Jump Time and Passage Time: The Duration ofs a Quantum Transition

Lawrence S. Schulman

Rong-Tao Qiu, Wu-Sheng Dai, Mi Xie

Lawrence S. Schulman

Under unitary evolution, systems move gradually from state to state. An unstable atom has amplitude in its original state after many lifetimes ($τ_L$). But in the laboratory, transitions seem to go instantaneously, as suggested by the term "quantum jump." The problem studied here is whether the "jump" can be assigned a duration, in theory and in experiment. Two characteristic times are defined, jump time ($τ_J$) and passage time ($τ_P$). Both use Zeno time, $τ_Z$, defined in terms of $H$ and its initial state as $τ_Z \equiv \hbar/\sqrt{}$, with $E_ψ\equiv $. $τ_J$ is defined in terms of the time needed to slow (à la the quantum Zeno effect) the decay: $τ_J \equiv τ_Z^2/τ_L$. It appears in several contexts. It is related to tunneling time in barrier penetration. Its inverse is the bandwidth of the Hamiltonian, in a time-energy uncertainty principle. $τ_J$ is also an indicator of the duration of the quadratic decay regime in both experiment and in numerical calculations (cf. Fig.~2 of PRA 57,1509 (1998).) The passage time, $τ_P$, arises from unitary evolution sans interpretation. It is based on a bound of Fleming (Nuov. Cim. 16 A, 232 (1973)): for any $H$ and $ψ$ a system cannot evolve to a state orthogonal to $ψ$ for $t< τ_P \equiv πτ_Z/2$. By including apparatus in $H$, $τ_P$ limits the observation of decay according to the quantum measurement ideas proposed in "Time's Arrows and Quantum Measurement," Cambridge U. Press, 1997, thereby allowing an experimental test of these ideas.

Jean-Luc Sauvageot

Lawrence S. Schulman

Experimental observations of `quantum jumps' suggest that one can associate a timescale shorter than `lifetime' with quantum transitions; one such `jump time' is proposed here. We also find that experimental temporal localization of the jump does affect it (a lá Bohr), and predict an `observational line broadening'.

Mathias Alexander Seidler, Ricardo Guti\'errez-J\'auregui, Alessandro Cer\`e +2 more

We present a method to estimate the time scale of quantum jumps from the time correlation of photon pairs generated from a cascade decay in an atomic system, and realize it experimentally in a cold cloud of 87Rb. Taking into account the photodetector response, we find an upper bound for the duration of a quantum jump of 21+/-11 ps.