C60 wave component interference question

[blutoski]

I came across a claim that C60 molecules can display interference in a double-slit apparatus.

I found this hard to believe, but there seems to be credible documentation. Up to yesterday, I had thought that only subatomic particles would be able to show this property.

My question is: is there a way to predict how large an object will need to get in order to stop showing this wave component interference in this type of experiment? Is velocity a factor?

eg: would calculating the deBroglie wavelength and comparing to the size of the object be the key?

[Ziggurat]

I came across a claim that C60 molecules can display interference in a double-slit apparatus.

I found this hard to believe, but there seems to be credible documentation. Up to yesterday, I had thought that only subatomic particles would be able to show this property.

Anything can in principle show interference, given an interferometer with dimensions appropriate to its de Broglie wavelength. The longer the wavelength, the larger the interference pattern, which makes observing the interference easier from a practical standpoint. And it's easier to prepare lighter objects with longer de Broglie wavelengths, which is why it's commonly done with subatomic particles (especially electrons). But there's nothing intrinsic about them being subatomic that's needed for interference.

My question is: is there a way to predict how large an object will need to get in order to stop showing this wave component interference in this type of experiment? Is velocity a factor?

eg: would calculating the deBroglie wavelength and comparing to the size of the object be the key?

The deBroglie wavelength (which depends upon momentum, and hence both velocity and mass) is indeed what you want to look at. But it's not simply a matter of comparing the wavelength to the size of the object, it's more a matter of comparing the wavelength to the dimensions of your aparatus. Even with pointlike particles like electrons, the wavelength can always get too small for a given interferometer to resolve interference.

[blutoski]

Anything can in principle show interference, given an interferometer with dimensions appropriate to its de Broglie wavelength. The longer the wavelength, the larger the interference pattern, which makes observing the interference easier from a practical standpoint. And it's easier to prepare lighter objects with longer de Broglie wavelengths, which is why it's commonly done with subatomic particles (especially electrons). But there's nothing intrinsic about them being subatomic that's needed for interference.

The deBroglie wavelength (which depends upon momentum, and hence both velocity and mass) is indeed what you want to look at. But it's not simply a matter of comparing the wavelength to the size of the object, it's more a matter of comparing the wavelength to the dimensions of your aparatus. Even with pointlike particles like electrons, the wavelength can always get too small for a given interferometer to resolve interference.

Is there a practical limit to this? ie: can I crank out an equation that describes the largest mass whose interference can be observed given apparatus with slits Xnm apart? (would the solution be a line? - probably not... my recollection is that both velocity and mass are inputs to the deBroglie equation, so the solution is a surface in three dimensions at least)

[Ziggurat]

Is there a practical limit to this?

Depends on what you consider practical. But macroscopic objects (like, say, a baseball) are pretty clearly beyond the limit of practicality. For molecular-sized objects, I don't know what our limits are, but I know some of the basic issues involved in setting those limits.

ie: can I crank out an equation that describes the largest mass whose interference can be observed given apparatus with slits Xnm apart?

It would be a little more complex than that. What you start with is an equation describing the size of the interference fringes as a function of the wavelength of the particle and the dimensions of your slits. The smaller the wavelength, the less separation in your interference fringes. If that separation distance gets too small, you cannot resolve it, because your detector will always have imperfect spatial resolution. There are a number of things you can do to your interferometer to change the separation distance (including increasing the separation distance between the slits and the screen), but these have limits as well. For example, you can't make that distance larger than the size of the earth. In fact, even if you make it, say, the size of a football field, you run into other problems (more in a moment).

OK, so you've got practical limits on your spectrometer which you can't past, so you might consider increasing the wavelength of your object in order to see the interference pattern. Well, this can introduce problems of its own. First off, it can be difficult to produce particles with uniform but small momentum, but let's ignore that for now (only because I don't know how hard it is, not because it's not a problem). Even assuming you can set the particles up with whatever momentum you want, however precisely you want, if the object has low momentum, it's moving slowly. The slower it moves, the more time it has to be affected by gravity. We'd like to use as physically large an interferometer as we can. But the larger the spectrometer, the longer it takes for the object to travel through it. Which means it spends more time being affected by gravity. And gravity will be changing its momentum. If you set up the experiment horizontally, you need to get the object from one side to the other before it falls on the floor of your apparatus, and that imposes a minimum velocity (and hence momentum) on your particle. If you set up the experiment vertically (by, say, dropping the particle through the slits), you can make the apparatus as big as you want, but the momentum will increase as the particle progresses, so increasing size provides diminising returns.

And of course, all of this needs to be done in a vacuum, and it's expensive to make large vacuum chambers. And the larger the chamber, the better the vacuum needs to be (since you need the mean free path to be larger if the interferometer is larger), which makes it cost even more.

Edit to add: so in short, current limits are probably set by costs, which will rise quickly for more massive objects.

my recollection is that both velocity and mass are inputs to the deBroglie equation,

Correct: the wavelength is inversely proportional to the momentum (wavelength = h/p).