Optimal dynamic discrimination of similar quantum systems with time series data

A moment-based Kalman filtering approach for estimation in ensemble systems

A persistent challenge in tasks involving large-scale dynamical systems, such as state estimation and error reduction, revolves around processing the collected measurements. Frequently, these data suffer from the curse of dimensionality, leading to increased computational demands in data processing methodologies. Recent scholarly investigations have underscored the utility of delineating collective states and dynamics via moment-based representations. These representations serve as a form of sufficient statistics for encapsulating collective characteristics, while simultaneously permitting the retrieval of individual data points. In this paper, we reshape the Kalman filter methodology, aiming its application in the moment domain of an ensemble system and developing the basis for moment ensemble noise filtering. The moment system is defined with respect to the normalized Legendre polynomials, and it is shown that its orthogonal basis structure introduces unique benefits for the application of Kalman filter for both i.i.d. and universal Gaussian disturbances. The proposed method thrives from the reduction in problem dimension, which is unbounded within the state-space representation, and can achieve significantly smaller values when converted to the truncated moment-space. Furthermore, the robustness of moment data toward outliers and localized inaccuracies is an additional positive aspect of this approach. The methodology is applied for an ensemble of harmonic oscillators and units following aircraft dynamics, with results showcasing a reduction in both cumulative absolute error and covariance with reduced calculation cost due to the realization of operations within the moment framework conceived.

Optical Indistinguishability via Twinning Fields

Here we introduce the concept of the twinning field-a driving electromagnetic pulse that induces an identical optical response from two distinct materials. We show that for a large class of pairs of generic many-body systems, a twinning field which renders the systems optically indistinguishable exists. The conditions under which this field exists are derived, and this analysis is supplemented by numerical calculations of twinning fields for both the 1D Fermi-Hubbard model, and tight-binding models of graphene and hexagonal boron nitride. The existence of twinning fields may lead to new research directions in nonlinear optics, materials science, and quantum technologies.

Quantum Ensemble Classification: A Sampling-Based Learning Control Approach

Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.

Coherent manipulation of free amino acids fluorescence

Coherent manipulation of molecular wavepackets in biomolecules might contribute to the quest towards label-free cellular imaging and protein identification. We report the use of optimally tailored UV laser pulses in pump-probe depletion experiments that selectively enhance or decrease fluorescence between two aromatic amino acids: tryptophan (Trp) and tyrosine (Tyr). Selective fluorescence modulation is achieved with a contrast of ~35%. A neat modification of the time-dependent fluorescence depletion signal of Trp is observed, while the Tyr transient trace remains unchanged. The mechanism invoked for explaining the change of the depletion of Trp is a less efficient coupling between the fluorescing state and the higher non-radiative excited states by the optimally shaped pulse, than by the reference pulse.

Attaining persistent field-free control of open and closed quantum systems

Persistent quantum control (PQC) aims to maintain an observable objective value over a period of time following the action of an applied field. This paper assesses the feasibility of achieving PQC for arbitrary finite-level systems and observables. The analysis is carried out independent of the particular method used for state preparation. The PQC behavior is optimized over the set of physically accessible prepared states for both open and closed systems. The quality of observable value persistence in the postcontrol period was found to vary with the required duration of persistence, the system temperature, the chosen observable operator, and the energy levels of the system. The alignment of a rigid diatomic rotor is studied as a model system. The theoretical estimates of PQC behavior are encouraging and suggest feasible exploration in the laboratory using currently available technology.

How shaped light discriminates nearly identical biochromophores

We present a general mechanism for successful discrimination of spectroscopically indistinguishable biochromophores by shaped light. For this purpose we use nonadiabatic dynamics in excited electronic states in the frame of the field-induced surface hopping method driven by the experimentally shaped laser fields. Our findings show that optimal laser fields drive low-frequency vibrational modes localized in the side chains of two biochromophores, thus selecting the parts of their potential energy surfaces characterized by different transition dipole moments leading to different ionization probabilities. The presented mechanism leads to selective fluorescence depletion which serves as a discrimination signal. Our findings offer a promising perspective for using optimally shaped laser pulses in bioanalytical applications by increasing the selectivity beyond the current capability.

Quantum control study of multilevel effect on ultrafast isotope-selective vibrational excitations

Quantum optimal control calculations have been carried out for isotope-selective vibrational excitations of the cesium iodide (CsI) molecule on the ground-state potential energy curve. Considering a gaseous isotopic mixture of (133)CsI and (135)CsI, the initial state is set to the condition that both (133)CsI and (135)CsI are in the vibrational ground level (v=0) and the target state is that (133)CsI is in the v=0 level while (135)CsI in the first-excited level (v=1). We find that, using the density-matrix formalism, perfect isotope-selective excitations for multilevel systems including more than ten lowest vibrational states can be completed in much shorter time scales than those for two-level systems. It is likely that this multilevel effect comes from the large isotope shifts in the vibrational levels of v>1. To check the reliability of the calculation we also carry out optimal control calculations based on the conventional wave-packet formalism, where the wave-function amplitude is temporally propagated on the grid points in real space, and obtain almost the same results as those with the density-matrix formalism.

Identification of biological microparticles using ultrafast depletion spectroscopy

We show how an ultrafast pump-pump excitation induces strong fluorescence depletion in biological samples, such as bacteria-containing droplets, in contrast with fluorescent interferents, such as polycyclic aromatic compounds, despite similar spectroscopic properties. Application to the optical remote discrimination of biotic versus non-biotic particles is proposed. Further improvement is required to allow the discrimination of one pathogenic among other non-pathogenic micro-organisms. This improved selectivity may be reached with optimal coherent control experiments, as discussed in the paper.

Pulse shaping for optimal control of molecular processes

In this paper, a new method is proposed to design optimized control fields with desired temporal and/or spectral properties. The method is based on penalizing the difference between an optimized field obtained from an iterative scheme and a reference field with desired temporal and/or spectral properties. Compared with the standard optimal control theory, the current method allows a simple, experimentally accessible field be found on the fly; while compared with parameter space searching optimization, the iterative nature of this method allows automatic exploration of the intrinsic mechanism of the population transfer. The method is illustrated by examing the optimal control of vibrational excitation of the Cl-O bond with both temporally and spectrally restricted pulses.

Optimal dynamic discrimination of similara quantum systems in the presence of decoherence

Optimal dynamic discrimination (ODD) of a mixture of similar quantum systems with time series signals enables the extraction of the associated concentrations with reasonable levels of laser-pulse noise, signal detection errors, and imperfect signal detector resolution [Li et al., J. Chem. Phys. 122, 154103 (2005)]. The ODD paradigm is reexpressed in the density-matrix formulation to allow for the consideration of environmental decoherence on the quality of the extracted concentrations, along with the above listed factors. Simulations show that although starting in a thermally mixed state along with decoherence can be detrimental to discrimination, these effects can be counteracted by seeking a suitable optimal control pulse. Additional sampling of the temporal data also aids in extracting more information to better implement ODD.