Measuring Schrodinger's Cat

Most recent answer: 04/24/2014

Q:
Why can't one attach a heart monitor to Schroodinger's cat and monitor it's macro state? I.e. Bitfit type device. Thank you!
- N. Lustig (age 61)
New York
A:

Hi N. Lustig,

You could hook a heart rate monitor to Schrödinger's cat, or you could just look and see if the cat is moving, or you could listen for meowing. In any such case, you would be performing a measurement which would ask the question "is the cat Dead or Alive?" When you do such a classical measurement on a quantum mechanical state, you collapse the state. So, as soon as you measure it, you will destroy the superposition state that you worked so hard to create, and you won't have a Schrodinger's cat anymore. You will just have a regular cat which is either dead or alive.

In fact, this is a general property of all superposition states. You can't tell that they are in superposition states of some basis (like Alive/Dead) by directly testing in that basis. Furthermore, any interaction with the environment is effectively a partial measurement of whether the cat is Alive or Dead, so you have to isolate the cat completely from heart monitors, air molecules, light, and all types of external influences. Even then, how do we verify that we have a superposition state? The answer, ultimately, is interference.

The first indication that objects existed in superposition states was basically the double-slit interference pattern. If you do this classic experiment with only one particle at a time (which is what is usually done in experiments), then you get an interference pattern which has only one simple explanation: the particle has two separate wave amplitudes which each travel through one slit, and then the amplitudes interfere. So, as it passed through the two slits, we know it was in a superposition of two different positions.

Similarly, if you wanted to prove that your Schrödinger's cat was both alive and dead, then you'd have to find some way to "recombine" the two possibilities. No one has any idea how to do this... honestly, I don't even know what it means. No one seriously wants to try the famous thought experiment, since the state of being dead or of being alive is just far too complicated and distributed through too many degrees of freedom.

Instead, researchers tend to focus on states that they understand, like double slits or springs. To give you an idea of how we might actually measure a large superposition state, I'll sketch a recent theoretical proposal. The nice thing about this proposal is that we will probably be able to actually implement it within a decade or two, and in doing so create a superposition state almost large enough for the eye to see (though of course, you can't watch while doing the experiment, for the very reasons explained above).

In the proposal (e.g. here ), light bounces between two high-quality mirrors, one of which is on a spring. A single photon is split into a superposition of two paths, one of which enters this mirror cavity. The amplitude ("half") of the photon which enters the cavity interacts with the mirror, depositing some energy and causing the mirror to oscillate. Because the photon was in a superposition of entering and not entering the cavity, the mirror is now in a superposition state of oscillating and not oscillating. After a while, assuming the mirror coherently maintains its full quantum superposition, the mirror transfers the energy back to the photon, after which we recombine the two photon amplitudes and see if they interfere.

If we see interference at the end of this experiment, then we know that the mirror was in a superposition state. If the mirror decoheres and loses its quantum superposition state, then when we measure the photon, we won't see interference. In the near future, the mirrors in these experiments will be very small, perhaps 10 microns on each side. Still, this is about the radius of a small human hair, and would be by far the most macroscopic object put in an interference to date, around 10^14 atoms!

If you are interested, you could google "macroscopic superposition states" and"optomechanics". It's an amazing, rapidly-growing field!

David Schmid


(published on 04/24/2014)