Elitzur-Vaidmann Quantum Imager with Mach-Zender Polarization Interferometer

Elitzur-Vaidmann Quantum Imager with Mach-Zender Polarization Interferometer

Elitzur-Vaidmann Quantum Imager with Mach-Zender Polarization Interferometer requires only the possibility of an interaction, not the actual interaction to be able to create an image. It is especially useful for scanning objects that you don't want to spoil via an actual interaction.

The original challenge was to know which sensors were active and which were inert without actually triggering the sensors. With classical physics, the only way to know which are active and which are inert is to actually attempt to activate the sensors.

A signal can be derived from quantum interferometer testing when there is only the possibility that the sensor will activate, even when it does not actually do so.

The EV scheme was originally described as a thought experiment using a set of "photon-triggered bombs". Suppose that you are given a set of photon-triggered bombs housed in light-proof cases. There is a hole in each bomb through which light may pass. Some of the devices are "live" bombs, constructed so that when any single photon of light enters the hole, the bomb explodes. There are also "dud" bombs that will allow any photon to pass completely through the hole and exit without an explosion. You are given the task of identifying as many devices as possible that are certain to be live bombs but that have not yet been detonated.

This problem is impossible to solve with classical physics concept. If all the devices are exposed to photons, the live bombs will all be destroyed and only the dud bombs will remain. The EV (Elitzur-Vaidmann) scheme employs the peculiarities of quantum mechanics to solve the problem. A signal can be derived from a quantum interferometer testing when there is only the possibility that the bomb will explode, even when it does not actually do so.

The Mach-Zender interferometer is a standard optical tool used to measure the index of refraction of gases. The interferometer uses a 50%-50% beam splitter to divide incoming light into two beams. These beams are then deflected by mirrors along paths that form a rectangle. They meet at a second beam splitter, which recombines them. The combined beams then goes to one of two photon detectors.

The light source emits photons one at a time on command. A photon emerges from the source and passes through the upper beam-splitter, which has the characteristic that 50% of the time the photon will be reflected by 90º and 50% of the time it will be transmitted straight through. It may then travel to mirror A or to mirror B where it will be reflected by 90º. Along either path, the photon reaches the lower beam-splitter, where it may again be transmitted or reflected, reaching either photon detector D1 or D2.

If the paths between the beam-splitters in the Mach-Zender interferometer have precisely the same path lengths, all photons will go to detector D1 and none will go to detector D2. The single photon must be treated as a wave that travels along both paths. After each beam-splitter, the emerging reflected wave is 90º out of phase with the emerging transmitted wave. This causes the waves at detector D1 to be in phase and to reinforce, while the waves at detector D2 will be 180º out of phase and will cancel.

If an opaque object is placed on the lower path after mirror A, it will block light waves along the lower path, insuring that all of the light arriving at the lower beam splitter had come along the upper path and been reflected by mirror B. In this case, there is no interference, and the lower beam splitter sends equal components of the incident wave into the two detectors.

When we do the single photon measurement with no opaque object, we detect the photon at D1 100% of the time. If we do the same measurement with the opaque object blocking the lower path, we detect a photon at D1 25% of the time, a photon at D2 25% of the time, and detect no photon at all 50% of the time because it was absorbed. Detection of a photon at D2 guarantees that an opaque object is blocking the lower path but has not actually intercepted the photon. Detecting a photon at detector D1, on the other hand, gives no information on whether or not an object blocks the lower path.

What distinguishes quantum mechanics from classical physics is the "collapse of the wave function". In a situation like the interferometer, in which light waves that travel along two paths can interfere, the interference can take place only if we have no way of determining which path was taken. Any measurement that determines the path will "collapse" the wave function to that particular path, after which there can be no two-path interference.

In a completely light-free laboratory, we place a photon-triggered sensor in the lower path. If the sensor is live, then sending a single photon through constitutes a "which-path" measurement. If the sensor activates, we know that the photon took the lower path. If it does not activate, we know that the photon took the upper path. In either case, the wave function collapses to the indicated path. Therefore, if we detect a photon in detector D2 in this situation, it means that a photon did not take the lower path. In this case, we are guaranteed that the object in the lower path is a live sensor rather than inert. Although no photon has reached it and it has not activated, we have identified an active sensor. The Elitzur Vaidmann scheme detects the possibility of a photon interaction with the sensor, even though no photon actually interacts with it. The photon that might have interacted with it has instead traveled along the upper path via mirror B.

If we perform this test on the set of photon-triggered sensors, 50% of the time the sensor will activate, 25% of the time we will receive an inconclusive D1 signal, and 25% of the time we will receive a D2 signal indicating an unactivated live sensor. If the test gives a D1 signal, we gain no information, but we can send in another photon and try again. After we have tried many times and always received a D2 signal, we may conclude that the lower path is open and that the sensor is inert. The net result is that we will be able to identify one third of the live sensors without activating them, while activating two thirds of the active ones, on average, but we will identify 100% of the inert sensors. If we are searching for inert sensors, these are good numbers. If we are searching for active sensors without actually activating them, this has a high mortality rate.

The improved version of the Elitzur Vaidmann technique produces interaction-free high-resolution profiles of small objects using events in which no photons interact with the objects being "viewed" and plotted their profiles.

A technique for improving the efficiency of the Elitzur Vaidmann procedure, in effect reduces the number of activated sensors to zero. They use another peculiarity of quantum mechanics associated with wave function collapse and called the Quantum Zeno Effect.

The Problem of the Arrow is one of the paradoxes proposed by the Greek philosopher Zeno of Elea. Imagine an arrow in flight. At some instant during its flight, it is in a fixed position. At another instant it is in another fixed position. In fact, at any instant, its position is always fixed. When, Zeno asked, does the arrow move? It is as if the act of examining the arrow's position prevents its motion.

Theoretical physicists noticed that quantum mechanics contained the analog of Zeno's arrow paradox.

Suppose you have a photon that is initially polarized horizontally (H) but that passes through a series of optical elements that progressively make small rotations of its polarization direction with the cumulative effect to rotate the photon's polarization to vertical (V).

Quantum measurements cannot simply measure a photon's polarization direction, instead we must pass it through a Horizontal (H) polarizing filter and see if it survives. If so, it has Horizontal polarization, if not, it has Vertical polarization. The measurement collapses the wave function, which resets the photon's polarization to be precisely Horizontal or Vertical.

After each rotator we place a Horizontal polarization filter, the photon is repeatedly reset to Horizontal and must emerge with Horizontal polarization. This is the quantum Zeno effect, the quantum equivalent of "a watched pot never boils". A "watched" (repeatedly measured) photon can't change its polarization, while a photon not watched can change its polarization freely.

The quantum Zeno effect applied to horizontally polarized photons are recycled through one optical device that rotates the polarization orientation by a small angle. The photon proceeds to a splitter that transmits Vertical polarization and reflects Horizontal polarization. Because there was only a tiny rotation in the polarization, the probability of transmission Vertical is much weaker than that of reflection Horizontal. This split is followed by mirrors and a device that recombines light on the Horizontal and Vertical paths back into one beam.

The Elitzur Vaidmann Test is made by sending a single photon into the apparatus and intercepting the weak Vertical beam path with an opaque object (the equivalent of passing it through the sensor). The apparatus is arranged so the light is repeatedly cycled through, so there are many successive Elitzur Vaidmann tests using the Vertical component of the beam.

The net result is that if no opaque object (inert sensor) is in the Vertical path, there is no measurement and the recycled light beam after a number of passes will rotate from Horizontal to Vertical polarization. However, if an opaque object (active sensor) is in the Vertical-beam, the survival of the photon constitutes a path measurement, and the photon polarization is repeatedly reset to the Horizontal polarization state. Therefore, final H polarization of the photon indicates the presence of an opaque object (active sensor) in the Vertical path, while final Vertical polarization of the photon indicates no opaque object (inert sensor) in the Vertical path.

If the beam makes N passes through the system and the polarization rotator changes the polarization direction by an angle of 90º/N on each pass, the probability that the photon will interact with the opaque object (sensor will activate) is P(N) = 1 - [Cos(90º/N)]^2N, a probability that decreases roughly as 1/N as the number of passes N is made large. For example, with 10 passes the probability of activation is 21.95%, with 100 passes it is 2.4%, 1000 passes is 0.25%, and so on. After 500 passes, for each 2 times more passes is 2 times less chance of activation.

This technique is used on biological molecules that are light-sensitive and might be altered or destroyed by interaction with a photon, or on atomic or quantum scale systems where the act of measurement alters their properties. Another application is quantum computing, a non-interacting connection to a quantum computing element entangles the photon with the state of the system, permitting transfer of un-collapsed quantum information to another part of the system. Effectively, the quantum information is teleported from one part of the computer to another.

Interaction-Free Measurements: Elitzur and L. Vaidman, Foundations of Physics 23, 987 (1993).

Interaction-Free Imaging: Andrew G. White, et al, Phys. Rev. A58, 605-608 (1998) and , preprint quant-ph/9803060 , LANL Archive, (26 April, 1998).

Quantum Zeno Interaction-Free Measurements: P. G. Kwiat, et al, Phys. Rev. Letters (in press), preprint quant-ph/9909083, LANL Archive, (27 Sept., 1999); see also Scientific American, pp. 72-78 (Nov-1996), and http://p23.lanl.gov/Quantum/kwiat/ifm-folder/ifmtext.html

As bizarre, exotic and bleeding edge as this sounds, it dates back to 1993.

The modern circa 2531 Concordat 49431 version uses a penetrating potential particle instead of a photon to view the interior of an object instead of just the surface. So long as the particle has a polarization, this scheme is workable.

Because of the recycling of the particle polarization, the scans can take a long time. The lower the tolerable risk of interaction, the more passes that have to be made by the polarization recycler.

The time taken for a scan is compounded by the desired resolution. If the resolution is micrometer scale instead of millimetre scale, one has to make 1 billion more scans. A nanometer scale scan will require 10^18 (a billion billions) more scans than the millimetre scale scan.

If one has a base of 10^18 scans, and has a zero tolerance, one must have 10^18 * 10^18 = 10^36 scans per cubic millimetre. If you could do a trillion scans per second, then it would take 2.8 billion times the age of the universe to complete the scan of 1 cubic millimetre with absolutely zero percent chance of actual interaction. Either cut down the resolution, be more risk tolerant or use many such scans running in parallel.

There are time saving methods such as starting with rough resolution and eliminating certain volumes and concentrating more upon others.