Quantum sensors have amazing powers. They can detect the presence of an obstacle without ever interacting with it. For instance, consider a bomb that is coated with a light sensitive layer that sets off the bomb if it absorbs just a single photon. Then put this bomb inside a quantum sensor system and shoot photons at it. Remarkably, using the weirdness of quantum mechanics, it is possible to design the system in such a way that you can detect the presence of the bomb using photons without ever setting it off. How can photons see the bomb without illuminating it? The answer is a bizarre side effect of quantum physics in which quantum wavefunctions are recognized as the root of reality as opposed to the pesky wavefunction collapse at the moment of measurement.
The ability for a quantum system to see an object with light, without exposing it, is uniquely a quantum phenomenon that has no classical analog.
All Paths Lead to Feynman
When Richard Feynman was working on his PhD under John Archibald Wheeler at Princeton in the early 1940’s he came across an obscure paper written by Paul Dirac in 1933 that connected quantum physics with classical Lagrangian physics. Dirac had recognized that the phase of a quantum wavefunction was analogous to the classical quantity called the “Action” that arises from Lagrangian physics. Building on this concept, Feynman constructed a new interpretation of quantum physics, known as the “many histories” interpretation, that occupies the middle ground between Schrödinger’s wave mechanics and Heisenberg’s matrix mechanics. One of the striking consequences of the many histories approach is the emergence of the principle of least action—a classical concept—into interpretations of quantum phenomena. In this approach, Feynman considered ALL possible histories for the propagation of a quantum particle from one point to another, he tabulated the quantum action in the phase factor, and he then summed all of these histories.
One of the simplest consequences of the sum over histories is a quantum interpretation of Snell’s law of refraction in optics. When summing over all possible trajectories of a photon from a point above to a point below an interface, there are a subset of paths for which the action integral varies very little from one path in the subset to another. The consequence of this is that the phases of all these paths add constructively, producing a large amplitude to the quantum wavefunction along the centroid of these trajectories. Conversely, for paths far away from this subset, the action integral takes on many values and the phases tend to interfere destructively, canceling the wavefunction along these other paths. Therefore, the most likely path of the photon between the two points is the path of maximum constructive interference and hence the path of stationary action. It is simple so show that this path is none other than the classical path determined by Snell’s Law and equivalently by Fermat’s principle of least time. With the many histories approach, we can add the principle of least (or stationary) action to the list of explanations of Snell’s Law. This argument holds as well for an electron (with mass and a de Broglie wavelength) as it does for a photon, so this not just a coincidence specific to optics but is a fundamental part of quantum physics.
A more subtle consequence of the sum over histories view of quantum phenomena is Young’s double slit experiment for electrons, shown at the top of Fig 1. The experiment consists of a source that emits only a single electron at a time that passes through a double-slit mask to impinge on an electron detection screen. The wavefunction for a single electron extends continuously throughout the full spatial extent of the apparatus, passing through both slits. When the two paths intersect at the screen, the difference in the quantum phases of the two paths causes the combined wavefunction to have regions of total constructive interference and other regions of total destructive interference. The probability of detecting an electron is proportional to the squared amplitude of the wavefunction, producing a pattern of bright stripes separated by darkness. At positions of destructive interference, no electrons are detected when both slits are open. However, if an opaque plate blocks the upper slit, then the interference pattern disappears, and electrons can be detected at those previously dark locations. Therefore, the presence of the object can be deduced by the detection of electrons at locations that should be dark.
Fig. 1 Demonstration of the sum over histories in a double-slit experiment for electrons. In the upper frame, the electron interference pattern on the phosphorescent screen produces bright and dark stripes. No electrons hit the screen in a dark stripe. When the upper slit is blocked (bottom frame), the interference pattern disappears, and an electron can arrive at the location that had previously been dark.
Consider now when the opaque plate is an electron-sensitive detector. In this case, a single electron emitted by the source can be detected at the screen or at the plate. If it is detected at the screen, it can appear at the location of a dark fringe, heralding the presence of the opaque plate. Yet the quantum conundrum is that when the electron arrives at a dark fringe, it must be detected there as a whole, it cannot be detected at the electron-sensitive plate too. So how does the electron sense the presence of the detector without exposing it, without setting it off?
In Feynman’s view, the electron does set off the detector as one possible history. And that history interferes with the other possible history when the electron arrives at the screen. While that interpretation may seem weird, mathematically it is a simple statement that the plate blocks the wavefunction from passing through the upper slit, so the wavefunction in front of the screen, resulting from all possible paths, has no interference fringes (other than possible diffraction from the lower slit). From this point of view, the wavefunction samples all of space, including the opaque plate, and the eventual absorption of a photon one place or another has no effect on the wavefunction. In this sense, it is the wavefunction, prior to any detection event, that samples reality. If the single electron happens to show up at a dark fringe at the screen, the plate, through its effects on the total wavefunction, has been detected without interacting with the photon.
This phenomenon is known as an interaction-free measurement, but there are definitely some semantics issues here. Just because the plate doesn’t absorb a photon, it doesn’t mean that the plate plays no role. The plate certainly blocks the wavefunction from passing through the upper slit. This might be called an “interaction”, but that phrase it better reserved for when the photon is actually absorbed, while the role of the plate in shaping the wavefunction is better described as one of the possible histories.
Quantum Seeing in the Dark
Although Feynman was thinking hard (and clearly) about these issues as he presented his famous lectures in physics at Cal Tech during 1961 to 1963, the specific possibility of interaction-free measurement dates more recently to 1993 when Avshalom C. Elitzur and Lev Vaidman at Tel Aviv University suggested a simple Michelson interferometer configuration that could detect an object half of the time without interacting with it [1]. They are the ones who first pressed this point home by thinking of a light-sensitive bomb. There is no mistaking when a bomb goes off, so it tends to give an exaggerated demonstration of the interaction-free measurement.
The Michelson interferometer for interaction-free measurement is shown in Fig. 2. This configuration uses a half-silvered beamsplitter to split the possible photon paths. When photons hit the beamsplitter, they either continue traveling to the right, or are deflected upwards. After reflecting off the mirrors, the photons again encounter the beamsplitter, where, in each case, they continue undeflected or are reflected. The result is that two paths combine at the beamsplitter to travel to the detector, while two other paths combine to travel back along the direction of the incident beam.
Fig. 2 A quantum-seeing in the dark (QSD) detector with a photo-sensitive bomb. A single photon is sent into the interferometer at a time. If the bomb is NOT present, destructive interference at the detector guarantees that the photon is not detected. However, if the bomb IS present, it destroys the destructive interference and the photon can arrive at the detector. That photon heralds the presence of the bomb without setting it off. (Reprinted from Mind @ Light Speed)
The paths of the light beams can be adjusted so that the beams that combine to travel to the detector experience perfect destructive interference. In this situation, the detector never detects light, and all the light returns back along the direction of the incident beam. Quantum mechanically, when only a single photon is present in the interferometer at a time, we would say that the quantum wavefunction of the photon interferes destructively along the path to the detector, and constructively along the path opposite to the incident beam, and the detector would detect no photons. It is clear that the unobstructed path of both beams results in the detector making no detections.
Now place the light sensitive bomb in the upper path. Because this path is no longer available to the photon wavefunction, the destructive interference of the wavefunction along the detector path is removed. Now when a single photon is sent into the interferometer, three possible things can happen. One, the photon is reflected by the beamsplitter and detonates the bomb. Two, the photon is transmitted by the beamsplitter, reflects off the right mirror, and is transmitted again by the beamsplitter to travel back down the incident path without being detected by the detector. Three, the photon is transmitted by the beamsplitter, reflects off the right mirror, and is reflected off the beamsplitter to be detected by the detector.
In this third case, the photon is detected AND the bomb does NOT go off, which succeeds at quantum seeing in the dark. The odds are much better than for Young’s experiment. If the bomb is present, it will detonate a maximum of 50% of the time. The other 50%, you will either detect a photon (signifying the presence of the bomb), or else you will not detect a photon (giving an ambiguous answer and requiring you to perform the experiment again). When you perform the experiment again, you again have a 50% chance of detonating the bomb, and a 25% chance of detecting it without it detonating, but again a 25% chance of not detecting it, and so forth. All in all, every time you send in a photon, you have one chance in four of seeing the bomb without detonating it. These are much better odds than for the Young’s apparatus where only exact detection of the photon at a forbidden location would signify the presence of the bomb.
It is possible to increase your odds above one chance in four by decreasing the reflectivity of the beamsplitter. In practice, this is easy to do simply by depositing less and less aluminum on the surface of the glass plate. When the reflectivity gets very low, let us say at the level of 1%, then most of the time the photon just travels back along the direction it came and you have an ambiguous result. On the other hand, when the photon does not return, there is an equal probability of detonation as detection. This means that, though you may send in many photons, your odds for eventually seeing the bomb without detonating it are nearly 50%, which is a factor of two better odds than for the half-silvered beamsplitter. A version of this experiment was performed by Paul Kwiat in 1995 as a postdoc at Innsbruck with Anton Zeilinger. It was Kwiat who coined the phrase “quantum seeing in the dark” as a catchier version of “interaction-free measurement” [2].
A 50% chance of detecting the bomb without setting it off sounds amazing, until you think that there is a 50% chance that it will go off and kill you. Then those odds don’t look so good. But optical phenomena never fail to surprise, and they never let you down. A crucial set of missing elements in the simple Michelson experiment was polarization-control using polarizing beamsplitters and polarization rotators. These are common elements in many optical systems, and when they are added to the Michelson quantum sensor, they can give almost a 100% chance of detecting the bomb without setting it off using the quantum Zeno effect.
The Quantum Zeno Effect
Photons carry polarization as their prime quantum number, with two possible orientations. These can be defined in different ways, but the two possible polarizations are orthogonal to each other. For instance, these polarization pairs can be vertical (V) and horizontal (H), or they can be right circular
and left circular. One of the principles of quantum state evolution is that a quantum wavefunction can be maintained in a specific state, even if it has a tendency naturally to drift out of that state, by repeatedly making a quantum measurement that seeks to measure deviations from that state. In practice, the polarization of a photon can be maintained by repeatedly passing it through a polarizing beamsplitter with the polarization direction parallel to the original polarization of the photon. If there is a deviation in the photon polarization direction by a small angle, then a detector on the side port of the polarizing beamsplitter will fire with a probability equal to the square of the sine of the deviation. If the deviation angle is very small, say Δθ, then the probability of measuring the deviation is proportional to
(Δθ)2, which is an even smaller number. Furthermore, the probability that the photon will transmit through the polarizing beamsplitter is equal to 1-(Δθ)2
, which is nearly 100%.
This is what happens in Fig. 3 when the photo-sensitive bomb IS present. A single H-polarized photon is injected through a switchable mirror into the interferometer on the right. In the path of the photon is a polarization rotator that rotates the polarization by a small angle Δθ. There is nearly a 100% chance that the photon will transmit through the polarizing beamsplitter with perfect H-polarization reflect from the mirror and return through the polarizing beamsplitter, again with perfect H-polarization to pass through the polarization rotator to the switchable mirror where it reflects, gains another increment to its polarization angle, which is still small, and transmits through the beamsplitter, etc. At each pass, the photon polarization is repeatedly “measured” to be horizontal. After a number of passes N = π/Δθ/2, the photon is switched out of the interferometer and is transmitted through the external polarizing beamsplitter where it is detected at the H-photon detector.
Now consider what happens when the bomb IS NOT present. This time, even though there is a high amplitude for the transmitted photon, there is that Δθ amplitude for reflection out the V port. This small V-amplitude, when it reflects from the mirror, recombines with the H-amplitude at the polarizing beamsplitter to produce a polarization that has the same tilted polarizaton that it started with, sending it back in the direction from which it came. (In this situation, the detector on the “dark” port of the internal beamsplitter never sees the photon because of destructive interference along this path.) The photon is then rotated once more by the polarization rotator, and the photon polarization is rotated again, etc.. Now, after a number of passes N = π/Δθ/2, the photon has acquired a V polarization and is switched out of the interferometer. At the external polarizing beamsplitter it is reflected out of the V-port where it is detected at the V-photon detector.
Fig. 3 Quantum Zeno effect for interaction-free measurement. If the bomb is present, the H-photon detector detects the output photon without setting it off. The switchable mirror ejects the photon after it makes π/Δθ/2 round trips in the polarizing interferometer.
The two end results of this thought experiment are absolutely distinct, giving a clear answer to the question whether the bomb is present or not. If the bomb IS present, the H-detector fires. If the bomb IS NOT present, then the V-detector fires. Through all of this, the chance to set off the bomb is almost zero. Therefore, this quantum Zeno interaction-free measurement detects the bomb with nearly 100% efficiency with almost no chance of setting it off. This is the amazing consequence of quantum physics. The wavefunction is affected by the presence of the bomb, altering the interference effects that allow the polarization to rotate. But the likelihood of a photon being detected by the bomb is very low.
On a side note: Although ultrafast switchable mirrors do exist, the experiment was much easier to perform by creating a helix in the optical path through the system so that there is only a finite number of bounces of the photon inside the cavity. See Ref. [2] for details.
In conclusion, the ability for a quantum system to see an object with light, without exposing it, is uniquely a quantum phenomenon that has no classical analog. No E&M wave description can explain this effect.
Further Reading
I first wrote about quantum seeing the dark in my 2001 book on the future of optical physics and technology: Nolte, D. D. (2001). Mind at Light Speed : A new kind of intelligence. (New York, Free Press)
More on the story of Feynman and Wheeler and what they were trying to accomplish is told in Chapter 8 of Galileo Unbound on the physics and history of dynamics: Nolte, D. D. (2018). Galileo Unbound: A Path Across Life, the Universe and Everything (Oxford University Press).
Paul Kwiat introduced to the world to interaction-free measurements in 1995 in this illuminating Scientific American article: Kwiat, P., H. Weinfurter and A. Zeilinger (1996). “Quantum seeing in the dark – Quantum optics demonstrates the existence of interaction-free measurements: the detection of objects without light-or anything else-ever hitting them.” Scientific American 275(5): 72-78.
References
[1] Elitzur, A. C. and L. Vaidman (1993). “QUANTUM-MECHANICAL INTERACTION-FREE MEASUREMENTS.” Foundations of Physics 23(7): 987-997.
[2] Kwiat, P., H. Weinfurter, T. Herzog, A. Zeilinger and M. A. Kasevich (1995). “INTERACTION-FREE MEASUREMENT.” Physical Review Letters 74(24): 4763-4766.
Galileo Unbound 