Kaleidoscopic Optical Schrödinger Cats

Oktay Pashaev & Aygul Koçak, Izmir Institute of Technology

Most mornings I begin my day by looking at two of my favorite web sites -- NASA's Astronomy Picture of the Day (APOD) where you are sure to find some stunning view of our Universe to lift you out of your daily grind and the Cornell/Los Alamos ArXiv which publishes preprints of fresh new science papers in dozens of different specialties, putting anyone with an iPad in daily touch with some of the most brilliant minds on the planet. All this while sipping a cup of exotic coffee from my friends at Boardwalk Beans in New Jersey.

A few days ago, I discovered a paper on the quantum physics arXiv by two mathematical physicists from Izmar, Turkey (formerly known as "Smyrna") entitled "Kaleidoscope of Quantum Coherent States". These two researchers, Oktay Pashaev and Ayguy Koçak, had devised an infinite set of brand new breeds of Schrödinger Cats.

Schrödinger's Cat in bra-ket notation

In quantum mechanics it is commonplace for a system to be in a SUPERPOSITION of states. An (unmeasured) electron's spin, for instance, can simultaneously exist in a spin-up state |UP> and a spin-down state |DOWN>. When measured, however, the electron is always observed to be in one definite spin state. Austrian physicist Erwin Schrödinger, shortly after he invented his famous quantum wave equation, argued that if unmeasured electrons could exist in two states at once, so could cats, and he devised a famous thought experiment in which an unobserved cat could, according to the laws of quantum physics, exist simultaneous as a live cat |ALIVE> and as a dead cat |DEAD>. Schrödinger's famous alive/dead cat conjecture has generated thousands of physics papers on the possible application of quantum superposition to macroscopic objects and numerous jokes, cartoons and T-shirts ("Schrödinger's Cat is a zombie" reads a T-shirt my neighbor Debi gave me for my birthday.).

Schrödinger's cat walks into a bar. And doesn't.

A brief note on notation. When physicists write down their quantum equations, they commonly use the compact and powerful bra-ket notation devised by British physicist Paul Dirac. In Dirac notation, a quantum initial state A is symbolized by a ket symbol |A> and a quantum final state B by a bra symbol <B|. When multiplied together <B|A> represents the probability amplitude that a quantum system A will be measured to have property B. The probability (different from probability amplitude) that A will be measured to have property B is given by the absolute square of the quantity: <B|A>

As a rough example of this kind of physics talk, let the ket |p,p> represent the initial quantum state of two protons. Let transformation T represent the act of accelerating each of these protons to an energy of 6 Gev in CERN's Large Hadron Collider and nudging them into a head-on collision. And let the bra <H,a| represent the final state that contains a Higgs boson and anything else.

Then, in Dirac's concise notation:

<H,a|T|p,p>

represents a number that expresses the probability amplitude of observing a Higgs boson. Square this quantity to get the probability of observing a Higgs boson.

Dirac's simple notation tells you basically what's going on by concealing a ton of detailed math that you really don't want to know about.

So, using Dirac's bra-ket notation, the quantum state of Schrödinger's cat can be simply represented as:

|ALIVE> + |DEAD>

Or, in a more picturesque description, as:

This is the picture one usual gets about Schrödinger's famous cat -- he's both dead PLUS alive.

Quantum mechanics, however, is more complicated than that, and allows for many more existential possibilities for this hapless quantum cat. Quantum mechanical superposition uses COMPLEX NUMBERS (which possess a direction: North, South, East, West,  for instance) as well as a magnitude. (Numbers that possess only magnitude but not direction -- the kind of numbers we use every day -- are called REAL NUMBERS).

Using the extra degrees of freedom provided by complex numbers, the |ALIVE> and |DEAD> states can be "added together" in an infinite number of ways. If we let the direction "East"  represent "+", then the direction "West" will represent "-". Using "West addition" to combine the two cat states we obtain what might be called a MINUS CAT KET.

Schrödinger's MINUS CAT KET, in pictures, might look like this:

In addition to the PLUS CAT state and the MINUS CAT state, the arithmetical freedom provided by complex numbers allows us to imagine NORTH CAT, SOUTH CAT and NNW CAT states. And, in fact, LIVE and DEAD cats may be added together along any conceivable compass direction.

Whether actual cats can be subjected to quantum superposition is still a matter of some controversy, but there does exist a class of macroscopic states of light that can be placed in a variety of quantum superpositions.

Today's physicists probably know more about light than about any other natural phenomenon. Starting with all the natural forms of electromagnetic radiation, we have created both in theory and in practice a large variety of "unnatural" forms of light, some of which were recently invented in this new paper by Pashaev and Koçak.

Pashaev and Koçak begin their work with a familiar quantum state of light |α> called the "Glauber State" after optical physicist Roy Glauber. The Glauber state is a quantum state (also called "coherent state", hence the title of P&K's paper) that most closely approximates a classical state of light, possessing Heisenberg uncertainty and photons (light quanta) which, however, the corresponding classical state of light does not.  The quantity "α" which labels the Glauber state is a complex number. The square of α represents the average number of photons in the Glauber state. And the direction of α (North, South, East or West) represents the location of the Glauber state in a flat space physicists call the "optical phase plane".

The larger the number α, the more photons in the Glauber state |α>. The special case of α =  0 represents no photons whatsoever, or the vacuum state. Many books could be written about the properties of |0>, the quantum vacuum state. "I've got plenty of nothing. And nothing's plenty for me." might well be the theme song of this particular Glauber state, a state that is completely empty of photons.

Prior to the P&K paper, the Optical Schrödinger Cat (OSC) was well known. It consisted of two states from which all other OSCs could be constructed: the PLUS OPTICAL CAT STATE

|plus optical cat state> = |α> + |-α>

and the MINUS OPTICAL CAT STATE :

|minus optical cat state> = |α> - |-α>

The heart of the Schrödinger Cat controversy concerns the question of how big a system can get before it becomes impossible to place it in a quantum superposition. Optical Schrödinger Cats are in a particularly fortunate position to investigate this question because the larger the number of photons in an optical S-Cat state, the "bigger" the state -- and the more it resembles a classical "cat". In the other direction, when α is small (close to 1 photon), the resulting optical states are sometimes referred to as "Schrödinger Kittens".

To construct their "Optical Cat Kaleidoscopes", the two Turks take advantage of the fact that both α and the coefficients multiplying the optical quantum states |α> are complex numbers -- that is, they possess direction as well as magnitude.

The well-known plus and minus optical cats may be considered "cats of order two (C2)." The first new cat in P&K's infinite series of kaleidoscopic cats may be labeled "cats of order three (C3)." Cats of order three are constructed by adding particular cats with different kinds of dead/aliveness along directions that are separated by 120 degrees (similar to the Mercedes emblem). A caricature of the P&K "three cat" might look like this:

Quantum optical trinity cats in Dirac ket notation.

Or, in keeping with the kaleidoscopic metaphor, C3 could look like this:

Three-fold kaleidoscopic optical Schrödinger's Cat (artist's conception)

Pashaev and Koçak go on to show how kaleidoscopic optical Schrödinger Cats of any order can be constructed, depending on which angle you tilt your mathematical mirrors. On its own terms, theirs is a simple but beautiful achievement of pure mathematics. But the authors go further and show how their kaleidoscopic optical cats may someday find a practical use in quantum computing -- each order of cat representing a different number of quantum bits. Thus, if I am not mistaken, the eighth-order cat (octopussy?) can encode eight quantum bits, the same byte size as the ancient Altair computer and many of its successors.

As a poetic reprieve from so much gratuitous quantum math, this may be a good place to quote British mystic William Blake from a letter to his friend Thomas Butts:

Now I a fourfold vision see

And a fourfold vision is given to me

Tis fourfold in supreme delight

And three-fold in soft Beulah's night

And twofold Always. May God us keep

From Single vision & Newton's sleep.

Four Meetings

Nick Herbert and Rudy Rucker: Boulder Creek, CA

These days I'm pretty much of a hermit living with my cat Onyx at the Boulder Creek Quantum Tantra Ashram, going into town a couple times a week for food and spending much too much time indoors browsing the Internet. Occasionally however I enjoy meeting offline with real people.

A few days ago my friend, science-fiction writer Rudy Rucker, dropped by for his traditional yearly pilgrimage to Reality House West and brought bread and cheese for lunch. Rudy is best known for his Ware Tetralogy, a high bizarro-density drama of near-future Earth. Rudy is also a publisher (Transreal Books, Los Gatos) and the editor of Flurb, an on-line anthology of high-weirdness sci-fi stories by Rudy and his pals. He also paints pictures in a primitive style suggestive of Grandma Moses on mescaline and is an accomplished photographer.

After the usual jokes about my Dogpatch lifestyle, Rudy and I exchanged gossip and he shared the excitement about his latest project Million Mile Road Trip in which Dark Matter is made of consciousness and is called "smeal". Consciousness is one of our favorite topics and we engaged in the usual speculations typical of humans at this stage of ignorance about the way the world really works. As he departed, Rudy gifted me with Transreal Cyberpunk, a recent collection of sci-fi "buddy stories" written in collaboration with his buddy Bruce Sterling, a similarly daring explorer of edge-science themes.

Gabriel Guerrer and Nick Herbert: Boulder Creek, CA

A week after lunch with Rucker, I was visited by Gabriel Guerrer, a physicist from South America (Sao Paulo, Brazil) who is also interested in the topic of consciousness. Gabriel had worked for a year at CERN investigating the properties of B-mesons -- a peculiar member of the particle zoo that violates time-reversal invariance, a puzzling glitch in the deep nature of things. Gabriel had worked both in high-energy physics and in high-finance but is now situated at the University of Sao Paulo's Center for Anomalous Psychology attempting to replicate Dean Radin's elegant experiment measuring the effect of human intention on a laser-sourced double-slit interference pattern.

We met at my German-born friend Reno de Caro's house where we were joined by Bruce Damer and Allan Lundell (Dr Future) who participated in a conversation centered around the life experiences that led Gabriel (and the rest of us as well) to take an interest in the risky off-beat territory of consciousness research. I was pleased to see that someone so smart, enthusiastic and qualified as Gabriel was carrying on the torch. A good time was had by all. And Reno captured most of our conversation on video.

Patricia Burchat and Nick Herbert: Stanford Physics Department

About this same time last year, Reno de Caro, who is interested in the history of WW II, decided to travel to the Hoover Institute at Stanford which houses one of the world's largest collections of original documents on World Wars I and II. I decided to tag along on Reno's trip to the German-language archives both as a tour guide and as a returning alumnus of the Stanford Physics Department (graduate class of 1967). Stanford is very picturesque, a reflection of its eccentric founders. Reno brought his camera and captured some beautiful scenes, including candid pictures of excited young men and women dressed in suits and gowns to celebrate their graduation from this prestigious institution.

While Reno was busily copying microfilmed pages of the Joseph Goebbels Diaries onto a thumb drive, I ambled over to Stanford's physics and engineering sector which seemed to have quadrupled in size since I left its hallowed halls. I decided to stop in the physics office to inquire who was around during graduation break and immediately ran into Patricia Burchat, whom I recognized from alumni publications as a former head of the physics department. Jackpot! We talked about the changes in the department and what we both found exciting in the field. Before we parted, I mentioned the old grad student Christmas Party tradition of spoofing the professors and the field of physics with corny, insider-joke skits. Burchat replied that this tradition was still going on. And that she was often one of the organizers of these amateur theatrics. I told her about Les Blatt, a fellow grad student, who, if he had not majored in physics, might have made a name for himself writing Broadway musicals. I mentioned that I still possessed the script from Les's clever parody of My Fair Lady and would send her a copy when I returned to Boulder Creek.

Like Gabriel Guerrer, Patricia Burchat had spent time investigating the kinky behavior of B-mesons, not at CERN but at the BaBar B-meson factory powered by the Stanford Linear Accelerator. Burchat was a prime mover of the BaBar collaboration which published hundreds of scientific papers on the behavior of B-mesons and anti-B-mesons -- symbolized by B-bar, an upper case "B" with a line on top, hence the whimsical name for the project and its association with Babar the French elephant who naturally became the mascot of this giant particle physics collaboration. Patricia is presently associated with the Large Synoptic Survey Telescope in Chile which, when completed in 2023, will take high-resolution photographs of the entire sky every three nights for at least 10 years. One of the primary goals of this full-frame sky video is to discern the effect of invisible Dark Matter on the matter we can actually see.

Blas Cabrera and Nick Herbert: Stanford Physics Department

On a second occasion when Reno was copying documents at the Hoover Institute, I took him and his camera on a tour of campus hot spots ending up again at the Stanford Physics Department. Once there I discovered that my old grad student office was now occupied by Blas Cabrera who is famous for designing a detector of magnetic monopoles that picked up a single signal of the right magnitude on St. Valentine's Day 1982. But Cabrera's detector and others like it were never able to repeat this momentous event, leading physicists to conclude that if monopoles really exist they are very rare in this part of the Universe.

In my former office I discussed with the new occupant changes in the department that had taken place since the sixties while Reno took pictures of our conversation. I was especially curious about the giant black-and-white diagrams posted in the hall outside Cabrera's office. They looked like some kind of labyrinth or the esoteric badges of a mysterious secret society. Turns out that they are the detector design drawings for the Cryogenic Dark Matter Search (CDMS). As Cabrera explained to me how these sophisticated detectors were expected to respond to Dark Matter (an explanation I could barely follow), I asked him if these giant charts represented the actual size of the Dark Matter detectors. "No," he replied. The actual detectors are only about 3 inches in diameter" "And made out of Germanium."

I found it a bit odd that the two physicists with whom I spent the most time at Stanford were both involved in experimental searches for Dark Matter: Patricia Burchat in the foothills of the Andes in Chile; and Blas Cabrera thousands of feet underground in an abandoned iron mine in Canada.

Doubting Conventional Reality

Erwin's puss by Lynden Stone: housed at Centre for Quantum Dynamics, Griffiths University

"Should there not be sufficient space for all sorts of curiosities which in the end the distinction between "physical" and "psychical" loses meaning?"

With this quote from physicist Wolfgang Pauli, Queensland College artist Lynden Stone begins her PhD dissertation Doubting Conventional Reality: Visual Art and Quantum Mechanics. Her
dissertation surveys other visual artists' quantum-inspired attempts to blur the distinction between objective and subjective reality as well as describing her own works on this topic which include paintings such as Erwin's puss, video installations such as Kevin wondered if the Moon existed when he didn't look, experiments with a phantom-limb simulator, the Metaphase Typewriter Revival Project, projects using the Psyleron Mind Lamp and many more. Lynden was recently honored as Artist-in Residence at Crane Gallery in Philadelphia where she participated in a joint exhibition with conceptual artist Jonathon Keats. Next month (February) Lynden exhibits a sampling of her work as one final step in the completion of her doctorate degree.

Here's Lynden's press release for her exhibit. Readers of this blog who live near Queensland, Australia, will have a rare opportunity to test their ability to "doubt conventional reality" in several imaginative quantum-physics-inspired contexts created and constructed by Lynden Stone.

Announcement for Lynden Stone's Thesis Exhibition

Two Mars Bars and the love note from Robert Smeets is the final exhibition by Lynden Stone for examination of her PhD in Fine Art at the Queensland College of Art. Based on the premise that quantum physics demands a re-evaluation of conventional reality, Stone sets out to challenge the viewers’ conventional understanding of reality that is objective, mind independent and knowable.  Viewers can test their ideas of reality by using, for example, the mechanical Mind Dispenser. This work provides random quantum events that, arguably according to quantum theory, allow a viewer to select, in a race of gobstoppers, the colored lolly of their choice by using only their consciousness. The Mind Dispenser is a collaborative piece created by Stone and final year Griffith University engineering student Anderson Tepas and Professor Steven O’Keefe.

The title piece in the exhibition, In another universe, my mother gave me the two Mars bars and the love note from Robert Smeets, 1993--2013, is a work concerning the quantum theory of parallel universes. This theory states that at every moment of choice, all possibilities manifest into multiple, branching universes. Stone presents alternate scenarios behind two doors of a kitchen cupboard. Behind one door is a representation of her parallel life where, rather than hiding the Mars bars and the love note in the kitchen cupboard, her mother did give her these things. In that life, Stone has lived as the wife of Robert Smeets in London Ontario, winning some minor painting prize for an underwhelming pastel still-life at the local show. Behind the other door is a representation of the life she has lead in this time-line.

Two Mars bars and the love note from Robert Smeets is on show in the Webb Gallery, Level 1, Webb Centre, Queensland College of Art, 226 Grey Street, South Brisbane, Queensland from 5--15 February, 2014. Gallery opening hours are Tuesday -- Saturday, 11am--4pm. The opening night event is Friday 7 February, 6--9pm.

Lynden's daughter Madeline interacts with the Psyleron Mind Lamp

Schrödinger Cat Comix

Also see I can has Heisenburger?