Bell trajectories for revealing quantum control mechanisms

Abstract

The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a "beable" formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution onto an ensemble of stochastic trajectories over a classical state space. Detailed mechanism identification is illustrated with a model 7-level system. A general procedure is presented to extract mechanism information directly from closed-loop control experiments. Application to simulated experimental data for the model system proves robust with up to 25% noise.

Controllability of wavepacket dynamics in coherently driven double-well potential

“…It is interesting that whether or not the short-time optimization of the delocalized state is well-controllable by the other control methods, for example, noniterative method and so on, proposed by some groups [14,16].…”

“…On the other hand, in the experimental realization of control of the chemical reactions and the optical molecular devices, a design of the control field based on optimal control theory (OCT), is also an important topic [9,10,11,12,13]. Recently, some methods to control the transition between quantum states have been proposed [14,15,16,17,18,19,20,21,22]. Our main interest is in the controllability between the quantum states in, what we call, a quantum chaos system [23,24].…”

Bell's jump process in discrete time

“…The same construction can be applied to the case |Q| > 2 if U involves only pairs of configurations, i.e., if there is a partition of Q into subsets, all of which are either pairs or singlets, such that P (q)UP (q ′ ) = 0 whenever q and q ′ do not belong to the same subset. Then (10) still satisfies (8) and thus defines a process. An example of this is a quantum computing circuit, realized through a time sequence of single qubit unitaries and CNOT gates.…”

“…In the particularly simple situation |Q| = 2, there does exist a time-discrete analog ( Qt ) t∈τ Z to Bell's process. In this case, the expression (10) satisfies (8) and thus defines a process; in fact, the net probability current between the two configurations q ′ and q is already determined by the distribution (3) and must be…”

Some Jump Processes in Quantum Field Theory

“…For studies of Bell's process we refer to [Sud87, Vin93, BD99, Col03a, Col03b, DGTZ03c, GT03], and for some numerical simulations and applications to [DR03,Den03]. We return to it in more detail in the next section.…”