Decoherence 101

The Decoherence Interpretation of Quantum Mechanics

from “The New Quantum Universe” by Hey and Walters (2009)

A less extravagant (than the Copenhagen and Many Worlds  Interpretations) and rather more mundane attempt to solve the measurement problem goes by the name of “decoherence”. This approach argues that quantum systems can never be totally isolated from the larger environment and that Schrodinger’s equation must be applied not only to the quantum system but also to the coupled quantum environment. In real life, the “coherence” of a quantum state – the delicate phase relations between the different parts of a quantum superposition – is rapidly affected by interactions with the rest of the world outside the quantum system. Wojciech Zurek is one of the most prominent advocates of this “decoherence” approach to the measurement problem, and he speaks of the quantum coherence as “leaking out “ into the environment. Zurek claims that recent years have seen a growing consensus that it is interactions of quantum systems with the environment that randomize the phases of quantum superpositions. All we have left is an ordinary non-quantum choice between states with classical probabilities and no funny interference effects. This seems a very prosaic end to the quantum measurement problem! How does this come about? Does decoherence by the environment really supply an answer to all the problems? Let us look at an experiment that claims to see decoherence of “Schrodinger cat” states in action.

Serge Haroche and Jean-Michel Raimond, working in Paris with their research group, have recently performed some exciting experiments that give support to this decoherence picture. There are three different parts to an experiment that can all interact – the quantum system, the “classical” measurement apparatus, and the environment. In their experiment the quantum system consists of an atom that can be prepared in one of two states. They measure the quantum state of the atom by injecting the atom into a cavity and using the electromagnetic field of the “cavity” as a classical “pointer.” What happens if we prepare the atom in a quantum superposition of the two states? If we treat the cavity as a second quantum system in its own right, we find that the supposedly classical counter is now predicted to be in a “Schrödinger cat” state. – a quantum superposition of two classical states of the pointer.  Schrodinger’s thought experiment just highlighted the peculiarity of this situation by using his cat as a classical pointer. How do we escape from this apparent paradox? According to the decoherence picture, we must include the unavoidable coupling of the pointer to the environment. The pointer – or cavity – is under a constant bombardment from random photons, air molecules and so on that constitute the “environment.” Models of this random process as a third quantum system show that all phase information between the two original atomic states with their corresponding pointer positions is very rapidly lost. For the usual classical pointer fields with many photons, this decoherence is predicted to take place in an immeasurably short time. Remarkably, by using pointer cavity fields consisting of only a few photons, Haroche and Raimond have been able to observe and measure the decoherence time of this system. They do this by sending a second atom into the cavity at varying times after the first atom and measuring interference effects that depend on the continued coherence of the wavefunction of the first atom. By observing how fast these interference effects fall off with the time delay between the traversals through the cavity of the first and second atoms, they claim to have “caught decoherence in the act”!

Einstein’s problem with the Moon can be “explained” by using a similar decoherence argument. The Moon is not an inert system – not only are its individual molecules constantly interacting with their neighbors but also its surface is under constant bombardment by particles and radiation, mainly from the Sun. The coherence of any Schrodinger cat state involving the Moon would rapidly be destroyed by these constant interactions. According to such decoherence arguments, we can rest assured that the Moon is really there after all, even when we are not looking at. Bombardment by solar photons is enough to constitute a measurement and to destroy any quantum coherence.

Would these decoherence arguments have satisfied John Bell as an explanation of the measurement problem? Probably not! We have described not only the quantum system under observation but also the measuring apparatus as a quantum system. The quantum wavefunction for the combined system will be in a superposition of states corresponding to different classical states of the measuring apparatus, as in the experiment of Haroche and Raimond. The decoherence argument says we must include the environment as a third quantum system interacting with our measuring apparatus. As a result, phase randomization rapidly sets in and the quantum superposition is effectively reduced to a sum of different possible outcomes with classical probabilities. Bell had two problems with this approach. Firstly, all quantum states – for system, measuring apparatus, and environment – evolve according to the Schrödinger equation. It is mathematically impossible for such evolution to turn a coherent quantum superposition into an incoherent probabilistic sum. Although it is certainly true that the particular measurements one usually chooses to make display little or no quantum coherence, Bell argues that there is nothing “in principle” to stop us considering different types of measurements for which this will not be true. As Bell has said:

“So long as nothing, in principle, forbids consideration of such arbitrarily complicated observables, it is not permitted to speak of wave packet reduction. While for any given observable one can find a time for which the unwanted interference is as small as you like, for any given time one can find an observable for which it is as big as you do ‘not’ like.”

In Bell’s view, any mechanism for the collapse should also be applicable to small systems and should not be dependent on “the laws of large numbers.”  His second problem, concerned the actual measurement itself. Even if one accepts that decoherence reduces the problem to a probabilistic choice between outcomes, nowhere does decoherence say how any particular outcome is achieved. Bell did not disagree about the practicality of measurements in quantum mechanics, but he felt strongly that unless we know “exactly when and how it [wavefunction reduction] takes over from the Schrödinger equation, we do not have an exact and unambiguous formulation of our most fundamental physical theory.”