The Schrödinger’s Cat thought experiment.
This thought experiment was posed in a short paragraph in an essay by Schrödinger on the conceptual problems in quantum mechanics. The paradox itself is put forward as an example of the theory going against common sense.
The setup for the thought experiment consists of a box, containing a cat and a device that is dependant on a single decaying nucleus. The device consists of some radioactive substance that has an equal probability of a single nucleus decaying or not decaying during any one hour period. By the laws of quantum mechanics, until the state is measured, the nucleus has both decayed and not decayed. There is a detector that triggers a hammer device, which, in turn breaks a vial of Hydrocyanic acid and kills the cat.
The thought experiment consists of closing this box and leaving it for an hour. Due to the behavior of the nucleus under detection, the vial has both broken and not broken, and hence the cat itself is in a superposition of states, both alive and dead. This is obviously in conflict with the classical interpretation of this situation.
It is generally accepted that there is a phenomenon called “decoupling” or “decoherence”, where the quantum nature of the radioactive decay is not exhibited due to interactions with objects around it. In this case, the nucleus’s wave function is disturbed by interactions, or “observation”, with photons or the air in the box or the box itself.
Another obvious problem with this situation is that the cat itself is an observer, though the line between an observer and a non-observer is difficult to pinpoint. Hence, interactions of any sort are generally considered to decouple a system and stop macroscopic objects from routinely displaying quantum mechanical properties.
There have been a number of experiments devised to show truly macroscopic effects of quantum superposition. In this website we explore three of these experiments.
1. The SUNY-Stony Brook SQUID experiment.
2. NIST Beryllium atom self-interference experiment.
3. Diffraction pattern exhibited by Bucky-Balls.
Material from University of Oregon:
*http://zebu.uoregon.edu/~js/21st_century_science/lectures/lec14.html
IDMON (main page http://www.idmon.freeserve.co.uk/)
*http://www.idmon.freeserve.co.uk/cation.htm
And Swarthmore College:
*http://chaos.swarthmore.edu/courses/phys6_2004/QM/24_CatDecoherence.pdf
Quantum decoupling or decoherence:
Quantum superposition is not easily shown on a macroscopic scale. It’s extrapolation in such realms also leads to illogical outcomes, such as the Schrödinger’s Cat Paradox. Physicists had to find a solution to this problem, and thus a theory of decoherence was formed.
Any system, unless completely isolated, interacts with some form of external environment. Throughout this environment, the state of quantum determinacy cannot be completely known. The interaction of the environment with the quantum superposition of states results in a decay over time, into one state or the other. This phenomenon is known as decoherence.
This theory explains why a physicist may be able to keep a single electron or other quantum particle in a superposition of states for long periods of time, while Mr. Schrödinger’s theoretical cat would very quickly be either alive or dead. This creates an intuitive element to an otherwise difficult theory to visualize.
The rate of decoherence is difficult to measure for a system of many atoms. Researchers at the American National Institute of Standards and Technology (NIST) demonstrated this for a coupling between a Beryllium ion and a specific environment. This is investigated on the NIST Beryllium atom self-interference page.
Material from Swarthmore College:
*http://chaos.swarthmore.edu/courses/phys6_2004/QM/24_CatDecoherence.pdf
And University of Oregon:
*http://zebu.uoregon.edu/~js/21st_century_science/lectures/lec14.html
The SUNY-Stony Brook SQUID experiment.
Jonathan Freidman and co-researches in the State University of New York have successfully created a superposition of states in a SQUID. They consider this to be “truly macroscopic”, as the currents measured involve the movement of billions of electrons.
The experimental setup is essentially two potential wells, each containing bound states, and separated by a potential barrier. The system is created with a current of approximately 1microamp traveling in an arbitrary, known, direction. It is then excited with microwaves, so that there is enough energy for the states to tunnel from traveling one direction to the other.
When measurements were taken as the shape of the potential was changed, the resulting probability distribution showed exactly what is predicted if there was a macroscopic superposition of states. The difference between current flowing clockwise and anticlockwise is around 2 microamps, or a magnetic moment of 10 billion Bhor magnetons.
A research team at the Delft University of Technology in The Netherlands has designed a smaller-scale superposition, with greater application to quantum computing. Some of the reasons for this are explained in the SQUID page. The SQUID’s can be used in quantum computing because they are a superposition of two states, hence they can be used as a qbit (a quantum bit, with one state as zero and one state as one). The small devices used by the Delft University team can be, and have been, fitted onto a chip in large numbers, with the Delft University team fabricating a chip containing many loops.
-http://www.trnmag.com/Stories/111500/SQUID_Quantum_Computing_111500.html
Graduate student, Casper van der Wal believes that their system is better than other quantum-computing solutions because "controlled inductive coupling means that the magnetic field produced by one loop can be picked up by a neighboring loop such that the behavior of the two depends on each other. We can engineer the strength of this coupling and probably make it even tunable. This is the main advantage of our system with respect to microscopic systems like atoms. Our microfabricated system allows for much more engineering of the system's parameters. The parameters of atoms are set by nature."
Freidman, from the SUNY, says that “The big advantage about SQUIDs is that they can be fabricated en masse on a chip. Large-scale integration is quite conceivable.”
Material from Technology Research News Magazine:
*http://www.trnmag.com/Stories/111500/SQUID_Quantum_Computing_111500.html
And PhysicsWeb:
*http://physicsweb.org/articles/news/4/7/2/1
Note: The physicsweb.org article references: Nature 406 43 as the source of the original SUNY-Stony Brook SQUID experiment article.
NIST Beryllium atom self-interference experiment
A research team at the American National Institute of Standards and Technology (NIST), consisting of Christopher Monroe, Dawn Meekhof, Brian King and Dave Wineland, has successfully created a superposition of states on what they term a “mesoscopic” scale, using a beryllium ion confined within an electromagnetic cage. They also investigated the rate of decoherence when this system interacted with a controlled environment.
The beryllium ion (with only one outer electron instead of two) is first confined within an “electromagnetic trap”, and then cooled to near absolute zero by the use of finely tuned lasers. This results in the ion being in a space less than a millionth of a centimeter across and resting with nearly zero motion. The outer electron can now either be in the spin up state or the spin down state, with equal probability.
A diagram showing an idealized up and down spin superposition.
-http://abyss.uoregon.edu/~js/cosmo/lectures/lec08.html
Next, pulses of radiation are applied to the ion, so as to create a force on the outer electron. This force pushes in different directions for each spin and separates them. The states actually became two separate states, instead of a pair of superimposed states, these were separated by 80nm, 11 times the size of the original ion.
NIST say: “This bizarre state, of being in two well-separated places at once,
can be visualized by imagining a large, shallow, round-bottomed bowl
with a marble simultaneously at opposite sides of the bowl, rolling from
side to side and through itself at the center.”
The team performed the experiment may times, varying the direction of the force. They found that when the states began to overlap, there was an interference pattern, and the width of this was inversely proportional to the initial separation.
A idealized diagram of the positions of each state, as measured by the NIST team.
The images are snapshots in time, with an interference pattern at the centre.
-http://www.nist.gov/public_affairs/taglance/tag96sum/tag96sum.htm
The team thinks that this may have applications in making a more accurate atomic clock. They believe that trapped atoms may provide a way to measure time up to 1000 times more accurately.
In further developments, Wineland and fellow researchers used the same setup as in the above experiment. They then tailored the coupling between the ion and the surrounding environment, thereby inducing decoherence. They showed that (in essence) the amount of superposition of states decreased with time, as predicted by quantum theory. They found that the larger the superposition, the greater the observed decoherence. Finally, by manipulating the coupling with the environment, simulating shrinking the environment, they observed slowing and even reversals in decoupling. This vindicates the theory of decoherence by scientific investigation.
Material from the American National Institute of Standards and Technology
*http://www.nist.gov/public_affairs/releases/n96-18.htm
*http://www.nist.gov/public_affairs/taglance/tag96sum/tag96sum.htm
IDMON (main page http://www.idmon.freeserve.co.uk/)
*http://www.idmon.freeserve.co.uk/cation.htm
The University of Oregon
*http://abyss.uoregon.edu/~js/cosmo/lectures/lec08.html
*http://zebu.uoregon.edu/~js/21st_century_science/lectures/lec14.html
And Swarthmore College
*http://chaos.swarthmore.edu/courses/phys6_2004/QM/24_CatDecoherence.pdf
SQUID
A Superconducting Quantum Interference Device (SQUID) is a ring-shaped device in which a current can flow either clockwise or anticlockwise without decay, due to the device’s superconductivity. Current is induced by use of a magnetic field.
The device used by SUNY researchers in their superposition experiment is made from niobium (superconducting at 40millikelvin) and aluminium oxide (acting as a barrier) and is protected from the environment (to avoid decoherence) by a palladium-gold shield. This device has a flow of billions of electron pairs. There has been one other example of superposition demonstrated in SQUID’s, by a team at the Delft University of Technology in the Netherlands.
The Delft University of Technology research team uses a smaller device, with a current flow of millions of electron pairs. This is less applicable to testing the macroscopic limits of quantum mechanics, but more useful for quantum computing, as it has three junctions in the loop, whereas the SUNY team’s loop has only one. These extra junctions mean that the loop can be much smaller and hence can be isolated from the environment more effectively (to avoid decoherence).
Material from Technology Research News Magazine:
*http://www.trnmag.com/Stories/111500/SQUID_Quantum_Computing_111500.html
And PhysicsWeb:
*http://physicsweb.org/articles/news/4/7/2/1
Note: The physicsweb.org article references: Nature 406 43 as the source of the original NIST-Stony Brook SQUID experiment article.
Complete bibliography
The American National Institute of Standards and Technology
*http://www.nist.gov/public_affairs/releases/n96-18.htm
*http://www.nist.gov/public_affairs/taglance/tag96sum/tag96sum.htm
IDMON (main page http://www.idmon.freeserve.co.uk/)
*http://www.idmon.freeserve.co.uk/cation.htm
The University of Oregon
*http://abyss.uoregon.edu/~js/cosmo/lectures/lec08.html
*http://zebu.uoregon.edu/~js/21st_century_science/lectures/lec14.html
Swarthmore College
*http://chaos.swarthmore.edu/courses/phys6_2004/QM/24_CatDecoherence.pdf
Material from Technology Research News Magazine:
*http://www.trnmag.com/Stories/111500/SQUID_Quantum_Computing_111500.html
PhysicsWeb:
*http://physicsweb.org/articles/news/4/7/2/1
Note: The physicsweb.org article references: Nature 406 43 as the source of the original NIST-Stony Brook SQUID experiment article.