Control of quantum phenomena: past, present and future

Abstract

Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. Among numerous theoretical insights and technological improvements that produced the present state-of-the-art in quantum control, there have been several breakthroughs of foremost importance. On the technology side, the current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. On the theory side, the two most critical insights were (i) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (ii) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control (AFC), which is a laboratory procedure employing measurement-driven, closed-loop optimization to identify the best shapes of femtosecond laser control pulses for steering quantum dynamics towards the desired objective. Optimization in AFC experiments is guided by a learning algorithm, with stochastic methods proving to be especially effective. AFC of quantum phenomena has found numerous applications in many areas of the physical and chemical sciences, and this paper reviews the extensive experiments. Other subjects discussed include quantum optimal control theory, quantum control landscapes, the role of theoretical control designs in experimental realizations and real-time quantum feedback control. The paper concludes with a perspective of open research directions that are likely to attract significant attention in the future.

Nonlinear and Nonequilibrium Dynamics of Quantum-Dot Optoelectronic Devices

“…A precondition for such effects is thus a sufficiently long lifetime of the microscopic polarization, i.e., a slow dephasing. Investigations of this topic are therefore often limited to systems at low temperature and with only few emitters [FRY93,SCU97,PHI01,BRI10], in order to keep the number of possible dephasing processes small [CHO03].…”

Quantum arithmetics via computation with minimized external control: The half-adder

“…Digital approaches are normally used in systems with a high degree of control, such as transmon-based superconducting systems [1] or ion traps [2], and have the advantage of enabling the use of error-correcting codes [3]. In digital computers, genuine quantum many-body effects are normally considered detrimental, and ideally one would like to switch on and off the interactions between pairs of constituents at will, e.g., via continuous control [4] on the system. However, spurious interactions (e.g., cross-talk) generally remain, because of either imperfect switching, imperfect isolation from the environment, or from the other qubits.…”

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

“…The goal of quantum control, then, is to find a control Hamiltonian H C (t) such that dynamical evolution over some time T accomplishes the desired transformation. For two-level systems (qubits) most aspects of this problem are well understood [1], but for systems with Hilbert space dimension d > 2 (qudits) questions remain regarding the design of control Hamiltonians [2] and the feasibility of robust implementation [3,4]. If the control task is simple or special symmetries are present, it is sometimes possible to find a high-performing control Hamiltonian through intuition, or to construct one using group theoretic methods [5].…”

“…A more general approach is provided by "optimal control," a well established procedure in which H C (t) is parameterized by a set of control variables, and a numerical search performed to optimize the fidelity with which the control objective is achieved [2]. The application of optimal control to quantum systems originated in NMR [1] and physical chemistry [2], and has expanded to include ultrafast physics [6], cold atoms [7,8], biomolecules [9], condensed matter spins [10], and superconducting circuits [11].…”

“…1d, from which we estimate "benchmark" fidelities F B = 0.982 (2) and F B = 0.971(1) for robust and non-robust control waveforms. Similar data yield fidelities F B = 0.984 (2) for unitary maps on the F (+) subspace, F B = 0.995 (1) for maps between randomly chosen 2-dimensional subspaces H i , H f , and F B = 0.995(1) for state maps, in all cases using robust waveforms. Note that the measured F B lie consistently below our design goal of ≥ 0.999, the more so for complex tasks requiring longer waveforms.…”