Reply
 
Thread Tools Display Modes
  #1  
Old 06-11-2016, 07:21 PM
DSeid DSeid is offline
Guest
 
Join Date: Sep 2001
Location: Chicago, IL
Posts: 19,646
Help understanding quantum cat states and artificial atoms

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!
Quote:
Here, we deterministically create a two-mode cat state of microwave fields in two superconducting cavities, using the strong dispersive interaction with a Josephson junction–based artificial atom.
Anyone up for explaining it?
  #2  
Old 06-11-2016, 07:57 PM
TipTapTwo TipTapTwo is offline
Guest
 
Join Date: Jan 2016
Location: I am an idiot
Posts: 137
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.

http://webcache.googleusercontent.co...&gbv=1&ct=clnk

so, i guess at worst, if you really want to know what they did then have wikipedia open in another tab to act as a translator for all the new words and ideas they are using.

So sorry, explaining anything about this is beyond me.
  #3  
Old 06-11-2016, 08:42 PM
DSeid DSeid is offline
Guest
 
Join Date: Sep 2001
Location: Chicago, IL
Posts: 19,646
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?
  #4  
Old 06-11-2016, 09:48 PM
Asympotically fat Asympotically fat is offline
Guest
 
Join Date: Jan 2008
Posts: 3,032
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).

Last edited by Asympotically fat; 06-11-2016 at 09:50 PM.
  #5  
Old 06-12-2016, 07:42 AM
Half Man Half Wit Half Man Half Wit is offline
Guest
 
Join Date: Jun 2007
Posts: 6,210
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.
  #6  
Old 06-12-2016, 07:55 AM
Chronos Chronos is online now
Charter Member
Moderator
 
Join Date: Jan 2000
Location: The Land of Cleves
Posts: 73,037
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.
  #7  
Old 06-12-2016, 09:11 AM
Half Man Half Wit Half Man Half Wit is offline
Guest
 
Join Date: Jun 2007
Posts: 6,210
Quote:
Originally Posted by Chronos View Post
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.
They're not considering states of any definite photon number at all (Fock states), but rather, coherent states of opposite phases, which are put into superposition.
  #8  
Old 06-12-2016, 12:14 PM
DSeid DSeid is offline
Guest
 
Join Date: Sep 2001
Location: Chicago, IL
Posts: 19,646
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.)

Thanks.
  #9  
Old 06-12-2016, 01:07 PM
Half Man Half Wit Half Man Half Wit is offline
Guest
 
Join Date: Jun 2007
Posts: 6,210
Quote:
Originally Posted by DSeid View Post
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?
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'.

Quote:
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?
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).

Quote:
And hijacking my own op, how difficult is it for traditional computing to manipulate geometric forms in modest n Hilbert spaces?
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.

Quote:
(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.)

Thanks.
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.
  #10  
Old 06-12-2016, 01:37 PM
DSeid DSeid is offline
Guest
 
Join Date: Sep 2001
Location: Chicago, IL
Posts: 19,646
Thank you for the link. An interesting read but my thoughts had been more inspired by this book and tying it to creativity as an unexpected good fit of analogy making leading to novel ideas.

The bit about computational power comes from my limited understanding of this in the article:
Quote:
Compared with single-cavity quantum states, the addition of the second cavity mode increases the quantum information capacity significantly. Despite the modest mean photon numbers, a full tomography of the two-mode cat state (partly shown in Fig. 3) requires a Hilbert space of at least 100 dimensions to be described (capturing 99% of the population), comparable to a six- or seven-qubit Greenberger-Horne-Zeilinger (GHZ) state. Our conservatively estimated quantum state fidelity is comparable to that reported for an eight-qubit GHZ state in trapped ions (10) and the largest GHZ state in superconducting circuits (five qubits) (11).

An important motivation for creating multicavity cat states is to implement a promising paradigm toward fault-tolerant quantum computation (7, 8), where information is redundantly encoded in the quasi-orthogonal coherent state basis (6).
Reply

Bookmarks

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -5. The time now is 02:20 PM.

Powered by vBulletin® Version 3.8.7
Copyright ©2000 - 2017, vBulletin Solutions, Inc.

Send questions for Cecil Adams to: cecil@chicagoreader.com

Send comments about this website to: webmaster@straightdope.com

Terms of Use / Privacy Policy

Advertise on the Straight Dope!
(Your direct line to thousands of the smartest, hippest people on the planet, plus a few total dipsticks.)

Publishers - interested in subscribing to the Straight Dope?
Write to: sdsubscriptions@chicagoreader.com.

Copyright © 2017 Sun-Times Media, LLC.

 
Copyright © 2017