I Quantum Jumps and Schrodinger's Cat are predictable

[Tom.G]

Quantum Jumps are predicted using microwave monitoring. Weird.

https://phys.org/news/2019-06-physicists-schrodinger-cat.html

 

[PeterDonis]

I'm always highly skeptical of sensational-sounding claims on phys.org. I'm doubly skeptical when there isn't even a link to a paper (not even an arxiv preprint) in the article, which tells me that the article writer doesn't want me to look up the actual paper and find out that, while their article says "man bites dog!", the actual paper is more like "dog bites man, and now we have a more detailed model of the tooth marks".

 

[f95toli]

The paper just appeared in Nature

https://www.nature.com/articles/s41586-019-1287-z

 

[A. Neumaier]

Quantum Jumps are predicted using microwave monitoring. Weird.

Quantum jumps were observed (as predicted) in the lab long ago; see ''Are there quantum jumps?'' from my Theoretical Physics FAQ.

The paper just appeared in Nature

https://www.nature.com/articles/s41586-019-1287-z

But there are no relations to Schrödinger's cat.

From the abstract:

we experimentally demonstrate that the jump from the ground state to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable ‘flight’, by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the evolution of each completed jump is continuous, coherent and deterministic. We exploit these features, using real-time monitoring and feedback, to catch and reverse quantum jumps mid-flight—thus deterministically preventing their completion. Our findings, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory

This is serious work about tracking and controlling the continuous measurement of single quantum systems. One of the coauthors is Carmichael, a well-known expert in quantum optics and author of two volumes on Statistical methods in quantum optics.

From the main text:

despite the long-term unpredictability of the jumps from |G〉 to |D〉, they are preceded by an identical no-click record from run to run. Whereas the jump starts at a random time and can be prematurely interrupted by a click, the deterministic nature of the uninterrupted flight comes as a surprise given the quantum fluctuations in the heterodyne record Irec during the jump—an island of predictability in a sea of uncertainty. [...]

From the experimental results of Fig. 2a one can infer, consistent with Bohr’s initial intuition and the original ion experiments, that quantum jumps are random and discrete. Yet the results of Fig. 3 support a contrary view, consistent with that of Schrödinger: the evolution of the jump is coherent and continuous. The difference in timescales in the two figures allows the coexistence of these seemingly opposed point of views and the reconciliation of the discreteness of countable events, such as jumps, with the continuity of the deterministic Schrödinger’s equation. [...]

although all 6.8 × 106 recorded jumps (Fig. 3) are entirely independent of one another and stochastic in their initiation and termination, the tomographic measurements as a function of Δtcatch explicitly show that all jump evolutions follow an essentially identical, predetermined path in Hilbert space—not a randomly chosen one—and, in this sense, they are deterministic. These results are further corroborated by the reversal experiments shown in Fig. 4, which exploit the continuous, coherent, and deterministic nature of the jump evolution

I'm always highly skeptical of sensational-sounding claims on phys.org.

The claim there is the usual unjustified amplification of science made sensational for the public.

 

[Demystifier]

The paper just appeared in Nature

https://www.nature.com/articles/s41586-019-1287-z

As far as I can see, this is not much more than an experimental demonstration of the known fact that decoherence lasts a finite time.

 

[Cthugha]

This is a very nice work with respect to the experiments involved, but I consider it as somewhat oversold. If you go to the methods section, their operational definition of a quantum jump is "Sections of the (continuous) measurement record are converted into state assignments, as discussed above, such as B, G or D. In the experiment, long sequences of such measurements yield the same result, that is, GGG… or DDD… When the string of results suddenly switches its value, we say that a quantum jump has occurred".

Here, they just drive the bright state transition and the dark state transition simultaneously and consider the absence of deexcitation from the bright state as some evidence that the system is in the dark state. However, I do not fully agree to this idea. When you drive the dark state transition with a low Rabi frequency and you notice that there is no emission from the bright state, this first and foremost means that the probability amplitude for dark state occupation is close to one in the Rabi oscillation cycle. Of course you will get an "identical no-click record from run to run" in this scenario as the probability of the system ending up in the dark state follows the standard Rabi cycle. Accordingly, their "catching the quantum jump" is essentially just going back the Rabi cycle downwards towards the ground state after going up part of the way to the dark state. In other words: they do not "reverse" quantum jumps, but they drive the system towards states, where there is a finite probability amplitude for this quantum jump to occur (if the system becomes perturbed randomly), introduce a threshold for this probability amplitude and as soon as the experimental parameters cross this threshold, they reduce this probability again. The jump is not reversed. It never happens.

However, doing that in the presence of the comparably strong driving field towards the bright state is a really nice experimental demonstration of what is possible with fast electronics, FPGAs and feedback.

 

[nettleton]

If this is the case, is the the triggering of the decay of a individual atom in a radioactive solid also predictable?

 

[A. Neumaier]

If this is the case, is the the triggering of the decay of a individual atom in a radioactive solid also predictable?

Probably not. The system in the experiments reported is very special, and a single system, while a radioactive solid consists of a huge number of radiactive atoms, of which a random one will decay, and then another random one.

Based on what is in the paper, it could perhaps be feasible one day to prepare a single radioactive atom in some controllable ion trap and know just a little ahead of the time that it is going to decay. But this would be surely another experimental challenge.

 

[Heikki Tuuri]

There is an anecdote that Erwin Schrödinger threatened to quit physics, if people keep talking about "quantum jumps".

The wave function always develops smoothly in time. There are no jumps. It is the measurement which makes the wave function to collapse in the standard Copenhagen interpretation.

Here we answer this question affirmatively: we experimentally demonstrate that the jump from the ground state to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable ‘flight’, by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the evolution of each completed jump is continuous, coherent and deterministic.

https://www.nature.com/articles/s41586-019-1287-z
They "monitor a population of an auxiliary energy level". That sounds like making a "weak measurement" of the system in the Aharonov style. If I am right, the system develops in separate steps toward an end state. They notice when it has made a step, and then force it back to the start state.

The authors say that the result is consistent with standard quantum mechanics.

The authors should not talk about quantum jumps, as the term does not exist in standard quantum mechanics. Also, talking about a predictable "flight" sounds like a hidden variable theory. It is a bad choice of words.

 

[A. Neumaier]

There is an anecdote that Erwin Schrödinger threatened to quit physics, if people keep talking about "quantum jumps".

Please give a reliable source. Or did you mean that he said the following?

Wenn es bei dieser verdammten Quantenspringerei bleiben soll, so bedaure ich, mich mit der Quantentheorie überhaupt befaßt zu haben.

''If I had known we were going to go on having all this damned quantum-jumping, I would never have got involved in the subject.''
(This is a - not completely faithful - translation from here, with reference to the original.)

 

[Heikki Tuuri]

https://motls.blogspot.com/2019/06/experimenters-and-especially.html
Lubos Motl criticizes harshly the language which the authors of the Nature paper use. A "quantum leap" and a "trajectory" are not terms of the standard quantum mechanics.

Nature should be more careful in their editorial policy.

 

[StevieTNZ]

https://www.quantamagazine.org/quantum-leaps-long-assumed-to-be-instantaneous-take-time-20190605/
Another article written about the experiment - well, one wonders how accurate it is (it may be, it may not be).

EDIT: I see the post above deals with this article.

 

[PeroK]

''If I had known we were going to go on having all this damned quantum-jumping, I would never have got involved in the subject.'' (not completely faithful) translation from here, with reference to the original)

It's interesting how much slicker German can be than English. The German has not a wasted word, which is quite hard to achieve in English. In any case, perhaps a better translation is:

"If there is to be no end to this damned quantum-jumping, then I'm sorry I ever had anything to do with quantum theory."

Or:

"If this damned quantum-jumping is here to stay, then I'm sorry I ever had anything to do with quantum theory."

 

[A. Neumaier]

Lubos Motl criticizes harshly the language which the authors of the Nature paper use. A "quantum leap" and a "trajectory" are not terms of the standard quantum mechanics.

Nature should be more careful in their editorial policy.

Or Lubos Motl in his critique; he is not the ultimate arbiter of science.

Terms in physics evolve and are adapted to whatever they are needed for. Otherwise we would have never progress in physics.

 

[Demystifier]

Terms in physics evolve and are adapted to whatever they are needed for. Otherwise we would have never progress in physics.

Yes, but in typical experimental quantum foundations papers in Nature, the purpose of changing the terminology is not a progress in understanding quantum foundations. The purpose is to rise hypes, which helps to publish in Nature, which helps to get funds for producing next papers of a similar kind, ...

 

[Demystifier]

Progress in understanding quantum foundations can be achieved in two ways: either by further developments of the theory, or by experiments the results of which differ from predictions of standard quantum theory. The present work achieved neither of those two.

 

[A. Neumaier]

Yes, but in typical experimental quantum foundations papers in Nature, the purpose of changing the terminology is not a progress in understanding quantum foundations. The purpose is to rise hypes, which helps to publish in Nature, which helps to get funds for producing next papers of a similar kind

They don't change terminology for the purpose of getting publicity. They use long established terminology in their field that just happens to be rejected and miscredited by Lubos Motl.

Progress in understanding quantum foundations can be achieved in two ways: either by further developments of the theory, or by experiments the results of which differ from predictions of standard quantum theory. The present work achieved neither of those two.

Many Nobel prizes were given for experimental work demonstrating existing features of Nature that were either predicted or later explained by standard quantum theory.

 

[Demystifier]

Many Nobel prizes were given for experimental work demonstrating existing features of Nature that were either predicted or later explained by standard quantum theory.

Demonstrating the existence of a feature is one thing, understanding its existence is another. Typically the former comes from experiments and the latter from theories.

 

[A. Neumaier]

Demonstrating the existence of a feature is one thing, understanding its existence is another. Typically the former comes from experiments and the latter from theories.

The paper under discussion is about such a demonstration (though not of Nobel prize quality), and an explanation of it in terms of existing theory. Thus it is progress.

 

[A. Neumaier]

https://motls.blogspot.com/2019/06/experimenters-and-especially.html
Lubos Motl criticizes harshly the language which the authors of the Nature paper use. A "quantum leap" and a "trajectory" are not terms of the standard quantum mechanics.

Read the original Nature paper rather than discussions of popular versions of it!

The authors of the Nature paper give reference to [5-9] where ''modern quantum trajectory theory'' is discussed in detail. Reference [5] is a well-known and very respectable textbook on quantum optics by Carmichael (one of the authors), and [8] is a thick and time-honored (almost 1200 citations in google scholar) survey paper about ''The quantum jump approach to dissipative processes in quantum optics'' by Plenio and Knight, both very accomplished quantum optics experts.

Note that quantum jumps are so much part of the Copenhagen interpretation (the long-time gold standard for quantum mechanics interpretations) that Erwin Schrödinger, who never liked them, wrote even as late as 1952 (but just before the interpretation questions came to the forefront again) a paper with the title ''https://www.jstor.org/stable/pdf/685552.pdf" - in vain.

Note also that nobody seriously claimed (or defended) that quantum jumps actually happen instantaneously, this was always just an idealization of the same sort of the idealization of measurements in Born's rule, which also take time.

The authors of the Nature paper do not talk about a "quantum leap", which is a typical pop-science notion without relevance in quantum physics. Indeed, this notion is used only in the pop-science account of the experiment in Quanta Magazine, to which Lubos Motl (who is an expert not in quantum optics but only in the completely unrelated subject of string theory) mainly refers.

 

[Demystifier]

The paper under discussion is about such a demonstration (though not of Nobel prize quality), and an explanation of it in terms of existing theory. Thus it is progress.

So I must have missed it, how does the paper explain it in terms of existing theory?

 

[A. Neumaier]

So I must have missed it, how does the paper explain it in terms of existing theory?

Read my post #20, the appendix of the paper, and references [5-9] on ''modern quantum trajectory theory''. Nowhere is any theory beyond that assumed.

 

[Lord Jestocost]

Indeed, the association with quantum foundations has convinced many observers that quantum trajectory theory is different from standard quantum mechanics, and therefore to be regarded with deep suspicion⁹. While it is true that stochastic Schr¨odinger and master equations of the type treated in quantum trajectories are sometimes postulated in alternative quantum theories^10–13, these same types of equations arise quite naturally in describing quantum systems interacting with environments (open systems) which are subjected to monitoring by measuring devices. In these systems, the stochastic equations arise as effective evolution equations, and are in no sense anything other than standard quantum mechanics (except, perhaps, in the trivial sense of approaching the limit of continuous measurement).

Todd A. Brun in "A simple model of quantum trajectories" https://arxiv.org/abs/quant-ph/0108132

 

[A. Neumaier]

Indeed, the association with quantum foundations has convinced many observers that quantum trajectory theory is different from standard quantum mechanics, and therefore to be regarded with deep suspicion [...] these same types of equations arise quite naturally in describing quantum systems interacting with environments (open systems) which are subjected to monitoring by measuring devices. In these systems, the stochastic equations arise as effective evolution equations, and are in no sense anything other than standard quantum mechanics

This criticism (should it be one) is very strange.

Quantum trajectory theory is nothing else than effective stochastic evolution equations for a class of open quantum optics systems. Thus it is quite natural and nothing to be suspicious about.

 

[Heikki Tuuri]

The quantum jump method is an approach which is much like the master-equation treatment except that it operates on the wave function rather than using a density matrixapproach. The main component of the method is evolving the system's wave function in time with a pseudo-Hamiltonian; where at each time step, a quantum jump (discontinuous change) may take place with some probability. The calculated system state as a function of time is known as a quantum trajectory, and the desired density matrix as a function of time may be calculated by averaging over many simulated trajectories.

https://en.wikipedia.org/wiki/Quantum_jump_method

Indeed, it is a numerical method for solving the wave equation. The authors should stress that this has nothing to do with quantum leaps of popular science.

 

[A. Neumaier]

The authors should stress that this has nothing to do with quantum leaps of popular science.

No. Scientific papers should ignore popular science, not give it credit for using poor terms.

 

[Cthugha]

They don't change terminology for the purpose of getting publicity. They use long established terminology in their field that just happens to be rejected and miscredited by Lubos Motl.

I am not too sure how I feel about that reply. In some sense you are of course right.

However, you took a similar approach some time ago in your insights article (https://www.physicsforums.com/insights/vacuum-fluctuations-experimental-practice/) which is an unjustified mixture of quoting stuff out of context, misapplying terminology that is used differently in different subfields and rejecting and miscrediting its usage in other fields.

Having reread the present Nature article several times now, I think it is indeed worthy of being published in Nature. However, I consider the experimental ability to control a quantum system as the really important point here. In some sense, this is similar to Haroche's seminal work on cavity QED (https://www.nature.com/articles/nature05589, https://www.nature.com/articles/nature10376).

 

[A. Neumaier]

you took a similar approach some time ago in your insights article (https://www.physicsforums.com/insights/vacuum-fluctuations-experimental-practice/) which is an unjustified mixture of quoting stuff out of context, misapplying terminology that is used differently in different subfields and rejecting and miscrediting its usage in other fields.

I don't think the paper I analyzed there is comparable in the quality of terminology to the one under discussion here. I'd appreciate if you would either moderate your severe accusations, or justify them in detail in the discussion thread associated with that Insight article.

Having reread the present Nature article several times now, I think it is indeed worthy of being published in Nature. However, I consider the experimental ability to control a quantum system as the really important point here. In some sense, this is similar to Haroche's seminal work on cavity QED (https://www.nature.com/articles/nature05589, https://www.nature.com/articles/nature10376).

This is an important experimental point.

The interest for foundations is that monitoring and controlling the state of an individual quantum system can now be done to a point where earlier, more idealized instantaneous quantum jumps can be resolved in time, adding insight to the nature of these ''jumps''.

 

[Cthugha]

I don't think the paper I analyzed there is comparable in the quality of terminology to the one under discussion here. I'd appreciate if you would either moderate your severe accusations, or justify them detail in the discussion thread associated with that Insight article.

I do not mean to be insulting and apologize if my statement came across as such, but I really think your comment is questionable and based on erroneous assumptions. But that is indeed a discussion to be continued elsewhere.

This is an important experimental point.

The interest for foundations is that monitoring and controlling the state of an individual quantum system can now be done to a point where earlier, more idealized instantaneous quantum jumps can be resolved in time, adding insight to the nature of these ''jumps''.

Here, I fully agree. To me it is interesting that this kind of experiment (this is good to see in the ones by Haroche) actually show examples where "weak" measurements actually bring some benefit. In most cases, they are just performed because the experimentalist could do something that sounds cool.

 

[A. Neumaier]

As you bring this "quantum jumping" up again, just have a look at this (all standard QT, no discontinous jumps) (including the theory part which is in the supplements):

https://www.nature.com/articles/s41586-019-1287-z

Since this is about the measurement of a single quantum system, I'd be interested how the minimal (statistical) interpretation makes sense of the correspondence between state and measurement results in this particular case.

 

[vanhees71]

Well, where is there a problem. They measure pretty many "quantum-jump events" in their given setup. You can do statistics using a single "artificial atom" ("quantum dot"). E.g., in the caption of Fig. 3 it's stated that it consists of about 7 Mio. "experimental realizations". If you check the theory in the supplemental material, there's nothing beyond standard QED used there to very accurately describe these findings. I see no contradiction whatsoever to the standard probabilistic interpretation, and I don't see any need of any assumption beyond this minimal interpretation to understand their findings.

 

[A. Neumaier]

Well, where is there a problem. They measure pretty many "quantum-jump events" in their given setup.

But on a single system. They can approximately tell from their measurements when this single system is in which energy eigenstate.

 

[vanhees71]

But on a single system. They can approximately tell from their measurements when this single system is in which energy eigenstate.

So, where is the problem with the standard minimal statistical interpretation? I've only glanced over the theoretical evaluation part (in the addons to the paper), but I don't see anything which is not in accordance with the standard interpretation, and this analysis explains the data.

Whether you do the repeated measurements on one and the same single electron or on always other new electrons, doesn't play a role at all. The only thing you have to do is to prepare it always in the same state and then do the same measurements under the same conditions. Instead of claiming that there's a conflict with the statistical interpretation, I'd say it's a paradigmatic example for its applicability to a real-world experiment. Also the dynamics is in accordance with modern QED rather than with some undynamical instantaneous quantum jumps. If consolidated, it's another experiment in very good accordance with standard QED/quantum optics.

 

[A. Neumaier]

Whether you do the repeated measurements on one and the same single electron or on always other new electrons, doesn't play a role at all. The only thing you have to do is to prepare it always in the same state and then do the same measurements under the same conditions.

But how is your condition realized in this experiment??

Prepared is only the initial state. It then changes through the in this case nearly continuous observation, which apparently (by the natural evidence gathered from the experimental results) collapses it to one of the energy eigenstates - different ones at different times. But your minimal interpretation has no collapse, so how do you find out about the state of this single system after each measurement? You seem to regard the state as a measure of knowledge of the observer - but the observer only knows the initial preparation and the measurement results, which show jumps between noisy observations of two energy levels. Without knowing the intermediate states, how can you assert that the system is ''prepared always in the same state''? When in fact it isn't, since one observes quantum jumps between the two possible energy eigenstates?

Thus you need to invoke much more than the minimal interpretation to interpret the result in the way it is done.

 

[vanhees71]

Where do I have to invoke more than the minimal interpretation? I don't think it makes sense to summarize the supplemental material, where everything is well explained, and of course they make very many observations on very many equally prepared systems to get the curves in Fig. 3 of the main text.

Always the "atom" is prepared in the same initial state and then they read out the population of the ground state as function of time. Everything discussed in the supplemental material is based on standard quantum mechanics. It's of course an open system, but in its description there's nothing used that's not derived beyond the usual minimal statistical interpretation. To see this, it is sufficient to read just Sect. I of the supplement, particularly the caption of Fig. S2.

 

[George Jones]

I'm always highly skeptical of sensational-sounding claims on phys.org. I'm doubly skeptical when there isn't even a link to a paper (not even an arxiv preprint) in the article, which tells me that the article writer doesn't want me to look up the actual paper and find out that, while their article says "man bites dog!", the actual paper is more like "dog bites man, and now we have a more detailed model of the tooth marks".

Today is the first time that I have looked at the article, and I see that "A study announcing the discovery appears in the June 3 online edition of the journal Nature" in the phys.org article, and that a link to the Nature article appears at the bottom of the phys.org article.

Also, the article was not written by a phys.org writer; the article was supplied to phys.org by Yale University ("by Yale University" at the top, and "Provide by Yale University" at the bottom). I do think that it is valid to criticize phys.org for uncritically accepting the Yale-supplied hyperbole. This highights what is becoming a major problem: too often, university PR departments put out over-ther-top bs versions of research performed.

 

[vanhees71]

What Einstein said concerning theorists is also valid for experimentalists: don't listen to their words (or in this case those of the popular press) but look at their deeds, i.e., read the Nature article (including the very valuable supplement). What has been observed are not "quantum jumps" (which do not exist according to modern QT since 1925/26) but the continuous spontaneous and induced transitions from one energy level of a system through coupling to external perturbations.

If confirmed, it's a great step forward, i.e., away from old-fashioned instantaneous "quantum jumps" of the old Bohr-Sommerfeld model to the empirical verification of the predictions of modern quantum theory.

 

[Heikki Tuuri]

Bohr conceived of quantum jumps in 1913, and while Einstein elevated their hypothesis to the level of a quantitative rule with his AB coefficient theory, Schrödinger strongly objected to their existence. The nature and existence of quantum jumps remained a subject of controversy for seven decades until they were directly observed in a single system. Since then, quantum jumps have been observed in a variety of atomic and solid-state systems. Recently, quantum jumps have been recognized as an essential phenomenon in quantum feedback control, and in particular, for detecting and correcting decoherence-induced errors in
quantum information systems .

https://arxiv.org/abs/1803.00545

The authors definitely claim in the introduction that they have observed "quantum leaps" of popular science. As we have several times noted in this thread, quantum leaps do not exist in standard quantum mechanics. Erwin Schrödinger was right.

A. Neumaier brought up that quantum jumps and trajectories are a numerical method of quantum optics. But the authors seem to claim that the numerical method would prove the existence of quantum leaps.

I have to repeat my opinion that Nature has published a paper which is confusing terms of quantum mechanics. Nature made a mistake. The confused philosophical part of the paper should be removed and the authors should just report the experiment.

 

[vanhees71]

Well, this is often the case with Nature papers. I find this disturbing too! The only point is that if you read the text, it becomes clear that the abstract and introduction is just "popular-science gibberish", and in the rest of the paper the science usually gets correctly stated. That's the difference to many popular-science articles, where often you don't even understand the science, if you are an expert in the field ;-)).

 

[A. Neumaier]

What Einstein said concerning theorists is also valid for experimentalists: don't listen to their words (or in this case those of the popular press) but look at their deeds

I wonder if anyone knows the source of this saying.

If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds.

I found in several places the precise wording quoted above, but nowhere an attribution to the precise source.

By the way, adhering to Einstein's advice, I was lead to my thermal interpretation of quantum physics!

 

[A. Neumaier]

I found in several places the precise wording quoted above, but nowhere an attribution to the precise source.

Actually, a more thorough search lead me to a https://www.jstor.org/stable/pdf/184387.pdf, but it had another formulation, though with essentially the same meaning:

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don't listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.

Maybe he said similar things at multiple occasions...

 

[Cthugha]

If confirmed, it's a great step forward, i.e., away from old-fashioned instantaneous "quantum jumps" of the old Bohr-Sommerfeld model to the empirical verification of the predictions of modern quantum theory.

I kind of disagree and this is the thing, which disappoints me a bit about this paper. If you have a look at the derivation of the dynamics of the "quantum jump", especially equations 11 and 14 in the SOM, you will find that the timescale of this continuous evolution is given by the effective transition time scale t_{mid}, which is given by t_{mid}=(\frac{\Omega_{BG}^2}{2\gamma_B})^{-1} \ln{(1+\frac{\Omega_{BG}^2}{\gamma_B \Omega_{DG}})},
where \Omega_{BG} and \Omega_{DG} are the Rabi frequencies of the drives for the bright and dark state transitions, respectively and \gamma_B is the loss rate of the bright state, which is proportional to its spectral width.
Now the interesting thing is that the dominant time scale for the "quantum jump" to the dark state is not given by the Rabi frequency for the driving field that couples the ground and the dark state, but the one that couples the ground and the bright state. This is explained quite easily by the authors by pointing out that this is the quantity that determines the mean time between clicks for the weak measurement in the bright channel. This mean time between clicks is given by:
t_{click}=(\frac{\Omega_{BG}^2}{\gamma_B})^{-1}.
So in fact, the time scale of the transition is given by:
t_{mid}=\frac{t_{click}}{2} \ln{(1+\frac{1}{t_{click} \Omega_{DG}})}.
Now, \Omega_{DG} is of course just the inverse of the time t_{dark} a dark state Rabi cycle takes (up to some prefactors of 2 pi or 2 - I did not follow the normalization), so the whole time scale of the "quantum jump" is something like:
t_{mid}=\frac{t_{click}}{2} \ln{(1+\frac{t_{dark}}{t_{click}})}.
In other words: You can and will change this time scale just by driving the bright transition more strongly because you expect more counts in this case. Basically, this just gives you the probability to be in the dark state after so-and-so-many non-counting events on the bright state transition, which is just a function of how many absent counts you need to get some level of certainty and how long it takes to get to this absent count level. It is not directly related to anything concerning the dark state transition. If you just ramp up the driving field of the bright state transition, so that t_{click} becomes short, you can get arbitrarily close to an instantaneous jump again.

 

[vanhees71]

I don't think that you can come to an instantaneous jump again. There's nothing instantaneous in QT's time evolution.

 

[Cthugha]

In practice: Yes, I agree.
The bare time evolution of the probability amplitude for dark state occupation happens on a slower time scale, anyway. So there should be some point at which a finite time scale of the "quantum jump" (or coupling to the environment or decoherence or whatever you want to call it) emerges. In fact, I would have loved to see a measurement series that just investigates this "mid-time" for several Rabi frequencies of the bright transition. I wonder why the authors did not do that. Either it would have spoiled the mass appeal slightly (because the fact that the timescale is actually not that meaningful physically is a bit downplayed in the manuscript), or non-linearities become non-negligible at high pump powers or at some point the electronics would become too slow to follow the experiment adequately. Still, it would be interesting to perform such an experiment.

 

[vanhees71]

I guess it's also technically pretty difficult to cover all the possible time scales you discuss. I find it remarkable that one can nowadays start to resolve such quantum dynamics at all.

In some cases "timing" is even difficult to grasp theoretically. One example is the "tunnel time", i.e., the time it takes for a particle to tunnel through a potential barrier. I'm not sure whether this has been defined convincingly yet. At least it's a decade-long problem. Today, there's however some progress with the advent of "attosecond laser pules" to make it possible to measure such processes with the necessary time resolution. Of course the measured "tunnel times" also have to be analyzed taking into account the full experimental setup, then also providing the "correct" definition of "tunnel times", as measured by the specific experiment.

 

[A. Neumaier]

"quantum jumps" (which do not exist according to modern QT since 1925/26)

Why then did Schrödinger write in 1952 a paper with the title ''https://www.jstor.org/stable/pdf/685552.pdf" ?
Why then did accomplished quantum physicists again and again refer to quantum jumps?

the reaction shall not involve a jump in the quantum state of the electrons [Footnote 2: The possibility of chemical reactions without quantum jumps in the state of the electronic system has been first realized by F. London]

(Wigner, Calculation of the Rate of Elementary Association Reactions, 1937)

according to quantum mechanics we need, for a complete description of the universe, not only the laws of motion and the initial conditions, but also information about which quantum jump occurs in each case when a quantum jump does occur. The latter information must be included, together with the initial conditions, in that part of the description of the universe outside mathematical theory. [...] Quantum mechanics provides an escape from the difficulty. It enables us to ascribe the complexity to the quantum jumps, lying outside the scheme of equations of motion. The quantum jumps now form the uncalculable part of natural phenomena, to replace the initial conditions of the old mechanistic view.

(Dirac, The relation between mathematics and physics, 1940)

Radiation is emitted or absorbed by a transition of the electron from one quantum state to another - by a quantum jump - the energy difference between the two states being
emitted or absorbed as a light quantum of energy $h\nu'$ [...] Radiation results only through a quantum jump from such a state of positive energy to a lower state of positive or negative energy. [...] In addition, there is the rule that, so long as the interaction of the electrons is not very large, only those quantum transitions take place for which only one of the emission electrons makes a jump—that is, only one alters its $l$ value, the alteration being in accordance with the selection rule (I, 29):
$\Delta l = \pm 1$. [...] Transitions in which teo or more electrons jump at the same time are considerably weaker but are not forbidden by any strict selection rule. [...] one electron making the quantum jump (transition between even and odd terms) . [...] Such a radiationless quantum jump was first discovered by Auger, and is called after him the Auger effect

(Herzberg, Atomic spectra and atomic structure, 1944; then the bible for spectroscopy)

That the term ''quantum jump'' does not figure everywhere in the literature is simply because a ''transition'' between energy levels - an ubiquitous term in spectroscopy and photochemistry - is just a quantum jump called by a different name. It even occurs in the modern definition of the second:

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 atom.

(http://physics.nist.gov/cuu/Units/second.html)

Thus without quantum jumps no modern high precision measurement of time!

 

[Heikki Tuuri]

A. Neumaier, I think that in an earlier message I already wrote that the probability amplitudes (complex values) of a wave function develop smoothly in time.

A simple example is a single particle in a double potential well. We prepare the particle to be in the well A. Slowly, the probability amplitude leaks to the well B beside A. We measure the system and find the particle in B.

Should we say that the particle "jumped" from A to B? That language is not used in quantum mechanics. There is no definite path of the particle. It may "tunnel" to B if the wall between A and B is high, but that word is misleading, too.

 

[vanhees71]

Well, I don't know, why Schrödinger at all wrote against the clear evidence of their own theory.

I'd also be very interested to learn, where in the measurement of time, using atomic clocks like the "cesium fontain" or even more accurate measurements with more modern quantum-optical equipment (e.g., "frequency combs") you need to invoke "quantum jumps". I've no clue!

 

[Cthugha]

A. Neumaier, I think that in an earlier message I already wrote that the probability amplitudes (complex values) of a wave function develop smoothly in time.

A simple example is a single particle in a double potential well. We prepare the particle to be in the well A. Slowly, the probability amplitude leaks to the well B beside A. We measure the system and find the particle in B.

Should we say that the particle "jumped" from A to B? That language is not used in quantum mechanics. There is no definite path of the particle. It may "tunnel" to B if the wall between A and B is high, but that word is misleading, too.

How is this even related to the topic at hand? This has absolutely nothing to do with quantum jumps or quantum trajectories (or more formal: Monte Carlo wave function methods). The scenario is a totally different one. Consider for example simple emission from a two-level system. We all know that in non-qed quantum mechanics the excited state should be stable in the absence of external fields. Now one may perturb the system, which puts it into a superposition state of the excited state and the ground state, where the probability amplitudes for occupation of these states oscillate in time. One can either do this via external fields, which yields stimulated emission or one can consider QED and the properties of the vacuum state, which yields spontaneous emission. Anyway, you recover a picture similar to the classical one. In classical physics, you get electromagnetic radiation from accelerating charges. Here you get a state with time-dependent probability amplitudes for different charge configurations which in turn couple to probability amplitudes for photon emission.
So in a nutshell, a correct description of the system will more or less be similar to a dressed state picture, where the state of the atom is necessarily entangled with the state of the light field. This also means that you do not have to do a measurement on the atom to get it into an eigenstate. Performing a measurement on the photon is sufficient. For a local experimentalist sitting next to the atom, information about the light field is usually unavailable. So he has an open system and an environment perturbing his atom, which frequently "resets" his system to one of the eigenstates. This would be an example of a quantum jump. And at more than 1000 citations (https://www.osapublishing.org/josab/abstract.cfm?uri=josab-10-3-524), this is also far from being non-mainstream. The are also some good explanations demonstrating what is not meant by quantum jumps. The introduction of this paper by Wiseman ( https://journals.aps.org/pra/abstract/10.1103/PhysRevA.60.2474 ) for example is a good read.

 

[vanhees71]

Exactly, we just have to read the first paragraph of the introduction of the above cited PRA paper to set the records straight:

Wiseman et al, PRA 60, 2474 (1999)
The quantum jump, the effectively instantaneous transi-
tion of an atom from one state to another, was the first form
of nontrivial quantum dynamics to be postulated [1]. Of
course Bohr’s theory did not survive the quantum revolution
of the 1920s. In particular, the idea of jumps appeared to be
in sharp conflict with the continuity of Schro¨dinger’s wave
mechanics [2]. In the aftermath of the revolution, quantum
jumps were revived [3] with a new interpretation as state
reduction caused by measurement. But Wigner and Weis-
skopf [4] had already derived the exponential decay of spon-
taneous emission from the coupling of the atomic dipole to
the continuum of electromagnetic field modes. That is, they
did not require the hypothesis of quantum jumps. Later, more
sophisticated theoretical techniques, such as the master equa-
tion, were developed for dealing with the irreversible dynam-
ics of such open quantum systems [5-7]. In the master equa-
tion description, the atom’s state evolves smoothly and
deterministically. Perhaps as a consequence, interest in quan-
tum jumps as a way of describing of atomic dynamics faded.

Indeed, for a textbook treatment of "quantum jumps" (neglecting however spontaneous emission) see the famous Wigner-Weisskopf treatment of decays, nicely covered in

O. Nachtman, Elementary Particle Physics, Springer