So the May 27 issue of Science has this article which claims to demonstrate a “cat state” (an observable real world Schrödinger’s cat two states existing at the same time occurance, I think the same thing sometimes also called a “Schrödinger’s kitten”) “in two separate locations at the same time.”
Anyone able to help explain what they actually did? I understand that Hilbert spaces are just large-n geometric spaces of which the basic rules of geometric transformation/translation, calculus, etc. all apply. But what is “a superconducting artificial atom”? How does it bridge the two cavities?
From the article, this is where I knew I was in need of help to understand this!
I do not really understand much of what they did. There are two papers inside this link here: one being the full published paper and another seeming to be a supplementary about the mechanics of creating the experiment itself.
Oh I have the article (and I think the link can get you there without even a paywall problem). Individual words are not the issue so much as how they string together into sentences and concepts …
The basic claim I get. Schrödinger’s kittens are macroscopic states which are coherent from a quantum phase POV and are observably in more than one state at a time … in this case I guess groups of coherent photons that have two sorts of oscillations at the same time. And somehow now in two locations at once too? By way of an artificial atom?
I haven’t completely read the article, but this is how I read it:
In the Schrodinger’s cat gedankenexperiment , you have one box which contains a cat which is in an equal superposition of states of [alive] and [dead]. The experiment in the article “recreates” the state of affairs of having a “large-ish” system which is in an equal superposition of two intuitively opposing states, but the twist is the system is spread over two spatially separated boxes rather than a single box.
Specifically, in the experiment they have two boxes, A and B, and the number of photons bouncing around in each box is in a near equal superposition of states of [box A contains an even number of photons and box B contains an odd number of photons] and [box A contains an odd number of photons and box B contains an even number of photons].
This is achieved by entangling the states in the boxes which is itself achieved by connecting them via a nanoparticle of semiconducting material (i.e. the artificial atom).
A ‘cat state’ typically is a superposition of two coherent states with opposite phases. A coherent state is, in some sense, the most ‘classical-like’ state of an electromagnetic field—it moves on a classical trajectory through phase space, for instance. So, such a cat state is a superposition of opposing classical states of affairs; hence the name.
They generalize that concept (as Asympotically fat already explained above) by generating a superposition of two cavities containing two coherent states (cavity A and B containing coherent state 1 and cavity A and B containing coherent state 2). (Just parenthetically, I would like to point out that one can’t think of coherent states as containing a definite number of photons; they’re instead superpositions of definite-photon-number states, the so-called Fock states.)
An ‘artificial atom’ is generally something like a two-level (or more) system: the two possible states of the system mirror an atom being in one energy state or another. In this case, it’s implemented via a Josephson junction, which can hold different levels of charge.
Basically, the ‘artificial atom’ is used to couple the radiation fields in the two cavities: depending on the level it’s in, different transformations are implemented on the fields via microwave interactions; thus, it’s used to build (and perhaps read out) the cat state.
That sounds fishy to me. If they’re considering the even-odd state of the photons in each box to be entangled, that seems to suggest that they’re assuming that the total number of photons is conserved. But photon number is not only not conserved, it’s not even invariant.
Now, it may be that they’ve managed to contrive some way to keep the even-oddness of the total photon number conserved, but that would take a lot of contriving.
Thank you HMHW. That along with the cartoon schematic in the article got me to as much understanding as I at least can reasonably hope for.
Is a “cat state” fundamentally different than what gets called a “Schrödinger’s kitten” or a specific sort of instance of one dealing with entangled quasi-classical systems?
Am I right in understanding that Hilbert space in this case seems to just be used as the way to express how much is gained in increased potential computing power, in this case the concern for error correction?
And hijacking my own op, how difficult is it for traditional computing to manipulate geometric forms in modest n Hilbert spaces?
(My long-standing fantasy is related to concepts being represented as n-dimensional objects (e.g. the color spindle) and to creative analogy making being the discovery of an unexpectedly good fit of of one geometric object when transformed and applied to another domain. If concepts can be expressed geometrically then a computer that can transform objects in modestly large n-dimensional spaces would be engaging in creative analogy making, something that is a hallmark of human creativity.)
I have to admit I’ve never come across the term ‘Schrödinger’s kitten’ before; from quick googling, I found one reference in Science, where it’s used synonymous to what I’ve called ‘cat state’ above.
Sometimes, one also hears states that are superpositions of ‘contradictory’ properties called ‘cat states’ or similar—such as, for instance, a superposition of ‘all spins up’ and ‘all spins down’.
Hilbert space generally is just the abstract mathematical space where quantum states live—that is, all the information of a quantum system can be represented by a point (or rather, a ray, i.e. a set of points that only differ by a global phase factor) in Hilbert space. Hilbert spaces themselves are not terribly abstract concepts: indeed, you’re sitting in one right now—ordinary space is a three dimensional Hilbert space. The main difference is that it’s a ‘real’ space (as in, coordinates take real values) in position space, while in quantum mechanics, it’s generally a complex one.
The nice feature of Hilbert space is that there is a way of multiplying two points (vectors) A and B (scalar multiplication) such that the square of the result is the probability of finding state A if the system is in state B.
I’m not sure what you’re aiming at in terms of computational power—however, in a sense, quantum states are very complex objects (the number of parameters needed to describe an n-particle system is exponential in n, while in classical mechanics, each ‘particle’ only adds 6 coordinates—three for position, and three for momentum).
The above complexity issue means that classical computers incur an exponential slowdown when computing quantum systems; however, quantum computers don’t. As for the general complexity of carrying out calculations in high dimensional vector spaces, depending on the application, ordinary computers get you quite far, though for specifics, you’d have to ask an expert in computational complexity. But the limiting factor isn’t necessarily going to be dimension, but the task you want to perform—there are fairly easily characterized sets even in high dimensions—convex polytopes, for example, are simple to describe and to solve, e.g., optimization problems over, while even more general convex sets (such as the set of quantum correlations) become quickly intractable.
You should check out Giulio Tononi’s Integrated Information Theory, in particular the notion of qualia space, for something that seems to go in that general direction.