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The Quantum Eraser

by John G. Cramer

Alternate View Column AV-90
Keywords: quantum mechanics nonlocality Wheeler delayed choice eraser interferometer retroactive action
Published in the June-1998 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 12/17/97 and is copyrighted ©1997 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

     Tests of quantum phenomena that were previously featured in this column have recently been popping up in the popular press. Early in 1997, physicists in Zurich demonstrated the extent of nonlocality of Einstein-Podolsky-Rosen experiments (see my column "Einstein's Spooks and Bell's Theorem", Analog, January, 1990) using fiber optic cables belonging to the Swiss Telephone System to show the nonlocal correlations of two detectors separated by more than a hundred kilometers. Last December, the first demonstration of the quantum teleportation of photons (see "The Quantum Physics of Teleportation", Analog, December, 1993) was performed in Austria. In this column I want to describe another test of quantum mechanics, the quantum eraser, which brings some of the most peculiar and counter-intuitive aspects of the theory into sharp focus.

    Richard Feynman observed that if you wish to confront all of the mysteries of quantum mechanics, you have only to study quantum interference in the two-slit experiment. So let's start there. A light source S which emits only one photon at a time illuminates an opaque screen which contains two narrow vertical slits (call the slits A and B) through which the light may pass. Some distance beyond this screen is D, a flat light detector (perhaps photographic film or a silicon CCD) which senses and records the photons of light that pass through the slits and strike it.

    In this situation, after enough photons are sent through the slits the detector will record an "interference pattern", a pattern of vertical stripes of maximum light intensity separated by stripes where there is no intensity at all. Observation of these interference stripes constitutes a quantum measurement, because the distance between the stripes depends on the wavelength of the light. Since the momentum of the individual photons is Planck's constant divided by the wavelength, the interference pattern also measures the momentum of the photons passing through the slits.

    The interference pattern is present because light photons are presented with two alternative paths between source and detector, path SAD and path SBD. Quantum mechanics requires that when such alternatives are present, there is a quantum wave function for each, and that these wave functions must be added together (with appropriate phasing) and then squared to predict the outcome of a measurement. In other words, the interference pattern occurs because each photon must pass through both slits en route to the detector, taking path SAD and path SBD. If the difference in length of the two paths puts the wave functions in phase, the waves add and reinforce and a maximum (bright stripe) is produced at the detector. If the difference in path length puts the waves out of phase, the waves subtract and cancel and a minimum (dark stripe) results.

    One of the central themes of quantum mechanics is that this interference (reinforcement or cancellation) can happen only because we have no knowledge of whether the photon has taken path SAD or path SBD. If we modify the experiment to detect which slit the photon passed through, the stripes of the interference pattern will be replaced by a uniform pattern of light with no maxima and minima.

    Suppose, for example, we add a mechanism that covers one of the slits systematically, so that each photon sees only one open slit. In this case there will be no interference pattern. Similarly, if we place polarization filters over the slits so that one passes vertically polarized light and the other horizontally polarized light there will be no interference pattern (even if polarization at D is not actually measured). This is because a polarization sensitive detector could (in principle) determine which path the photon took. In the famous Bohr-Einstein, Einstein suggested a more subtle modification of the slits to sense the slight recoil as a photon passing through it is deflected toward the detector. Bohr demonstrated that this seemingly minimal modification would also destroy the interference pattern.

    A trickier version of the two-slit experiment, the "delayed choice" experiment was proposed by John A. Wheeler. Here, the detector D is mounted so that it can be rapidly retracted. Behind it are two telescopes TA and TB, each collimated to see the light passing through only one of the two slits and to detect it with a quantum sensitive photomultiplier tube placed at its image focus. Therefore, detection at D constitutes a measurement of the momentum of the photon, while detection at TA or TB measures the position of the photon, i.e., which slit it has passed through.

    Such apparatus is often used to illustrate the wave-particle duality of light. The light waves which form the interference pattern at D must have passed through both slits in order to interfere, while the photon particles which strike the photomultiplier surfaces can have passed only through the single slit at which the telescope was pointed. The position and momentum measurements are "complimentary" in Bohr's sense and mutually exclusive. The uncertainty principle is not violated, however, because only one of the two experiments can be performed on a given photon. But Wheeler is not done yet.

    The detector D is mounted on a fast-acting pivot mechanism so that it can on command either be raised into position to intercept the photon or alternatively dropped out of the way so that the photon can proceed to telescopes TA or TB. Thus when D is up, we make an interference measurement requiring the photon to pass through both slits. When D is down, we make a position measurement requiring that the photon pass through only one slit.

    Wheeler's innovative is this: the time duration required to insure that the photon has safely passed the slits but not yet reached the apparatus is known to the experimenter, and he refrains from deciding which experiment to do. Only after the photon has passed the slit plane does the experimenter decide whether to measure its one slit position (D down) or its two slit momentum (D up). Delayed-choice experiments of this type have actually been performed, and the interference pattern detected when D is up is not affected by the delayed choice. Somehow the photon can retroactively arrange to go through one slit or two depending on which measurement is ultimately made.


    The new quantum eraser experiments are high- tech descendents of Wheeler's delayed choice concept. They use a new trick for making "entangled" quantum states. If ultra-violet light from a 351 nanometer (nm) argon-ion laser passes through a LiIO3 crystal, non-linear effects in the crystal can "split" the laser photon into two longer wavelength photons at 633 nm and 789 nm in a process called "down-conversion". These two photons are connected non-locally because they constitute a single "entangled" quantum state. They are required to be in the same state of polarization, and a measurement performed on one of the photons affects the outcome of measurements performed on the other (see my column "Einstein's Spooks and Bell's Theorem", Analog, January, 1990).

    Further, in a recent version of the experiment performed by a group in Innsbruck, Austria (see reference below), the laser beam is reflected so that it makes two passes through the non-linear crystal, so that an entangled photon pair may be produced in either the first or the second pass. The experiment has the configuration of a six-pointed star formed of three lines (one horizontal and two diagonal) intersecting at a point occupied by the non-linear crystal. The laser beam passes through the crystal moving horizontally downstream, is reflected by a downstream mirror, and passes through the crystal again moving horizontally upstream. Along the two diagonal branches downstream of the laser the two down-converted photons made in the first laser- pass travel to mirrors, where they are reflected back to their production point and travel past it to upstream detectors. The laser beam making its second pass through the crystal has a second chance to make a pair of down-converted photons. If these are produced, they travel directly to the upstream detectors along the two upstream diagonal branches.

    The net result is that a photon arriving in coincidence at the two upstream detectors may have been produced in either the first laser pass through the crystal and reflected to the detector or in the second pass and traveled directly to the detector. There is no way of determining which "history" (direct vs. reflected) happened, so the states are superimposed. Therefore, the quantum wave functions describing these two possible production histories must interfere. The interference may be constructive or destructive, depending on the interference phase determined by the downstream path lengths (all about 13 cm) to the three mirrors of the system. Changing the path length to one of the mirrors (perhaps by moving the laser beam reflector) produces a succession of maxima and minima in the detectors.

    This experimental setup is governed by the same physics as the two-slit experiment, but, because there are two coincident photons and well separated paths for the two possible histories it is easier to play quantum tricks with the system. Now the experiment is modified to remove the quantum interference by placing distinguishing labels on the two possible photon histories (direct vs. reflected). A transparent optical element called a "quarter-wave plate" (QWP) is placed in front of one of the photon reflection mirrors. The QWP rotates the polarization state of the reflected photons from vertical to horizontal polarization as they pass twice through it.. This polarization modification allows the reflected and direct "histories" to be distinguished, because the reflected photons are horizontally polarized while the direct photons are vertically polarized.

    Since the two superimposed quantum states are now distinguishable (even if no polarization measurement is actually made) the interference pattern is eliminated, both in the arm of the experiment in which the QWP is placed and also in the other arm, where no modification was made. Finally, the "quantum eraser" is brought into use. Any vertically or horizontally polarized light beam can be separated into a light component polarized 45o to the left of vertical and a light component polarized 45o to the right of vertical. Therefore, for the photons with the QWP in front of their mirror, placing just in front of their detector a filter which passes only light polarized 45o to the left of vertical "erases" the label that has distinguished the two histories. When this is done, it is found that interference is restored.

    Further, the paths to the two detectors can have different lengths, with the path through the 45o filter made much longer than the other path. This has the effect of erasing the path- distinguishing label after the other photon has already been detected. This modification has no effect on the interference. The post-facto erasure still restores interference. The path label can be erased retroactively and has the same effect (retroactive or not) on the quantum interference of the waves. Effectively, the quantum eraser has erased the past!


    It may perhaps seem that the labeling and erasing in one arm of the two-photon experiment could be used to telegraph information to the other arm, with the presence or absence of interference in the second arm acting as a nonlocal faster-than-light signal. Unfortunately for the SF writer looking for a good faster-than- light gimmick, this doesn't work because the interference in the second arm is only observed in coincidence with the detection of a photon in the other arm. Once again, Nature has revealed the power of her FTL telegraph while forbidding us access to the telegraph key.


Reference:

"Complementarity and the Quantum Eraser", T. J. Herzog, et al., Physical Review Letters 75, 3034- 3037 (1995), and the references contained therein.

SF Novels by John Cramer:  my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .

AV Columns Online: Electronic reprints of about 177 "The Alternate View" columns by John G. Cramer, previously published in Analog , are available online at: http://www.npl.washington.edu/av.


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