## A “Schrodinger Cat” Superposition

** Sandra L. Manulat**

“**Schrodinger’s cat paradox** is a classical illustration of the conflict between the existence of quantum superpositions and our real-world experience of observation and measurement”[1].

The Principle of Superposition of States in quantum mechanics has become strikingly successful at describing physical phenomena at the atomic scale. Quantum superposition requires us to assume that between states there exists a peculiar relationship such that whenever the system is in one state we can consider it as partly in the other states.

Now, **what if we extend quantum superposition to macroscopic systems? **This is where the Schrodinger Cat comes to the picture.

Schrodinger Cat started out to be a thought experimenent: An unfortunate cat is placed in a quantum superposition of being dead and alive. How was this done? simply put, a cat was placed in a box together with a single radioactive atom that has and has not decayed. The state of the system can be represented by the entangled quantum mechanical wave function:

[eq]\Psi = \frac{|\ddot\smile\rangle |\uparrow\rangle + |\ddot\frown\rangle|\downarrow\rangle}{\sqrt{2}}[/eq]

where [eq]|\ddot\smile\rangle[/eq] and [eq]|\ddot\frown\rangle[/eq] refer to the states of a live and dead cat, and [eq]|\uparrow\rangle[/eq] and [eq]|\downarrow\rangle[/eq] refer to the internal states of an atom that has and has not radioactively decayed. We know that if the atom has not decayed the cat is alive **and** dead otherwise; but of course if we open the box, we only observe a live **or** dead cat and not both states.

Although it is quite impossible for a Schrodinger’s cat (SC) to exist in the macroscopic world, there is great interest in creating SC-like states in mesoscopic systems, or systems that have both microscopic and macroscopic features. SC-like states may provide a testing ground for the controversial theory of quantum measurement and the universality of the quantum theory.

The SC-like state was created by forming a superposition of two coherent-state wave packets of a single trapped atom with a sequence of laser pulses. Each wave packet is correlated with a particular internal state of the atom. A [eq]^9Be^+[/eq] ion was confined in a coaxial-resonator radio frequency trap that provides the harmonic oscillator frequencies. The ion was laser cooled to the zero point energy and then its internal (electronic) and external (motional-nearly classical) state was coherently manipulated by applying pairs of off-resonant laser beams. The SC superposition was verified by detection of the quantum mechanical interference between the localized wave packets[1]. The downside of the experiment is when the SC state is coupled to a thermal reservoir the superposition decays exponentially into a statistical mixture, that is the lifetime of the superposition shortens. This phenomenon is called decoherence which explains why superpositions are rare if not impossible in the macroscopic scale, and illustrates the difficulty in preparing and maintaining even mesoscopic superpositions.

[1]C. Monroe, et. al. A “Schrodinger Cat” Superposition State of an Atom

About the author:

Sandra Manulat is taking her master’s degree in physics at MSU-Iligan Institute of Technology. She aspires to become a physicist her country could be proud of.

April 26th, 2012 at 4:10 am

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