13
$\begingroup$

Ok the title might be slightly clickbaity. A better one might be "Why isn't the recent Nature paper by Minev et al. evidence of new physics?", but I didn't want to make too many assumptions given I don't fully understand the claims.

The paper I'm referring to is arXiv:1803.00545 (Nature version here). In the abstract, the authors state:

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

and shorty thereafter

Our findings, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory.

I assume from the wording that the authors aren't making any claim of new physics being observed, but I do find the statements made a bit hard to reconcile with a standard understanding of QM, probably due to my ignorance about "quantum trajectory theory", and of the experimental context.

In particular, I suppose "quantum jumps" in this context are to be understood as observations of the state after a collapse has occurred, i.e. the post-measurement states? In other words, is a "quantum jump" the observation of a system collapsing from one state to the other?

If so, I don't understand what is being observed in the paper. If I consider a time-evolution of some initial state $\rho$ via some channel $\Phi_t$ that depends continuously on the time $t$, aren't they observing the probabilities of the state collapsing in the computational basis at different times $t$? If so, how can this process be deterministic?

$\endgroup$
5
  • 1
    $\begingroup$ They seem to be talking about the evolution of the state kets of a system between two energy levels, correct? There would be nothing surprising about that: the state kets can be used to calculate the probability of measuring a value of some observable, but their time evolution is deterministic. $\endgroup$ – Obie 2.0 Jan 25 at 22:46
  • $\begingroup$ @Obie2.0 I might simply not fully understand what the "quantum jumps" referred to here should be taken to mean. If they are essentially performing tomography at every time step, then sure obviously the evolution is deterministic at the state level. But if that's what they are doing I don't understand the point of this "quantum jump" formalism here $\endgroup$ – glS Jan 25 at 23:00
  • $\begingroup$ Oot: What is a "superconducting atom" ? It must be a short. If so, poor wording for Nature level. $\endgroup$ – Alchimista Jan 26 at 10:44
  • $\begingroup$ can I ask whoever is voting to close this as opinion based, what is there of "opinion based" in the question? The fact that there is a standard way of explaining the results in the paper is absolutely not subjective, nor a matter of interpretation. This is essentially just asking clarification on a specific terminology $\endgroup$ – glS Jan 31 at 16:34
  • $\begingroup$ Maybe because of the title? $\endgroup$ – BioPhysicist Jan 31 at 17:46
11
$\begingroup$

The trick here in "observing a quantum jump" is that this is not equivalent to doing a strong measurement that "collapses" the wavefunction.

The archetypal quantum jump is a two level system with a ground state $\lvert G\rangle$ ("Ground")and an excited state $\lvert D\rangle$ ("Dark") (I'm naming the state kets like they do in the paper to avoid confusion). When we want to "observe the jump", we sit around and wait for a photon to be emitted in order to detect it and say "aha, the system has decayed back to $\lvert G\rangle$!". There's no room for continuous evolution here, when our detector clicks we know the system is in $\lvert G\rangle$.

The paper does something different, a complicated variant of the above that constitutes only a weak measurement saying "the system is currently not purely in the ground state". Whether what they do is meaningfully equivalent to the ordinary colloquial meaning of "quantum jump" I will leave the reader to decide, but its experimental observation is an impressive feat regardless.

Instead of observing the ground state with a strong measurement, they couple the ground state to another excited state $\lvert B\rangle$ ("Bright") via a Rabi drive $\Omega_{BG}$. Then they observe the decay of this excited state to the ground state by a photon counter. The state $\lvert D\rangle$ is explicitly not monitored (hence "dark") and is metastable compared to the bright state, i.e. has a much longer half-time for its radiative decay. So when they observe an emission from the bright state, they know the system just came from the ground state via Rabi oscillation, then decayed again to the ground state - this is the "initial state" of the experiment, we state with the system in the ground state and the ground and the dark state coupled via another Rabi drive $\Omega_{DG}$. Crucially, the Rabi frequencies here are chosen such that the BG transition is much quicker than the DG transition, so it is essentially impossible for the system to get to $\lvert D \rangle$ via Rabi oscillation alone.

So in this setup, we will generally have the detector clicking rapidly, and the system repeatedly being reset to $\lvert G\rangle$ via this variant of the Zeno effect. But because the measurement is not truly continuous, there is a small chance the detector suddenly stops clicking. This is random and not deterministic, so the experiment does nothing to resolve the measurement problem. But since the detector is only coupled to the system probabilistically via the Rabi oscillation to the bright state, this does not constitute a measurement that the system is in $\lvert D\rangle$ - we only become increasingly sure it is not purely in $\lvert G\rangle$ the longer we don't observe a click. This is not a strong measurement, it is a variant of a weak measurement. So when the detector stops clicking, we have some superposition of $\lvert G\rangle$ and $\lvert D\rangle$, but the detector often stops for much longer than one would expect if the system was just Rabi oscillating into $\lvert D\rangle$ - a "quantum jump" has occured, forcing the system into the state $\lvert D \rangle$ much faster due to the interaction with the detector and Rabi drive for the bright state.

When this happens - the detector stops clicking for long enough that the experimenters as satisfied a "jump" is occuring, they do relatively standard tomography on repeated realizations of this state to see in what kind of superposition it is in. They also do a run where they shut off the Rabi drive $\Omega_{DG}$ directly after the jump starts to occur where the tomography results are essentially the same to demonstrate the jump is not driven by the Rabi oscillation. Of course, there is still a random chance that the observation of the bright state might abort the jump and force the system back to the ground state - the entire paper is solely interested in the case where this does not occur.

Since they understand the tomography of the jump well, they also know how to manipulate the state via precise rotation of the state so that the jump "reverses". The time evolution of the system between two detector clicks is entirely deterministic, so this is not a surprise, it's just a neat demonstration. If you look into the actual formulae, you will find that the evolution of the state in this period is directly dependent on the frequency of the Rabi drive $\Omega_{BD}$, so please do not get the impression that this specific behaviour during a "quantum jump" is universal - it is specific to the experimental setup and chosen method of observation.

$\endgroup$
8
  • $\begingroup$ so if I understand, a photon clicks witnesses a transition $|B\rangle\to|G\rangle$. Because we start with $|G\rangle$, that means the system must have jumped $|G\rangle\to|B\rangle$ and then $|B\rangle\to|G\rangle$. Now, now getting a click means no backward transition. We are assuming that $B$ decays quickly, thus no clicks for some time must mean that the transition $|G\rangle\to|D\rangle$ occurred. I guess this makes sense assuming the information on what is the current state is periodically leaked into the environment (i.e. "measured"). $\endgroup$ – glS Jan 31 at 18:21
  • $\begingroup$ To connect with the original question, doesn't this mean that all the experiment verifies is that the type of dynamics they consider is not unitary, but rather amounts to repeated measurements/collapse occurring due to interactions with the environment? $\endgroup$ – glS Jan 31 at 18:23
  • $\begingroup$ @glS Yes - the experiment is a quantitative test of the predictions of (non-unitary) "quantum trajectory theory", as the authors themselves state in the abstract. $\endgroup$ – ACuriousMind Feb 1 at 8:42
  • $\begingroup$ well, "quantum trajectory theory", according to wikipedia, is but a way to simulate open quantum systems. So I'm not sure what it means to "test predictions" of it; I guess that's my main problem with the paper's claim. Unless they mean to test this method of predicting the dynamics of an open system under the specific circumstances in which repeated measurements are performed $\endgroup$ – glS Feb 1 at 9:57
  • $\begingroup$ @glS It is but a way to talk about open quantum systems. I'm not sure what your problem in that context is - if I do some experiment for a situation I have simulated via some specific approach, then that experiment is a test of the predictions of that approach. $\endgroup$ – ACuriousMind Feb 1 at 10:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.