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I watched a TED talk by the scientist Aaron D. O'Connell about actually seeing quantum superposition. The link to the talk is :-

http://www.ted.com/talks/aaron_o_connell_making_sense_of_a_visible_quantum_object

I researched on it a bit but I am still not able to understand how did his experiment work. Ultimately while measuring, the state of superposition would have been destroyed. What was it that made the experiment successful. I didn't even understand how could he conclude that everything is in two places at the same time. Especially when you see the talk, he mentions that his device was both vibrating and not vibrating at the "same time" which seems a bit ambiguous to me. How can you take two different measurements at the same time?

Here is a picture of the "diving board" his team used that was in a vibrating superposition: enter image description here

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    $\begingroup$ That talk is too general or cut too short to go into sufficient detail. I believe this is a PDF of the article $\endgroup$ – BMS Mar 22 '14 at 13:29
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    $\begingroup$ And the wikipedia page about the quantum machine is here. $\endgroup$ – BMS Mar 22 '14 at 13:48
  • $\begingroup$ @BMS thank you for the start but I am only 15 years old and do not understand the PDF properly. Could you please try to answer my question yourself in a simpler way. That would be much appreciated. $\endgroup$ – rahulgarg12342 Mar 22 '14 at 17:16
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You shouldn't think much of his statement about being in two places at once; it's a bunch of fluffy nonsense he's using to make his work sound sexier. A human-sized object at livable temperatures will never exhibit such behavior.

Their experiment actually used thousands of measurements to determine what was happening with the lever. I'll try to summarize, but please let me know if you need clarification.

The device they study is an electrical circuit that connects the macroscopic lever from your picture to a quantum bit (or "qubit"). At very low temperatures both the lever and the qubit are two-state systems, meaning they are individually described by two quantum states (e.g. "not vibrating" and "barely vibrating", which I'll respectively denote $\left| 0 \right\rangle$ and $\left| 1 \right\rangle$). The coupled system is found in combinations of these states, but the relevant ones in this experiment are when the qubit is barely vibrating and the lever isn't, and vice-versa. In my previous notation these states are $$ \left| 1 \right\rangle_q \left| 0 \right\rangle_l, \quad \left| 0 \right\rangle_q \left| 1 \right\rangle_l, $$ where $q$ and $l$ to refer to the qubit and the lever. After cooling down the circuit so the lever and qubit aren't vibrating ($\left| 0 \right\rangle_q \left| 0 \right\rangle_l$) they give the qubit a little energy so it is in the barely vibrating state ($\left| 1 \right\rangle_q \left| 0 \right\rangle_l$). Since the qubit and lever are connected, over time the energy moves from one to the other. Equivalently, the system evolves to a new quantum state where the lever is barely vibrating and the qubit isn't ($\left| 0 \right\rangle_q \left| 1 \right\rangle_l$). From a quantum mechanical viewpoint this evolution is attributed to the system being in a superposition of the two states $$ a(t) \left| 1 \right\rangle_q \left| 0 \right\rangle_l + b(t)\left| 0 \right\rangle_q \left| 1 \right\rangle_l. $$ The squares of the numbers $a(t)$ and $b(t)$ tell us the probability of finding the system in each of its quantum states at a certain time $t$. When $a=1$ only the qubit is vibrating, when $b=1$ only the lever is vibrating, and when $a$ and $b$ are both non-zero the lever is "simultaneously" vibrating and stationary.

O'Connell and his collaborators were able to measure the state of the qubit very accurately. They prepared the circuit in the way I described above, waited some amount of time, and looked to see if the qubit was vibrating or not. They repeated this process over and over, tallied up how often the qubit was vibrating, then calculated the probability they would find it vibrating if they performed the experiment again. For certain wait times they found that the qubit was sometimes vibrating and sometimes not vibrating. Going back to my expression for the superposition, this means that $a$ and $b$ are non-zero, or that the lever is in a superposition of stationary and vibrating states.

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  • $\begingroup$ That is the best explanation I could have expected. Good job but I still have to clarify some things. I just did not get the part from the last equation which involves "a(t)" and "b(t)" which I believe is the crux of the conclusion. Please clarify it a bit further. In short I want to know what is a(t) and b(t) and why do we square them and when can both be non-zero? I understand they can both be non - zero separately but how simultaneously? $\endgroup$ – rahulgarg12342 Mar 23 '14 at 6:45
  • $\begingroup$ @rahulgarg12342 a(t) and b(t) are called 'probability amplitudes.' The 'amplitude' part of the name refers to the fact that they always multiply quantum states in equations, and the 'probability' part reflects the fact that their squares (by definition) give the probability of finding the system in the state they multiply. The fact that both can be non-zero is ultimately concluded from experiments. Sometimes we prepare experiments where we get different outcomes for identical measurements (two measurements performed under the same conditions)... $\endgroup$ – vanasaur Mar 23 '14 at 18:24
  • $\begingroup$ In QM we conceptually view this as the system being in a "mixture" of states corresponding to the different outcomes we obtain. For example, in this experiment the qubit was sometimes found with energy and sometimes found without energy (after preparing the system in identical ways and waiting the same amount of time to perform the measurement). We would then view it as being in a mixture of the states corresponding to 'little energy' and 'no energy', and in our equation for the mixture the numbers a and b would tell us about the probability of getting each result with a measurement. $\endgroup$ – vanasaur Mar 23 '14 at 18:25
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    $\begingroup$ As a final note, I think his conclusion that the lever was "simultaneously" vibrating and not-vibrating is deceptive. The vibrations he measured are quantum mechanical vibrations, which are far more subtle than the ones we're familiar with. He could conclude that the lever was in a mixture of these quantum vibration states because his experiment tied them to unique states of the qubit; a qubit with no energy means vibrating lever, and a qubit with energy means stationary lever. If the qubit is in a mixture of the energy states, then the lever is in a mixture of vibration states. $\endgroup$ – vanasaur Mar 23 '14 at 18:44
  • $\begingroup$ But how can the qubit be in a mixture of vibration states? That is my main question which I cannot get into my head. The thing about simultaneously is irritating me. Please clarify that part for me. $\endgroup$ – rahulgarg12342 Mar 24 '14 at 13:12

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