What exactly is the experiment setup? What are you measuring?

There are no quantum jumps as such: when a system is in an eigenstate of the underlying time-independent Hamiltonian, theoretically it will remain in that state for ever. Transitions are caused by external agents, not taken into account as being part of the latter Hamiltonian. Take the ubiquitous electromagnetic field (the so-called vacuum fluctuations), which can cause transition -- the field being external, the eigenstate under observation cannot be an eigenstate of the total Hamiltonian, that is the Hamiltonian we considered as describing our system of interest plus the Hamiltonian we considered as being external to this system. In a solid, for instance, we have in addition ionic vibrations (phonons), which again precipitate transition between electronic eigenstates. It should also be taken into account that spectral broadening that we observe comes about by the agency of the limited instrumental / experimental resolution, in addition to the above-mentioned interaction with external fields. Limited experimental resolution is very relevant in the cases where eigen-energies of  interest are dense whereby one's observation is not of a specific eigenstate, but of a superposition of all eigenstates whose energies fall into one's energetic window of observation; such superposition not being an eigenstate, the observed dynamical behaviour deviates from what one expects of pure eigenstates. It should also be noted that experimentally one almost never, if at all, prepares a system in an eigenstate of the underlying Hamiltonian; what one has is always a superposition of eigenstates. Therefore in dealing with the dynamical behaviour of systems, theoretically one should consider the relevant density matrices, which, depending on the particular initial condition one imposes on them, take appropriate account of all eigenstates of the system under consideration.

In the light of the above discussion, it is interesting to note that one of the main ingredients of the celebrated Fermi's Golden Rule for transition rates is that either the initial state or the final state or both must be part of a continuum of states (the energy of the relevant state, or states, must be in a spectral continuum).

Note added: Effects of temperature must also be taken into account, since at any non-vanishing temperature what one measures is not the property of a single eigenstate, but of a thermal ensemble of states. Of course, to specify temperature one needs to introduce a heat bath, and thermal equilibrium between the system of interest and the heat bath is established through interaction of the two systems. To take precise account of the dynamics of the system of interest, this interaction should be appropriately taken into account.

Quantum jumps represent the collapse of the wave function due to a measurement.  The time taken depends on the type of measurement.  For a particular case in which quantum jumps have been observed, the time taken for the collapse has been calculated (see Pegg, D. T. 1991 "Wavefunction collapse time" Phys. Lett. A vol. 153, pp 263-264).

Remi Cornwall - let me know your email address and I shall email you a reprint.

David, could I please have a reprint too ? 

[email protected]

Many thanks

Dear David, 

If it takes finite time does this mean that it is described as a transition with continuous dynamics of the wave function(or the dynamics of operator if you use Heisenberg picture)

I would like to say

The time taken depends on the type of measurement.  It is the time needed to acquire sufficient information to determine the final state.  In some cases where this time is finite it might be possible to determine how the state changes with time but in general this would not be a unitary evolution.

There is no instantaneous jumps.  The time evolution of the wave function during the transition is continuous.  However to understand it's dynamics one needs the effect of the source field(radiation reaction)

David Pegg: I would also like a copy of your article

[email protected]

David Pegg: Would you be so kind as to send me a copy of your article?

[email protected]

Thank you very much in advance,

Algis

Dear Carringtone,

Researchers so far have not found any feature on the basis they can prove that jump is instantaneous.

Quantum jumps are not truly instantaneous and random.

Experimental result shows that while quantum jumps are unpredictable and discrete (as Bohr thought) on long timescales, they can be continuous (as Schrodinger suggested) and predictable on a short time scale,” says Devoret.

According to the Yale team, this is an important point: “while quantum jumps appear discrete and random in the long run, reversing a quantum jump means the evolution of the quantum state possesses, in part, a deterministic and non-random character,” say Devoret and Minev. “The jump always occurs in the same, predictable manner from its random starting point.”

“The findings are in complete agreement with the predictions of modern quantum trajectory theory,” Devoret tells Physics World, “with essentially no adjustable parameters. There is no instantaneous jump.

Hope it work out for you.

Ashish