Eds.): Quantum Theory and Measurement . Univ. Press, Princeton NJ, USA 1983, pp. 193 .
^ ^A ^b Vincent Jacques, E Wu, Frédéric Grosshans, François Treussart, Philippe Grangier, Alain Aspect and Jean-François Roch: Experimental Realization of Wheeler's Delayed-Choice Thought Experiment . In: Science . tape 315 , no. 5814 , 2007, p. 966-968 , doi : 10.1126 / science.1136303 .
↑ Herbert Walther, B.-G. Englert, Marlan Scully: Complementarity and Wave Particle Dualism . In: Spectrum of Science . tape 2 . Spectrum of Science Academic Publishing House, 1995, p. 50 ff .

[1] Delayed Choice Experiment. In: Lexicon of Physics. Spektrum der Wissenschaft Verlagsgesellschaft, 1998, accessed on February 21, 2019 .

[Weizsäcker1931-2] Determination of the position of an electron through a microscope . In: Journal of Physics . tape 70 , 1931, pp. 114-130 . See p. 128

[Wheeler1983-3] John A. Wheeler: Law without law . In: John A. Wheeler, Woijciech H. Zurek (Eds.): Quantum Theory and Measurement . Univ. Press, Princeton NJ, USA 1983, pp. 193 .

[Jacques2007-4] A ^b Vincent Jacques, E Wu, Frédéric Grosshans, François Treussart, Philippe Grangier, Alain Aspect and Jean-François Roch: Experimental Realization of Wheeler's Delayed-Choice Thought Experiment . In: Science . tape 315 , no. 5814 , 2007, p. 966-968 , doi : 10.1126 / science.1136303 .

[5] Herbert Walther, B.-G. Englert, Marlan Scully: Complementarity and Wave Particle Dualism . In: Spectrum of Science . tape 2 . Spectrum of Science Academic Publishing House, 1995, p. 50 ff .