What does it mean for a glass bead to be in a quantum state?

[Grinkle]

TL;DR Summary

What's being demonstrated or shown by managing to put this glass bead in what is described as its lowest quantum mechanical state?

https://www.guardianmag.us/2023/02/scientists-levitate-glass-nanosphere.html

"the nanosphere was suspended in its lowest quantum mechanical state, one of extremely limited motion where quantum behavior can start to happen."

To my reading, the glass bead was cooled down and then suspended with a carefully controlled electric field, and it determined that the bead was in its lowest QM state.

I call this a demonstration rather than an experiment because the write-up does not mention any measurements or tests or hypotheses. My thinking is that this is an engineering exercise to establish the practicality of preparing a large object for some kind of interesting experiment.

Can anyone help me understand what it means for an object with millions of particles to be in its lowest QM state and what kind of experiments would be done on such an object once it has been put in this state? Is this an interesting or exciting demonstration or is it more like setting a new world record for the most dominoes in a single tip-them-over stunt?

 

[Mordred]

Here is the article itself published in arxiv. It provides the details not in the first link. The quantum ground state refers to its lowest energy state (close as possible to zero point energy ) described by the quantum harmonic oscillator.

https://arxiv.org/abs/2103.03853

A straight forward explanation of quantum ground state can be found here
https://en.m.wikipedia.org/wiki/Gro...ound state of a,greater than the ground state.

 

[Grinkle]

@Mordred Thanks for linking the paper, it does indeed paint a fuller picture.

From the Abstract -

"our experimental platform offers a route to investigating quantum mechanics at macroscopic scales."

Asking anyone who knows - are there proposals and/or consensus on what the most interesting experiments would be when investigating QM at macroscopic scales?

 

[hutchphd]

How about superfluidity?. Superconductivity? Penning traps. There are many examples I believe.

 

[Grinkle]

@hutchphd Thanks for that link, I am still working to digest it and may post a separate thread with questions on it.

I think the questions I asked in this thread have been well answered, thanks.

 

[pines-demon]

TL;DR Summary: What's being demonstrated or shown by managing to put this glass bead in what is described as its lowest quantum mechanical state?

https://www.guardianmag.us/2023/02/scientists-levitate-glass-nanosphere.html

"the nanosphere was suspended in its lowest quantum mechanical state, one of extremely limited motion where quantum behavior can start to happen."

To my reading, the glass bead was cooled down and then suspended with a carefully controlled electric field, and it determined that the bead was in its lowest QM state.

I call this a demonstration rather than an experiment because the write-up does not mention any measurements or tests or hypotheses. My thinking is that this is an engineering exercise to establish the practicality of preparing a large object for some kind of interesting experiment.

Can anyone help me understand what it means for an object with millions of particles to be in its lowest QM state and what kind of experiments would be done on such an object once it has been put in this state? Is this an interesting or exciting demonstration or is it more like setting a new world record for the most dominoes in a single tip-them-over stunt?

This is a whole new field called quantum levitodynamics. Using electromagnetic fields, researchers are able to create a potential for the bead. The bead moves within the potential. The bead can be in any energy state in this potential, researchers managed to put the bead in the lowest quantum state of the potential. Know that this has nothing to do with the states within the bead itself, the bead could be quite hot for example from all those EM fields.

 

[hutchphd]

This is a whole new field called quantum levitodynamics.

Giving it a name does not make it a "whole new field". Can someone please explain why is this interesting and deserving of a new layer of jargon?

 

[Mordred]

There is a lot of study and practical uses behind it. This article describes several useful applications both in research and in engineering applications

https://arxiv.org/abs/2111.05215

 

[Grinkle]

Know that this has nothing to do with the states within the bead itself

What is required to claim a system is at its quantum ground state externally to its boundary without needing to care about its internal state? Is it that the system is closed in the thermodynamic sense and also in its external ground state? Does one call this "external ground state", something else, or is that (external vs internal) just implied by the context?

I tried googling and couldn't find a discussion of this, probably because I don't know how to frame an appropriate search question.

 

[hutchphd]

This article describes several useful applications both in research and in engineering applications

Yes thank you. I also found a reference in one of these articles very useful:
https://www.science.org/doi/10.1126/science.aba3993

 

[Mordred]

Your welcome one piece of advise look through the article references you can often get excellent articles searching through them

 

[hutchphd]

Yes the article I pointed to in #10 has a pretty complete description of the experiment, undigested (and therefore unconfused) by any intermediary science journalism.

 

[pines-demon]

What is required to claim a system is at its quantum ground state externally to its boundary without needing to care about its internal state? Is it that the system is closed in the thermodynamic sense and also in its external ground state? Does one call this "external ground state", something else, or is that (external vs internal) just implied by the context?

I tried googling and couldn't find a discussion of this, probably because I don't know how to frame an appropriate search question.

The thing is that a quantum system can have many degrees of freedoms that can be considered independent. If we can write the state as a tensor product $| \psi_{\text{important}}\rangle\otimes|\psi_{\text{other}}\rangle$ (important states that you keep track times other internal states) then we can forget about the other states and focus on lowering the energy of the important state space. For example you could have an electron in the "ground state" of hydrogen atom, meaning that the electron is at $n=1$ (lowest orbital) but there is still some energy associated to spin due to hyperfine structure that for some purposes we would consider it as independent and not important (other). In this levitodynamics experiment, the important state is the states of the well, you could model it as a single particle in an harmonic oscillator well, you want its quantum number associated to it to be $n\approx0$ as much as possible, you do not care if the nanoparticle is in its ground state whatever that means.

 

[Grinkle]

@pines-demon Thank your for framing the explanation conceptually for me.

there is still some energy associated to spin

An electron always has spin, either up or down, correct? It doesn't make sense to talk about putting an electron in a state where there is no spin, correct me if I am wrong. Or are you saying the hydrogen atom as a whole (nucleus plus electron) has a spin and you are talking about the hydrogen atom as an example of a simple macro-object?

Or am I totally missing your point?

 

[pines-demon]

@pines-demon Thank your for framing the explanation conceptually for me.



An electron always has spin, either up or down, correct? It doesn't make sense to talk about putting an electron in a state where there is no spin, correct me if I am wrong. Or are you saying the hydrogen atom as a whole (nucleus plus electron) has a spin and you are talking about the hydrogen atom as an example of a simple macro-object?

Or am I totally missing your point?

I was trying to convey that some states are separable. Separable meaning that modifying one part of the state does not modify the other. Modifying the spin in the hydrogen atom (almost) does not modify the orbital, you can treat the spin problem and the orbital problem separately.

For the rest of your question, yes the electron has a spin projection, it can be up/down in one direction or a superposition of both. Its spin can couple with the spin of the proton, leading to hyperfine corrections (very minor corrections in the energy levels).

 

[hutchphd]

For example you could have an electron in the "ground state" of hydrogen atom, meaning that the electron is at n=1 (lowest orbital) but there is still some energy associated to spin due to hyperfine structure that for some purposes we would consider it as independent and not important (other).

I dislike this characterization. The atom is a system and the atom (proton + elctron) is in its ground state. The coordinates that nearly allow separation of this system are the CM and relative coordinates: neither corresponds to the electron alone. The electron itself is strongly coupled to the proton. The hyperfine splitting from the spin spin interaction is as described

 

[Grinkle]

I was trying to convey that some states are separable.

You did convey this - thanks.

My understanding ...

Independent / separable / have-no-effect-on-each-other / orthogonal are all synonymous in our discussion, please introduce different vocabulary if there is importance nuance I am missing.

When you say state, you are talking about a point in a vector space that is bounded by independent scalars and your example of a two scalar space was spin / orbital. That some states are separable is certainly true for classical systems. For a quantum system, if one can measure property A and leave property B still in a state of superposition, is this necessary and sufficient to say they are separable, or is that completely beside the point?

A separate question - I think it does not make sense to talk about position and momentum as being separable or not separable any more than it makes sense in the classical domain to talk about time domain being separable from frequency domain. In this discussion, we are not talking about properties that are linked directly by uncertainty, is that right?

 

[Nugatory]

Independent / separable / have-no-effect-on-each-other / orthogonal are all synonymous in our discussion, please introduce different vocabulary if there is importance nuance I am missing.

For better or for worse, the only vocabulary that really works is math.

When you say state, you are talking about a point in a vector space that is bounded by independent scalars and your example of a two scalar space was spin / orbital.

It’s a vector not a point, and the vector space is the tensor product of the vector spaces of the two observables considered separately.

That some states are separable is certainly true for classical systems. For a quantum system, if one can measure property A and leave property B still in a state of superposition, is this necessary and sufficient to say they are separable, or is that completely beside the point?

Pretty much (although that phrase suggests a level of handwaving that is inconsistent with the rigor implied by “necessary and sufficient”). The operator corresponding to the measurement is the tensor product of a measurement operator on one space and the identity operator on the other.