Complete controllability of finite-level quantum systems

Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we investigate the question of complete controllability for finite-level quantum systems subject to a single control field, for which the interaction is of dipole form. Sufficient criteria for complete controllability of a wide range of finite-level quantum systems are established and the question of limits of complete controllability is addressed. Finally, the results are applied to give a classification of complete controllability for four-level systems.Comment: 14 pages, IoP-LaTe

Control of non-controllable quantum systems: A quantum control algorithm based on Grover iteration

A new notion of controllability, eigenstate controllability, is defined for finite-dimensional bilinear quantum mechanical systems which are neither strongly completely controllably nor completely controllable. And a quantum control algorithm based on Grover iteration is designed to perform a quantum control task of steering a system, which is eigenstate controllable but may not be (strongly) completely controllable, from an arbitrary state to a target state.Comment: 7 pages, no figures, submitte

Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group U(N) and the results of a few control computations are discussed briefly.Comment: 5 pages, orginal June 30, 2000, revised September 28, 200

Degrees of controllability for quantum systems and applications to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio

Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography

We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy data. Here we show how to generalize this approach to systems with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the process for a range of three-level quantum systems. The results suggest that the Bayesian estimation of the frequencies and dephasing rates is generally highly accurate and the main source of errors are errors in the reconstructed Hamiltonian basis.Comment: 6 pages, 3 figure

On the Contractivity of Hilbert-Schmidt distance under open system dynamics

We show that the Hilbert-Schmidt distance, unlike the trace distance, between quantum states is generally not monotonic for open quantum systems subject to Lindblad semigroup dynamics. Sufficient conditions for contractivity of the Hilbert-Schmidt norm in terms of the dissipation generators are given. Although these conditions are not necessary, simulations suggest that non-contractivity is the typical case, i.e., that systems for which the Hilbert-Schmidt distance between quantum states is monotonically decreasing form only a small set of all possible dissipative systems for N>2, in contrast to the case N=2 where the Hilbert-Schmidt distance is always monotonically decreasing.Comment: Major revision. We would particularly like to thank D Perez-Garcia for constructive feedbac

Experimental Hamiltonian Identification for Qubits subject to Multiple Independent Control Mechanisms

We consider a qubit subject to various independent control mechanisms and present a general strategy to identify both the internal Hamiltonian and the interaction Hamiltonian for each control mechanism, relying only on a single, fixed readout process such as $\sigma_z$ measurements.Comment: submitted to Proceedings of the QCMC04 (4 pages RevTeX, 5 figures

NuSTAR hard X-ray data and Gemini 3D spectra reveal powerful AGN and outflow histories in two low-redshift Lyman-α\alpha blobs

We have shown that Lyman-$\alpha$ blobs (LABs) may still exist even at $z\sim0.3$, about 7 billion years later than most other LABs known (Schirmer et al. 2016). Their luminous Ly$\alpha$ and [OIII] emitters at $z\sim0.3$ offer new insights into the ionization mechanism. This paper focuses on the two X-ray brightest LABs at $z\sim0.3$, SDSS J0113$+$0106 (J0113) and SDSS J1155$-$0147 (J1155), comparable in size and luminosity to `B1', one of the best-studied LABs at $z \gtrsim$ 2. Our NuSTAR hard X-ray (3--30 keV) observations reveal powerful active galactic nuclei (AGN) with $L_{2-10{\;\rm keV}}=(0.5$--$3)\times10^{44}$ erg cm$^{-2}$ s$^{-1}$. J0113 also faded by a factor of $\sim 5$ between 2014 and 2016, emphasizing that variable AGN may cause apparent ionization deficits in LABs. Joint spectral analyses including Chandra data constrain column densities of $N_{\rm H}=5.1^{+3.1}_{-3.3}\times10^{23}$ cm$^{-2}$ (J0113) and $N_{\rm H}=6.0^{+1.4}_{-1.1}\times10^{22}$ cm$^{-2}$ (J1155). J0113 is likely buried in a torus with a narrow ionization cone, but ionizing radiation is also leaking in other directions as revealed by our Gemini/GMOS 3D spectroscopy. The latter shows a bipolar outflow over $10$ kpc, with a peculiar velocity profile that is best explained by AGN flickering. X-ray analysis of J1155 reveals a weakly absorbed AGN that may ionize over a wide solid angle, consistent with our 3D spectra. Extinction corrected [OIII] log-luminosities are high, $\sim43.6$. The velocity dispersions are low, $\sim100$--$150$ km s$^{-1}$, even at the AGN positions. We argue that this is a combination of high extinction hiding the turbulent gas, and previous outflows that have cleared the escape paths for their successors.Comment: 15 pages, 17 Figures, accepted for publication in Ap