Quantum Zeno Effect (Script) (Patreon)

They say that a watched pot never boils. This has now been proven true by quantum mechanics.

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“A moving arrow is at rest.” This is obviously a nonsensical contradiction. But Zeno, Greek philosopher famous for his metaphysical trolling, devised a paradox whose conclusion is just this. Here’s how it goes: if you look at an arrow flying through the air at any instantaneous snapshot in time, the arrow doesn’t travel any distance. If time is composed of an infinite number of these snapshots, and the arrow doesn’t move in any of them, then the arrow is at rest during the entirety of its flight. The moving arrow is at rest.

Nowadays, most physicists and mathematicians don’t really see Zeno’s arrow as paradoxical. If we think of an instant as a vanishingly small interval of time, then during that time the moving arrow travels a vanishingly small distance - but the “vanishingly small” part cancel out and the arrow’s instantaneous velocity is very real. That’s what a mathematician might tell you - but quantum mechanics also has a thing or two to say about extremely tiny distances and time intervals. In fact, if we’re talking about a quantum arrow, there may be a way to freeze its motion simply by looking at it, through the aptly named quantum Zeno effect.

The quantum Zeno effect predicts that certain quantum events - like the electrons moving between atomic energy levels, or the decay of atomic nuclei, can be frozen through the simple act of observation. I’m going to tell you about some very real experiments that claim to have demonstrated this phenomenon. But first, let’s see if the quantum Zeno effect can save us from being shot by a quantum arrow.

First we’ll give our arrow a few weird behaviours befitting a good quantum object: we have quantization - certain properties of our arrow can only take on specific, discrete values - like how an electron can only occupy certain energy states in an atom. In this case let’s say our quantum arrow’s position is quantized - it can exist only at the start and end of its path, but not in between. In order to travel from start to end, it has to flick between these states without occupying intervening space.

One way to do that is by executing a quantum jump, which we discussed in our recent episode.

OK, the next quantum property we need is superposition. Just like Schrodinger’s cat,

our quantum arrow can exist in multiple states at once. That means it can be at the start and end of its path simultaneously. It could be 50-50 split between the two, or 25% in one, 75 in the other, etc. Now, you never actually see it in both states at once. Rather, each state has an amplitude that determines the probability of finding the arrow in that state were you to try to observe it. In the language of the Copenhagen interpretation of quantum mechanics, we say that the “wavefunction collapses” on observation. Prior to that observation, the arrow exists as just the distribution of probability amplitudes of its position; its wavefunction is spread between the start and end of the trajectory. But after observation it collapses to definitely one or the other - at least, according to Copenhagen - and we’ll be coming back to this craziness later.

This superposition thing actually gives our quantum arrow a way to travel its path smoothly and gradually, but still without occupying the space in between. And maybe for us to save ourselves in the end.

Here’s the scenario: someone shoots a quantum arrow at you. It begins in the pure state of being entirely at the start of its journey, but then it enters a superposition of states - mostly at the start, but also a little bit at the end. If you observe the arrow now, most likely it’ll “collapse” to the starting position, but there’s a small chance it would suddenly appear at the final state - having reached you. But if there’s no observation the wavefunction evolves - less and less amplitude at the starting state and more and more at the end state - until it finally enters the pure state of definitely hitting you.

Two ways this  can play out: the arrow leaves the quantum bow with a quantum twang. In shock you close your eyes for a second, which is your mistake - it allows the arrow’s wavefunction to evolve smoothly into the state of quantum ouch. But what if you keep your eyes open? Every observation you make of the arrow collapses its wavefunction into one of its possible positions - start or end. But because you start watching it close to the beginning of its journey, there’s very little probability of it collapsing to the end. Your observation resets the trajectory to the start, at which point the wavefunction has to start evolving from scratch - but you keep observing it and keep resetting it back again  through the magic of the quantum Zeno effect. So the message is clear - if anyone ever tries to shoot you with a quantum arrow, don’t blink.

Of course arrows don’t really behave this way, but it seems that this is exactly what real quantum systems should do. If a system can occupy two discrete states and transition between those states, that transition can be halted if you continuously measure the state - again, in theory. This has actually been tested for electron transitions in atoms - and I’ll tell you about the experiments in a minute. But in principle this would also work for radioactive decay, even chemical reactions

The basic idea of the quantum Zeno effect was first proposed by Alan Turing, but it got a full theoretical description in the 1970s. And then in 1990, a group of scientists headed up by David Wineland and Wayne Itano claimed to have demonstrated it in an experiment by halting electron energy transitions. These were some of the same people who first demonstrated quantum jumps, and using a similar scheme that we described in that episode. To recap - we have a collection of laser-cooled atoms in an electromagnetic trap. A constant radio-frequency field is tuned to cause electrons to oscillate smoothly between two energy levels - call them 1 and 2. Just like our quantum arrow, sometimes an electron is in state 1, sometimes state 2, but in between it’s a smoothly-varying superposition of both.

Next they flash the atoms with a laser whose frequency matches the energy difference between state 1 and a new state, state 3. If the electron is in state 1 when the laser pulse hits, it absorbs a laser photon and jumps to 3, and then immediately drop back down to 1, releasing the energy as a new photon that the researchers can detect - so the atoms glow during these laser pulses. On the other hand, if the atom is in state 2 during the pulse, it would not absorb a photon and the atom would stay dark.

But what if the laser hits while the electron is in the middle of a transition - in a superposition of states 1 and 2? According to the wavefunction collapse picture, it has to make a choice - the superposition must vanish and the electron will be seen in either state 1 or state 2. According to the researchers, the laser acts like a measurement - and remember, measurement should be able to freeze quantum arrows and presumably also electron transitions via the quantum Zeno effect.

To test this, the researchers start the atoms all in state one, and then hit them with a series of very rapid laser pulses. In theory, if these “measurements” are fast enough they should stop the wavefunction from evolving. And they report that it did exactly this. The faster the chain of pulses, the more likely that atoms remained in state 1 - which they could check with one final pulse to see if the atoms still glowed. Long story short: it appears you can freeze a quantum state by measuring it continuously.

Further studies have claimed successful observation of the quantum Zeno effect, including various studies of atomic energy levels, as well as the freezing of quantum tunneling - the same phenomenon that allows particles to “teleport” out of nuclei during nuclear decay. It’s even been proposed that the quantum Zeno effect plays a role in the photochemical reactions that give birds their ability to see magnetic fields - something we’ve talked about before.

So there we have it. Quantum Zeno effect verified? Well, not quite. A flurry of papers came out after the 1990 result disputing the claim on various grounds, and the arguments have continued. But I want to highlight one particular point. The physicist Leslie Ballentine argued that it’s not the abstract act of measurement that causes the quantum Zeno effect, but rather it’s a physical consequence of interacting with the system. In this case, hitting the atoms with a laser pulse. Ballentine’s objection gets to the very foundations of quantum mechanics: what exactly do we mean by a “measurement” and what do we mean by wavefunction collapse?  Let’s start with measurement.

It’s never possible to perform a measurement without interacting with a system, and that interaction has consequences beyond just increasing our knowledge. If the measurement interaction is subtle enough then you might hope to gain that info without perturbing the system too much. Ballentine showed that each laser photon perturbed the system in such a way that the electron had an increased chance to jiggle back to its starting location. And to achieve a true quantum Zeno-like freezing you’d need to hit the atom with many, many photons - and that was certainly not a “subtle” measurement. Recently, a group of researchers from Washington University claim to have proved that it’s perturbation, not measurement, that causes the quantum Zeno effect by demonstrating that with the right type of “jiggling” a quantum transition could be forced to speed up rather than to freeze - in what’s called the anti-Zeno effect.

Another way to think about measurement is in terms of how much information it extracts from the system. The idea is that measurement causes wavefunction collapse because it scrambles the delicate information connecting different parts of the superposition.  Superposition only exists if the different parts of the wavefunction are connected or correlated with each other. We would say that the wavefunction for different electron states or quantum arrow positions are in phase with each other, or “coherent”. But that coherence is easy to mess up. Any interaction causes information to quickly spread into the environment. Decoherence occurs, and the different parts of the wavefunction, representing possible realities, can no longer interact.

In fact, as argued by Ballentine, you can force a quantum system back to its starting state without true decoherence. But to get a full quantum Zeno effect - a perfect freezing of your electron or quantum arrow - you need to perfectly measure it, and that means decoherence - or the illusion of wavefunction collapse.

So on to wavefunction collapse. In the Copenhagen interpretation, only the part of the wavefunction corresponding to the measurement outcome survives.  But in the Many Worlds interpretation, the entire wavefunction survives and splits and you split with it.

Obviously we’ve talked about decoherence and many worlds before, but let’s talk about what  the quantum Zeno effect looks like in this picture. The effect should still exist, because Many Worlds gives the same predictions as Copenhagen. But in this case, you’re not forcing the wavefunction to collapse back to its starting position through the power of observation. Your interaction with the wavefunction causes it to decohere - which means two things - you perturb the system in a non-subtle way. For example, by forcing the electron or quantum arrow out of its superposition. In Many Worlds, that means generating separate realities corresponding to the possible outcomes. If you do it right you’ll produce more “worlds” in which the system goes back to its starting state. And then you enter the world of of the possible outcome states - again, most likely the starting position. But if your observation wasn’t perfect, there’ll be some worlds in which the final state is chosen rather than the starting state. Like I said, if someone shoots you with a quantum arrow, don’t blink.

The quantum Zeno effect appears to be real - but its interpretation is still hotly debated. And perhaps some of this is just semantic - for example, how do we really define measurement and interaction? And what is wavefunction collapse? But quantum zeno experiments are difficult, and perhaps future brilliant tests will give us clues to unravel the deepest mysteries at the heart of quantum mechanics. A watched pot never boils. How do you know? Because you watched space time.

What exactly do we mean by a measurement? Let’s look at the experiment and try to figure out when the measurement was made: since one of the atom’s electronic states emitted photons and the other did not, this established a correlation, or entanglement, between the state of the atoms and the electromagnetic field around them. This field in turn interacted with the vacuum chamber that contained the experiment, the lab around it, and the photomultiplier tube that detects the photons from the atoms. But even if this detector was off, few would dispute that this is still effectively a “measurement.” There’s nothing special about a conscious observer—a tree still falls if nobody is there to hear it.

So where did the measurement take place? It looks like a measurement is just a series of interactions, producing a cascade of more and more complicated entangled states, to the point where we can no longer keep track of all of the degrees of freedom, and we say the system has decohered. There is no well defined place where it transitions from being a coherent interaction to decoherence. It’s a gradual thing. Ballentine insists that an atom interacting with a laser field is not a measurement because it’s easy to keep track of the coherences in this relatively simple system, but at what point would he draw the line between interactions and measurement? Seems like an arbitrary line to draw.

And this gets to a huge challenge in interpreting quantum phenomena.

- including arguments that it wasn’t correct to describe the interaction with the laser as a “measurement”, nor that there was a true wavefunction collapse. I’ll come back to that …

Over the following few decades, various researchers…  https://en.wikipedia.org/wiki/Quantum_Zeno_effect#Experiments_and_discussion

And we also saw a possible manifestation of the quantum Zeno affect in our quantum jumps episode, where researchers were able to halt the evolution of an analog atom made from superconducting circuits.

There’s even a hypothesis that bird magnetoreception … previous episode.

That seemed to satisfy most people, and anyways, whether the suppression of the evolution was driven by measurement collapsing the wavefunction or by interaction with the environment sans collapse, the predicted result was the same. So did it really matter?

But we see the subtle differences between these two interpretations amplified when we apply the Quantum Zeno effect to explain the quantum jump experiment described in a previous episode.

If you don’t remember the episode, the setup of the experiment was actually very similar to the quantum Zeno effect described above, but in this case the “atom” was actually an artificial atom made from a superconducting device. They had the same elements: a bright state B, a dark state D, a weak coupling field which allowed transitions between states B and D, and a measurement field which coupled to the bright state, but not the dark state.

They were able to see these quantum jumps by monitoring the photon “clicks.” A click indicated that the atom was in the bright state B, while the absence of a click implied that the atom was in state D. When their photon detector suddenly stopped getting any clicks for a period of time, then they knew that the atom’s state had jumped from B to D. They found that, while they seemed to occur at random times, if you zoomed in on one of the jumps, it was clear that there was a smooth, continuous evolution from one energy level to another that took a few microseconds.

What did this have to do with the quantum Zeno effect? The act of measurement prevented the sinusoidal oscillation between states B and D, instead immediately collapsing the wavefunction back down to state B, preventing the atomic state from evolving as it normally would.

If the measurement were perfect, then that would be all there was to the story. But since their measurement wasn’t perfect, sometimes the atomic state would be allowed to evolve for a small amount of time when the detector didn’t register a click. This would mix a little bit more of the D state into the atom’s superposition. Then a subsequent measurement would have a slightly higher probability of measuring the atom to be in state D. If that happened, they said a quantum jump had occurred.

In addition to explaining these quantum jumps through the lens of the quantum Zeno effect, the theorists also made another claim: that in contrast to the microseconds-long jumps from B to D, the quantum jumps in the opposite direction were truly instantaneous.

How can this be? It all depends on exactly how you measure the states—this will determine what and how much information you obtain with each measurement. Inherent in this particular measurement scheme is a certain asymmetry between the two levels. If the scientists’ measurement device detected a photon, then they would know without a doubt that the atom was in the bright state, B. If they didn’t detect a photon, though, it could be that the atom was in the dark state, or it could be that it was in the bright state, but their imperfect measurement device failed to the detect the photon. But the longer the state remains dark, the more certain you can be that it is, indeed, in the dark state and not just a fluke due to imperfect measurement. This continuous, gradual increase in the knowledge of the state as the atom continues to remain dark is the reason for the continuous evolution that characterized the quantum jump from the bright state B to the dark state D. The timescale of this jump is therefore a function of the coupling between the atom and the detector and not something fundamental to the atom itself or to quantum jumps in general.

On the other hand, a jump from D to B would be signaled by a click of the photon detector. As soon as a click is registered, the atom’s wavefunction immediately collapses to being in the bright state B. So these jumps are really, truly instantaneous. Take that, Schrodinger.

The surprising thing about this explanation is the apparently essential role of the observer in the process. In the initial Quantum Zeno experiment, the concepts of “interactions with the environment” and “measurements” were used interchangeably, because both explanations produced the same results. But in this quantum jump experiment, we see how the act of measuring the system puts us in a subspace in which the quantum state evolves from bright to dark. Without the measurement, the quantum jumps wouldn’t exist. Physicists Martin Plenio and Peter Knight put it this way: “The jumps that occur in this description can be considered as due to the increase of our knowledge about the system which is represented by the wave-function.”

But another physicist, Howard Carmichael, warns us against taking this picture too literally, writing, “The trajectories are not to be interpreted as revealing the physical reality... What they do reveal is an aspect of the physical reality, and they do this in a way that permits talk about the system plus environment with reference to its parts, each part having attributes, the attributes being correlated.”

Sound confusing? That’s because it is. Even experts aren’t quite sure of what to make of this philosophically, despite its excellent match to experiment. But this does seem to be a loose thread, and if we keep on tugging, we may begin to unravel the mysteries of space time.

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We see this in some familiar examples: for example, an electron jumping between orbits.

Remember that One of the most fundamental aspects of quantum mechanics is that there are quantum objects that exist in these discrete states. Like electron energy levels.

Not only do they exist in these discrete state, it looks like they jump between them, which we call Quantum jump , as opposed to traveling from one to another. They don't occupy any of the intervening states. This  has always been hard to imagine for us used to continuous analogue tktk, we naturally ask, but what happens in between? Well, heisenberg says, there’s no in between or something like that (check in from his book)

One idea for how things might move between states, or in other words, what is happening during the quantum jump, is that rather than it being a sudden transition from one state to another, it may be this gradual transition, in which the electron occupies what we call a superposition in which it is simultaneously in both states. You know, like the classic schrodinger's cat.

So it starts mostly in the first state then gradually ends up in the second state. It's partially in one state and partially in the second state and the weight of this “partially” gradually changes. So this is still very weird, but at least the gradual part of the superposition is something that resembles more of the type of world we are used to.

Now back to the quantum arrow thought experiment:

In the quantum jumps episode we showed a cool experiment that seemed to verify that quantum jumps really do happen this way. The experiment used an analog atom - but it may be that real atoms behave this way. That experiment also found that quantum jumps could be stopped in their tracks … [authors say qze?]  And that gives us hope for stopping our quantum arrow.