Quantum transitions take time – the news is its experimental demonstration(blog.rongarret.info)
blog.rongarret.info
Quantum transitions take time – the news is its experimental demonstration
https://blog.rongarret.info/2019/06/quantum-transitions-take-time-this-is.html
44 comments
Sure, a quantum transition takes time. But demonstrating that point experimentally is not new this year.
In The Feynman Lectures on Physics, vol II, p. 35-4, Feynman describes an experiment by I.I. Rabi. I think Rabi did the work in the 1940s. The reciprocal of the transition time is the 'Rabi Frequency'. http://mriquestions.com/who-discovered-nmr.html
https://www.aps.org/programs/outreach/history/historicsites/...
Back to 2019, the dissertation abstract underlying the news story here doesn't appear to claim that this is the first experimental demonstration that quantum transitions take time. Which is probably good.
In The Feynman Lectures on Physics, vol II, p. 35-4, Feynman describes an experiment by I.I. Rabi. I think Rabi did the work in the 1940s. The reciprocal of the transition time is the 'Rabi Frequency'. http://mriquestions.com/who-discovered-nmr.html
https://www.aps.org/programs/outreach/history/historicsites/...
Back to 2019, the dissertation abstract underlying the news story here doesn't appear to claim that this is the first experimental demonstration that quantum transitions take time. Which is probably good.
Or more accurately: "The time it takes to make a quantum leap has been experimentally measured for the first time".
There is experimental news. Very cool and newsworthy. Just not new theoretical news.
There is experimental news. Very cool and newsworthy. Just not new theoretical news.
please tell us the amount of time it takes! It must be an incredibly small time, but no one in the discussion or the brief abstract did I see it.
> To go smoothly from 0 to 1, the system transitions through a series of superpositions of both states, i.e. it starts out entirely in state 0, and then transitions smoothly to being mostly in state 0 and a little bit in state 1, to being half in each state, to being mostly in 1 and a little bit in 0, to being entirely in 1.
Not really. An atom can be described by its quantum state only if it's isolated and in that case its energy is constant. If the states s_1 and s_2 have different energies E_1 and E_2 then the quantum state may be a superposition of the states s_1 and s_2 with an expected value for the energy between E_1 and E_2 but no "smooth transition" is possible.
For the transition to happen the atom has to be coupled with an external field. One way to think of it is as the evolution of the system composed of the atom plus a photon, where the transition between the states "excited atom and no emitted photon" and "unexcited atom and emited photon" happens at constant energy.
Edit: See https://en.m.wikipedia.org/wiki/Spontaneous_emission#Theory
Not really. An atom can be described by its quantum state only if it's isolated and in that case its energy is constant. If the states s_1 and s_2 have different energies E_1 and E_2 then the quantum state may be a superposition of the states s_1 and s_2 with an expected value for the energy between E_1 and E_2 but no "smooth transition" is possible.
For the transition to happen the atom has to be coupled with an external field. One way to think of it is as the evolution of the system composed of the atom plus a photon, where the transition between the states "excited atom and no emitted photon" and "unexcited atom and emited photon" happens at constant energy.
Edit: See https://en.m.wikipedia.org/wiki/Spontaneous_emission#Theory
That's picking a pretty fine nit. Yes, obviously if an atom undergoes an energy transition then that energy has to come from (or go to) somewhere. That doesn't change the fundamental point, which is that the process doesn't happen instantaneously or discontinuously, and the continuity is provided by transition through a series of superposition states. Yes, to be strictly correct you'd have to say that the superposition is a joint state of the atom and something else and not the atom in isolation. But this post was targeted to a lay audience, and that sort of detail would be more of a distraction than a clarification IMHO.
You are right for spontaneous emission, there we need to connect the system to something else, or to formulate a detailed-enough relativistic model with retarded EM fields that is able to lose energy (ordinary Hamiltonian of charged particle variables only cannot describe loss of energy to radiation).
But for spontaneous absorption/emission, you are not right. Describing atoms by psi function is extremely successful, it is what Schroedinger did in his papers, what got him the right results for positions and intensities of spectral lines and what put his equation to the center of interest. It is true this successful description has some problems, such as the question of consistency of different world cuts (into system and environment), but the ordinary way to do the split for atom-radiation interaction (time-independent atom Hamiltonian and time-dependent external EM field) describes stimulated emission and absorption very well.
Stimulated absorption/emission does require presence of external field, but this field can be taken into account in the usual psi function formulation - this is called semi-classical theory of radiation, it is what Schroedinger proposed in 1920's for simple atoms and is still heavily used for description of interaction of radiation with atoms and molecules.
But for spontaneous absorption/emission, you are not right. Describing atoms by psi function is extremely successful, it is what Schroedinger did in his papers, what got him the right results for positions and intensities of spectral lines and what put his equation to the center of interest. It is true this successful description has some problems, such as the question of consistency of different world cuts (into system and environment), but the ordinary way to do the split for atom-radiation interaction (time-independent atom Hamiltonian and time-dependent external EM field) describes stimulated emission and absorption very well.
Stimulated absorption/emission does require presence of external field, but this field can be taken into account in the usual psi function formulation - this is called semi-classical theory of radiation, it is what Schroedinger proposed in 1920's for simple atoms and is still heavily used for description of interaction of radiation with atoms and molecules.
You’re right, I was thinking of a time-independent Hamiltonian. I may be mistaken but I thought that there are no stationary states otherwise (so it wouldn’t make sense either to say that the state is a superposition of the states 0 and 1).
Not if we're really living in a simulation:
e.g. if you initiate the state change of an atom ( the example was the addition of one quanta of energy ), then eventually the state will change from quanta 0 to quanta 1, with possibly many superpositions of both states during the described finite lifetime of the transition.
This, to me, sounds so much like eventual consistency ( for observers ), that it's a bit scary.
This, to me, sounds so much like eventual consistency ( for observers ), that it's a bit scary.
The whole business of superposition and measurement so reeks of lazy initialization that you might want to worry about what performance constraints the simulation is trying to beat too.
"An atom can be described by its quantum state only if it's isolated and in that case its energy is constant."
How do you figure? As a contradiction, take your atom+electromagnetic field system, describe the transition from excited atom to unexcited atom + photon state, and project out the E&M field. Voila, now you have a quantum description of an atom transitioning between different energy states. Its dynamics may look funny, i.e. they may appear nonlocal, they may not conserve energy, etc. but that's different from saying "there is not a quantum description of these dynamics" which is what you're claiming.
How do you figure? As a contradiction, take your atom+electromagnetic field system, describe the transition from excited atom to unexcited atom + photon state, and project out the E&M field. Voila, now you have a quantum description of an atom transitioning between different energy states. Its dynamics may look funny, i.e. they may appear nonlocal, they may not conserve energy, etc. but that's different from saying "there is not a quantum description of these dynamics" which is what you're claiming.
https://en.m.wikipedia.org/wiki/Quantum_state
> project out the E&M field. Voila, now you have a quantum description
There is no wavefunction describing the state of the subsystem because the system is not separable.
> Its dynamics may look funny, i.e. they may appear nonlocal, they may not conserve energy, etc. but that's different from saying "there is not a quantum description of these dynamics" which is what you're claiming.
What is the “quantum description of these dynamics”?
Quantum mechanics is usually based on something like the following postulate: “The state of a physical system is described by a well-behaved function of the coordinates and time, Ψ(q, t). The function contains all the information that can be known about the system.”
> project out the E&M field. Voila, now you have a quantum description
There is no wavefunction describing the state of the subsystem because the system is not separable.
> Its dynamics may look funny, i.e. they may appear nonlocal, they may not conserve energy, etc. but that's different from saying "there is not a quantum description of these dynamics" which is what you're claiming.
What is the “quantum description of these dynamics”?
Quantum mechanics is usually based on something like the following postulate: “The state of a physical system is described by a well-behaved function of the coordinates and time, Ψ(q, t). The function contains all the information that can be known about the system.”
The system is separable after you measure out your ancilla. Imagine a stream of qubits B_1, B_2, ... prepared in +X who interact weakly with qubit A prepared in +X. and are then strongly measured projectively. After the brief interaction, A and a certain B will be entangled. Projectively measuring this B updates our knowledge of A, but due to the weak entanglement, the adjustment is small and incremental. The state of such B qubit is known and thus there is no remaining entanglement between A and B, and thus A and B are separable. After many such Bs, an outside observer privy to all measurement outcomes will understand that A is doing an absorbing random walk to the poles of the Bloch sphere. Throwing away this information and taking an ensemble average, you'd see an exponential decay of coherence.
This is a toy model of a qubit being weakly measured by an incident flying field.
This is a toy model of a qubit being weakly measured by an incident flying field.
> Throwing away this information and taking an ensemble average, you'd see an exponential decay of coherence.
That is described by a density matrix but is not a pure state. The true state may be a pure state (because as you said the systems are separable after the measurement) but our description is a mixture reflecting our imperfect information (and not a superposition of the pure states corresponding to the potential outcomes).
That is described by a density matrix but is not a pure state. The true state may be a pure state (because as you said the systems are separable after the measurement) but our description is a mixture reflecting our imperfect information (and not a superposition of the pure states corresponding to the potential outcomes).
Not sure exactly what you're linking the Wikipedia article on quantum states, but if you like it as a reference, check out https://en.wikipedia.org/wiki/Quantum_state#Mixed_states. The operation of "projecting out" the E&M field in my previous comment would be realized on the density matrix as a partial trace over the electromagnetic field. You can also take the partial trace of this field of the Hamiltonian operator to see the effective dynamics of the atom when "ignoring" the E&M field. This is a fully quantum description of the state, so I stand by the statement that your claim "An atom can be described by its quantum state only if it's isolated and in that case its energy is constant." is incorrect.
Do you agree that “The state of a physical system is described by a well-behaved function of the coordinates and time, Ψ(q, t). The function contains all the information that can be known about the system.”?
When the atom is coupled with the electromagnetic field and the state of the system is not separable there is no complete description of the atom given by a wavefunction defining its quantum state. You can have an incomplete description by tracing out the rest of the system, I agree.
Let’s say then that "An atom can be completely described by its quantum state only if it's isolated and in that case its energy is constant."
Edit: in any case, my point was (and I think that we will agree) that it is misleading to say “Consider a system that transitions from energy state 0 to an adjacent energy state 1. [...] To go smoothly from 0 to 1, the system transitions through a series of superpositions of both states”.
The atom goes from the state 0 to the state 1 but during the transition it’s not described by a superposition of those states (that would be a pure state). If anything, it is described by an (improper) mixture of those states, obtained by tracing out the rest of the system.
When the atom is coupled with the electromagnetic field and the state of the system is not separable there is no complete description of the atom given by a wavefunction defining its quantum state. You can have an incomplete description by tracing out the rest of the system, I agree.
Let’s say then that "An atom can be completely described by its quantum state only if it's isolated and in that case its energy is constant."
Edit: in any case, my point was (and I think that we will agree) that it is misleading to say “Consider a system that transitions from energy state 0 to an adjacent energy state 1. [...] To go smoothly from 0 to 1, the system transitions through a series of superpositions of both states”.
The atom goes from the state 0 to the state 1 but during the transition it’s not described by a superposition of those states (that would be a pure state). If anything, it is described by an (improper) mixture of those states, obtained by tracing out the rest of the system.
Yes, but note that I deliberately used the word "system" rather than "atom". The system is the combination of the atom plus whatever it's absorbing energy from or emitting energy to. And that (entangled) system is in a superposition.
Ok, I was confused because if you say “Consider a system that transitions from energy state 0 to an adjacent energy state 1” it sounds as if the energy of the “system” is changing and when you say that “a particle [...] can be in two different energy states at the same time” it seems that you are referring to the atom being in a superposition of states with different energy.
One can speak meaningfully of "an atom in a superposition of energy states" despite the fact that, strictly speaking, such a thing is not possible, just as one can speak meaningfully of "the force of gravity" despite the fact that, strictly speaking, there is no such force. The latter is understood as the force-like effect of curved spacetime, and the former is understood as "an atom being a component of a system in a superposition of states with different distributions of energy" (or something like that). Communications between humans becomes more productive when we cut each other a little terminological slack.
What puzzles me is where the photon goes when it bumps up the energy of the electron, and what does it look like when the electron shell drops back down. I realize too much "realism" in QM is just a waste of effort, but I keep seeing the field sort of pinching off a photon.
The photon goes into the energy of the electron. Because mass and energy are the same thing the mass of the photon is converted into the energy of the electrons new state.
This is incorrect. See the stochastic schroedinger equation. A quantum system will stay pure under measurement as long as the measurement process is completely efficient.
I’m not familiar with this extension of QM. What is the “system” here? Would the atom stay in a pure state or would a larger system stay in a pure state?
The whole system does. The trick is you never trace anything out. You needn't. A spin interacting with a flying field is itself a pure system. It's just when you trace out the flying field that the system may become impure. If the spin interacts with the field, and the field is measured with measurements local to the field subsystem, the entire system will stay pure, and you'll see the qubit's wavefunction "collapse."
Thanks. In that case I don’t think there is a contradiction with what I said, if there is no wave function corresponding to the atom (alone). I understood the original comment as saying that the quantum state of the atom during the transition between energy levels was a superposition of the corresponding pure states (i.e. a pure state) and I was objecting to that.
Yeah I mean that’s still fine. The entanglement between system and field never persists since the field is taken to be measured immediately. The systems are only non-separable as long as they’re entangled. See the notes by Steck on the derivation of the SME and SSE.
I agree that if the field is taken to be a degree of freedom entangled with the system under measurement, things are funnier. This experiment isn’t really like spontaneous or stimulated emission... where yeah, DURING the process, the photon pooped out is entangled with your subsystem. In the case of the present experiment there’s a much more subtle thing going on with a three level system where the bright-zero manifold is used as a witness to the dark-zero manifold, where the presence or lack thereof of fast jumps in the bright-zero manifold betray information about the dark-zero manifold, necessarily.
I agree that if the field is taken to be a degree of freedom entangled with the system under measurement, things are funnier. This experiment isn’t really like spontaneous or stimulated emission... where yeah, DURING the process, the photon pooped out is entangled with your subsystem. In the case of the present experiment there’s a much more subtle thing going on with a three level system where the bright-zero manifold is used as a witness to the dark-zero manifold, where the presence or lack thereof of fast jumps in the bright-zero manifold betray information about the dark-zero manifold, necessarily.
What "is still fine"?
I've been reading a bit about quantum state diffusion, continuous measurements and quantum trajectories. My superficial understanding of the subject is the following. Let's say that you have an open system described by a reduced density operator evolving according to some master equation. The system will be in general described by a mixed state.
You can have an alternative representation with the quantum state changing in a non-deterministic way according to a stochastic equation. In this representation the quantum state remains pure for one "trajectory" but to describe the system you need to consider the ensemble of realizations. So you still have a mixture and the same density matrix as before.
I've been reading a bit about quantum state diffusion, continuous measurements and quantum trajectories. My superficial understanding of the subject is the following. Let's say that you have an open system described by a reduced density operator evolving according to some master equation. The system will be in general described by a mixed state.
You can have an alternative representation with the quantum state changing in a non-deterministic way according to a stochastic equation. In this representation the quantum state remains pure for one "trajectory" but to describe the system you need to consider the ensemble of realizations. So you still have a mixture and the same density matrix as before.
I think it's a bit more subtle than this. Taking ensemble averages is itself a gesture of throwing information away, so yes, you do now have classical uncertainty that now may be represented by a density matrix. I think what I take issue with is "to describe the system." The master equations are deep down, kalman filters. They take some inputs and through bayes rule produce their best estimate of what state the system is in. Given perfect information, in this situation, they'll produce, somewhat miraculously, a complete description of the state of the system. If you had a person that was being bombarded by soccer balls from random directions you wouldn't say that an average of their muscle movements described the human-soccerball system. You'd wind up with something not particularly informative. Yes, you do need to take averages at some point... but you might want to average over a solid angle of impinging soccer balls... then you get somewhat deterministic, informative behavior.
I want to get across that this experiment is in some sense probing the way a quantum system processes quantum fluctuations. An ensemble average of traces therefore throws away/averages out the very thing that the system is responding to.
I want to get across that this experiment is in some sense probing the way a quantum system processes quantum fluctuations. An ensemble average of traces therefore throws away/averages out the very thing that the system is responding to.
> Given perfect information, in this situation, they'll produce, somewhat miraculously, a complete description of the state of the system.
I don't think that the complete description of the system when the atom is going from a pure excited state to a pure ground state will include pure states of the atom which are superpositions of the excited state and the ground state. If we have a complete description of the system, the atom may be part of a larger system which is in a pure state and in that case the quantum state of the atom may be an improper mixture of the excited state and the ground state. The atom may also be in a pure state on its own, but then it will be either in the excited state or in the ground state.
That's all I said. I may be wrong but I fail to see in your comments a reason to think so.
Edit: By the way, I know an atom can in principle be in a state which is a superposition of states with different energies (I said so in my first comment). It's just that I don't think that happens during the spontaneous transition from one state to another. If it does happen, I would be glad to learn about it.
Edit2: Looking again at some quantum optics papers I see people argue that stochastic equations have a physical meaning and are not just a calculation device. Anyway, those interaction models are quite complex and full of approximations so it's not clear what "pure" means anymore...
I don't think that the complete description of the system when the atom is going from a pure excited state to a pure ground state will include pure states of the atom which are superpositions of the excited state and the ground state. If we have a complete description of the system, the atom may be part of a larger system which is in a pure state and in that case the quantum state of the atom may be an improper mixture of the excited state and the ground state. The atom may also be in a pure state on its own, but then it will be either in the excited state or in the ground state.
That's all I said. I may be wrong but I fail to see in your comments a reason to think so.
Edit: By the way, I know an atom can in principle be in a state which is a superposition of states with different energies (I said so in my first comment). It's just that I don't think that happens during the spontaneous transition from one state to another. If it does happen, I would be glad to learn about it.
Edit2: Looking again at some quantum optics papers I see people argue that stochastic equations have a physical meaning and are not just a calculation device. Anyway, those interaction models are quite complex and full of approximations so it's not clear what "pure" means anymore...
For a transition of an electron between energy levels that emits a photon, should the time it takes for the transition be the same as the duration of the probability envelope of the photon?
If so, that's easily observable by looking at the width of the spectral line. If the transition is fast, that implies a short duration and therefore the spectral lines should be smeared out.
If so, that's easily observable by looking at the width of the spectral line. If the transition is fast, that implies a short duration and therefore the spectral lines should be smeared out.
Yes, that is exactly right. All of this just boils down to the energy-time version of the uncertainty principle: the more precisely you can measure when a transition happened, the less certain you can be about the change in energy of that transition.
Here is another example of this principle at work:
http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl...
http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl...
http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl...
Here is another example of this principle at work:
http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl...
http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl...
http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl...
What you're saying about uncertainty principle is strange. The principle says the longer the transition takes, the sharper the spectral line can be (but does not have to be, hence the inequality). There is nothing about uncertainty of measurement of time of some point event. The transition is not a point event. If the two states involved in the transition are known, then change of energy is known. How long the transition will take depends on strength and frequency characteristics of the external field, but the energy difference of energy of the molecule after the transition is over does not depend on that.
Yes, everything you say is correct. That's exactly what makes this experiment so interesting. They didn't just measure the energy state at one time and then again at another time. That wouldn't work (because of the quantum Zeno effect).
The paper’s abstract [1] states:
“certain classical phenomena, like tsunamis, while unpredictable in the long term, may possess a degree of predictability in the short term, and in some cases it may be possible to prevent a disaster by detecting an advance warning signal.”
Is there a name for such class of phenomena?
For the opposite, where small-scale unpredictability (e.g. particle motion) because large-scale decipherable (fluid mechanics), we have the law of large numbers and “emergent phenomena.”
[1] http://qulab.eng.yale.edu/documents/theses/Minev_ZK-Disserta...
“certain classical phenomena, like tsunamis, while unpredictable in the long term, may possess a degree of predictability in the short term, and in some cases it may be possible to prevent a disaster by detecting an advance warning signal.”
Is there a name for such class of phenomena?
For the opposite, where small-scale unpredictability (e.g. particle motion) because large-scale decipherable (fluid mechanics), we have the law of large numbers and “emergent phenomena.”
[1] http://qulab.eng.yale.edu/documents/theses/Minev_ZK-Disserta...
> To get around this problem, Devoret and colleagues employ a clever trick involving a second excited state. The system can reach this second state from the ground state by absorbing a photon of a different energy. The researchers probe the system in a way that only ever tells them whether the system is in this second “bright” state, so named because it’s the one that can be seen. The state to and from which the researchers are actually looking for quantum jumps is, meanwhile, the “dark” state — because it remains hidden from direct view.
This is absolutely brilliant work. I had no idea that experimenters had found a way around the quantum measurement problem.
I have always wondered "how in hell can people experiment with something that is actually affected by simply LOOKING at it?" This gives me my answer.
Even though this idea is only one step in the findings of this article, I am so glad I came across it.
This is absolutely brilliant work. I had no idea that experimenters had found a way around the quantum measurement problem.
I have always wondered "how in hell can people experiment with something that is actually affected by simply LOOKING at it?" This gives me my answer.
Even though this idea is only one step in the findings of this article, I am so glad I came across it.
I'd like to point out that this sort of story vitiates the Popperian tale of how scientific knowledge is created, i.e. it was "known" well in advance of experimental evidence that something is true, and the confirmation is seen as banal.
Which is ironic since popper had a real problem with QM.
Discussion on the Quant magazine article from yesterday: https://news.ycombinator.com/item?id=20105091
I love Hacker News
I have a elementary question about the Heisenberg Uncertainty Principle (my understanding is Quatum Leap/transitions are just a description of the uncertainty principle wave function)...
As we know from “flatland” as a sphere passes through the flatland plane, the sphere can be measured as a dot/circle at any given time.
https://demonstrations.wolfram.com/ASphereVisitsFlatland/
Wouldn’t that measurement of a higher dimensional object passing through the lower dimensional world sort of begin to appear and fit the definition of the uncertainty principle for particles in our own 3D world?
In other words as the 3D sphere is measured passing through the 2d flatland flatlanders can either know the position of the sphere or momentum, but as they measure one more accurately they can’t measure the other as accurately?
I guess what I’m trying to ask is it accurate to use the uncertainty principle as a flatlander describing a 3D sphere passing through flatland and if so, Would that give any credence to the bizarre possibility that particles in our world are actually 4D objects?
As we know from “flatland” as a sphere passes through the flatland plane, the sphere can be measured as a dot/circle at any given time.
https://demonstrations.wolfram.com/ASphereVisitsFlatland/
Wouldn’t that measurement of a higher dimensional object passing through the lower dimensional world sort of begin to appear and fit the definition of the uncertainty principle for particles in our own 3D world?
In other words as the 3D sphere is measured passing through the 2d flatland flatlanders can either know the position of the sphere or momentum, but as they measure one more accurately they can’t measure the other as accurately?
I guess what I’m trying to ask is it accurate to use the uncertainty principle as a flatlander describing a 3D sphere passing through flatland and if so, Would that give any credence to the bizarre possibility that particles in our world are actually 4D objects?
> Quatum Leap/transitions are just a description of the uncertainty principle wave function
That is almost right. But it's not a description of the uncertainty principle, it's a manifestation of the uncertainty principle, specifically the time-energy uncertainty principle.
But none of this has anything to do with flatland. It has to do with Fourier analysis: the more localized a signal is in the time domain the more spread out it is in the frequency domain, and vice versa.
That is almost right. But it's not a description of the uncertainty principle, it's a manifestation of the uncertainty principle, specifically the time-energy uncertainty principle.
But none of this has anything to do with flatland. It has to do with Fourier analysis: the more localized a signal is in the time domain the more spread out it is in the frequency domain, and vice versa.
Really, the right thing to do is go directly to the Nature article, and read the abstract. If you've been reading things about QM, even as a non-physicist, then you're probably pretty close to understanding the abstract.
Moreover, a quick reading of the Quanta Magazine article makes it seem as though they shifted the focus of the original result from predictability and determinism to instantaneous transitions. (Although I note I haven't had time to read and fully digest the Nature paper.)
From the abstract in Nature:
> The times at which the discontinuous jump transitions occur are reputed to be fundamentally unpredictable. Despite the non-deterministic character of quantum physics, is it possible to know if a quantum jump is about to occur? 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