Are there quantum jumps?
Although Schrödinger eliminated the idea of a quantum jump from the
early quantum physics, they reappeared much later again in specific
circumstances, after experimental capabilities were advanced enough.
In quantum optics, one routinely observes and analyzes quantum jumps,
the most conspicuous experimental demonstrations of collapse. See, e.g.,
RG Hulet, DJ Wineland, JC Bergquist, WM Itano,
Precise test of quantum jump theory,
Phys. Rev. A 37, 4544 - 4547 (1988)
or
N Gisin, PL Knight, IC Percival, RC Thompson, and DC Wilson,
Quantum State Diffusion Theory and a Quantum Jump Experiment,
Journal of Modern Optics 40, 1663 (1993)
A much-cited paper is
(Martin Plenio is Director of the Institute of Theoretical Physics at
Ulm University. Peter Knight is a Past-President of the Optical
Society of America.)
The Lindblad equations, universally used to describe the dynamics of
(mixed) states of open systems have dissipative terms, which are the
leftover of collapse when averaged over the quantum jumps.
The 50 page paper
R. Hanson et al.,
Spins in few-electron quantum dots,
http://arxiv.org/abs/cond-mat/0610433
gives a good overview over methods to control single electron spins.
''The experiments show that one or two electrons can be trapped in a
quantum dot; that the spin of an individual electron can be put in a
superposition of up and down states; that two spins can be made to
interact and become entangled in a singlet or triplet state; and that
the result of such manipulation can be measured on individual spins.
Quantum jumps of single electrons can be seen, e.g., in FIG. 13.
The measured current jumps between that for the two states
''electron in the dot'' (a matastable state reachable by tunneling)
and ''no electron in the dot'', being essentially constant in between.
A derivation of quantum jump processes from unitary dynamics of a
bigger closed system is given in the paper
H. P. Breuer, F. Petruccione,
Stochastic dynamics of reduced wave functions and continuous
measurement in quantum optics,
Fortschritte der Physik 45, 39-78 (1997).
In particular, pp.53-58 of this paper describe a fairly elementary
derivation of a quantum jump process responsible for photodetection,
starting with the unitary dynamics and involving no collapse but only
standard approximations from statistical mechanics.
The quantum jump processes for general measurement situations are
derived from unitarity in the more technical papers [30-32] by Breuer
and Petruccione cited in the paper mentioned above. All four papers
can be downloaded from
Breuer's web site.
See also the following discussions at PhysicsForums:
Collapse from unitarity
Papers on quantum jumps
Arnold Neumaier (Arnold.Neumaier@univie.ac.at)
A theoretical physics FAQ