Slow Decoherence of Superpositions of Macroscopically Distinct States

A Schrödinger cat state is a linear superposition of two quantum states that differ on a macroscopic scale. Whereas superpositions of quantum states are commonplace in the microscopic world, a superposition of macroscopically distinct states is practically never observed. The understanding of why this is so has evolved considerably with the development of the quantum mechanics of dissipative systems [1,2]. Dissipative systems are systems that are coupled to an environment (also called “heat bath”) with a large number of degrees of freedom. The coupling allows for an exchange of energy between system and bath. Therefore the motion of the system will slow down till only thermal fluctuations in equilibrium with the heat bath are left. This effect is also present in classical mechanics and takes place on a classical time scale, Tclass. But the coupling to the environment also very rapidly destroys quantum mechanical interference effects, and leads to an effectively classical behavior. The decoherence arises on a time scale Tdec which is typically much shorter than Tclass. As a general rule, if a seperation D in phase space can be assigned to the states involved in the Schrödinger cat state, the two time scales behave as Tdec/Tclass ∼ (h̄/D) where r is some positive power depending on the details of the coupling and the environment [3–8]. This separation of time scales has also been termed “accelerated decoherence”. The validity of this picture starts to be confirmed in experiments of Haroche et al., who were able to turn on the coupling to an environment in a controlled way and measure the decay of the coherences [9,10].