Laser-induced Population Transfer Research Articles

Subfemtosecond-resolved modulation of superfluorescence from ionized nitrogen molecules by 800-nm femtosecond laser pulses.

Superfluorescence emission around 391 nm is generated when nitrogen molecules are irradiated by a strong 800-nm pump laser and a delayed seed laser. The emission corresponds to the transition between N2+(B2Σu+,ν″=0) and N2+(X2Σg+,ν=0). When another weak 800-nm probe laser is injected and scanned after the pump laser, the superfluorescence intensity is observed to exhibit periodical modulation. The period is determined to be ~2.63 fs, corresponding to the transition frequency between N2+(A2Πu,ν'=2) and N2+(X2Σg+,ν=0). Based on theoretical derivation, these observations can be attributed to the laser-induced population transfer and polarization variation between the relevant electronic states of ionized nitrogen molecules.

Non-integrability of the optimal control problem for n-level quantum systems

We study the problem of optimal laser-induced population transfer in n-level quantum systems. This problem can be represented as an energy-optimal control problem, related to a sub-Riemannian problem on , and it is known (Boscain, Chambrion, Charlot, Gauthier) that for n = 2 and n = 3 the Hamiltonian system associated with the Pontryagin Maximum Principle PMP is integrable. We will show that this changes completely for . Specifically, for n = 4, we will prove that the adjoint equation of the PMP does not possess any meromorphic first integral independent of the Hamiltonian on the levels of the Casimir functions. This implies that the system is not B-integrable for any . In proving our nonintegrability results we will use differential Galois theory.

IR-induced conformational isomerization of a helical peptide in a cold ion trap

In this work, we use laser-induced population transfer techniques to study the conformational isomerization of a helical peptide, Ac-Phe-(Ala)5-LysH(+), in a cold ion trap. In one scheme, called IR-UV hole-filling spectroscopy, a single conformation is selectively excited with an IR pump laser via a distinct NH stretch vibration. After giving the vibrationally excited ions sufficient time to isomerize and re-cool in the trap, the new conformational redistribution is detected by UV photofragment spectroscopy. While we clearly observe a redistribution of the conformer populations due to isomerization, only those conformations that initially have population participate in this redistribution-we do not form conformers that were not initially present in the trap. In a second scheme, called IR-induced population transfer spectroscopy, we determine the fractional populations of the four stable conformations of Ac-Phe-(Ala)5-LysH(+) by scanning the IR laser while selectively detecting a specific conformation using UV photofragment spectroscopy.

Infrared laser induced population transfer and parity selection in (14)NH3: A proof of principle experiment towards detecting parity violation in chiral molecules.

We have set up an experiment for the efficient population transfer by a sequential two photon-absorption and stimulated emission-process in a molecular beam to prepare quantum states of well defined parity and their subsequent sensitive detection. This provides a proof of principle for an experiment which would allow for parity selection and measurement of the time evolution of parity in chiral molecules, resulting in a measurement of the parity violating energy difference ΔpvE between enantiomers of chiral molecules. Here, we present first results on a simple achiral molecule demonstrating efficient population transfer (about 80% on the average for each step) and unperturbed persistence of a selected excited parity level over flight times of about 1.3 ms in the beam. In agreement with model calculations with and without including nuclear hyperfine structure, efficient population transfer can be achieved by a rather simple implementation of the rapid adiabatic passage method of Reuss and coworkers and considering also the stimulated Raman adiabatic passage technique of Bergmann and coworkers as an alternative. The preparation step uses two powerful single mode continuous wave optical parametric oscillators of high frequency stability and accuracy. The detection uses a sensitive resonantly enhanced multiphoton ionization method after free flight lengths of up to 0.8 m in the molecular beam. Using this technique, we were able to also resolve the nuclear hyperfine structure in the rovibrational levels of the ν1 and ν3 fundamentals as well as the 2ν4 overtone of (14)NH3, for which no previous data with hyperfine resolution were available. We present our new results on the quadrupole coupling constants for the ν1, ν3, and 2ν4 levels in the context of previously known data for ν2 and its overtone, as well as ν4, and the ground state. Thus, now, (14)N quadrupole coupling constants for all fundamentals and some overtones of (14)NH3 are known and can be used for further theoretical analysis.

Wavepacket Dynamics of the Axially Chiral Molecule Cl-O-O-Cl under Coherent Radiative Excitation and Including Electroweak Parity Violation.

We report detailed calculations of the quantum wavepacket dynamics of Cl-O-O-Cl, which serves as a prototype molecule for the stereomutation dynamics of an axially chiral molecule. We include the effects both from electroweak parity violation and from the interaction with a coherent monochromatic laser field. We use the quasiadiabatic channel reaction path Hamiltonian approach to approximately solve the six-dimensional Schrödinger equation describing the vibrational motion, including rotation by an effective Hamiltonian. We calculate time-dependent wave functions based on the time-dependent Schrödinger equation. We study stereomutation dynamics due to tunneling motion and laser-induced population transfer and show results on efficient methods for selectively populating single molecular states in chiral molecules by frequency-modulated laser pulses. We also discuss laser-induced stereomutation (LISM) and a process that may be called resonance Raman induced stereomutation (RRISM). The results are discussed in relation to current experimental attempts to measure the parity violating energy difference ΔpvE between the enantiomers of chiral molecules. Furthermore, we show detailed quantitative simulations of a selection of well-defined parity levels in chiral molecules ("parity isomers") that form the basis of a possible measurement of ΔpvE by the time evolution of parity.

Trigonometric pulse envelopes for laser-induced quantum dynamics

We relate powers of trigonometric functions to Gaussians by proving that properly truncated cosn functions converge to a Gaussian as n tends to infinity. For an application, we analyse the laser-induced population transfer |X1Σ+⟩ → |A1Πx⟩ in a two-level model system of aluminium monochloride (AlCl) with fixed nuclei. We apply linearly x-polarized ultraviolet laser pulses with a trigonometric envelope function, whose square has full width at half-maximum of 2.5 fs and 5.0 fs. Studying population dynamics and optimized laser parameters, we find that the optimal field amplitude for trigonometric pulses with n = 20 and n = 1000 has a relative difference of 1%, which is below experimental resolution.

Attosecond Control of Electron Dynamics in Carbon Monoxide

Laser pulses with stable electric field waveforms establish the opportunity to achieve coherent control on attosecond time scales. We present experimental and theoretical results on the steering of electronic motion in a multielectron system. A very high degree of light-waveform control over the directional emission of C(+) and O(+) fragments from the dissociative ionization of CO was observed. Ab initio based model calculations reveal contributions to the control related to the ionization and laser-induced population transfer between excited electronic states of CO(+) during dissociation.

Local control of population transfer in molecules under fluctuating perturbations

We investigate the laser induced population transfer between electronic states of Na 2 molecules which are subject to additional perturbations by an environment. In a former paper [S. Gräfe, M. Erdmann, V. Engel, Phys. Rev. A 72 (2005) 013404] it was shown that within the formalism of Local Control Theory, laser fields can be constructed which are able to selectively transfer population from the electronic ground to a target excited electronic state. Here, we address the question in how far the efficiency of the control process is influenced by additional perturbations. Therefore, we employ a stochastic Schrödinger equation including a fluctuation-term in the Hamiltonian.

The role of phases and their interplay in molecular vibrational quantum computing with multiple qubits

Within the scope of molecular quantum computing with vibrational qubits, we analyse the impact of phases that are present during the quantum computation processes. While the phase relation in superposition states and its temporal evolution are crucial to any implementation of quantum computing, we elucidate the special challenge that emerges for phase control of qubits encoded in molecular vibrational eigenstates. Phase correctly prepared superposition states in general exist only for a finite time and with the inherent entanglement in molecular vibrational qubit systems their development displays a complex pattern. We show that the free relative phase evolution in such qubit systems can be utilized for the implementation of quantum phase gates. Moreover, a practical experimental realization of phase correct quantum gates acting on molecular vibrational qubits could be accomplished by a decomposition into laser-induced population transfer and free evolution phase gates. This concept adds to the flexibility in the implementation of quantum gate sequences and algorithms. A modification, where only a reduced number of selected relative phases needs to be adjusted, will make this scheme more robust and versatile. Finally, we also disclose and discuss another key feature for the implementation of phase correct quantum gates, i.e. the dependence of the quantum gate fidelity on the absolute or carrier-envelope phase of the driving femtosecond laserfield.

Rotational averaging and optimization of laser-induced population transfer in molecules

The dynamics of a molecule subject to a short laser pulse is investigated, with focus on the averaging over initial rotational states and on the optimization of laser parameters for the efficient population transfer between vibrational and electronic states. A relation is established between final-state populations obtained with a fixed orientation and those based on a full treatment of the rotational degrees of freedom. In the short-pulse approximation, rotational averaging amounts to integrating the fixed molecule results over all orientations. The theory is applied to a variety of model systems and verified with numerical calculations using Gaussian pulses. We calculate target state populations with three procedures, optimizing the laser pulse for a fixed orientation without orientational averaging, averaging without changing the laser parameters, and reoptimizing the parameters after averaging. The analysis of the two-level system provides a reference for the order of magnitude of the effects of averaging. The three-level system brings out the relevant role of the geometry of polarization vectors and transition dipoles. The multiphoton excitation of a Morse oscillator shows the importance of taking into account the dependence of resonance frequencies on the laser intensity. Within a proton transfer model we discuss the results obtained with and without chirping and we show that "optimizing after averaging" can be as effective as choosing a more refined pulse shape.

Resonance of minimizers forn-level quantum systems with an arbitrary cost

We consider an optimal control problem describing a laser-induced population transfer on a n-level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for n=2 and n=3): instead of looking for minimizers on the sphere one is reduced to look just for minimizers on the sphere . Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer.

Optimal Control on a N-Level Quantum System

We apply techniques of subriemannian geometry on Lie groups to laser-induced population transfer in a n-level quantum system. The aim is to induce transitions by n-1 laser pulses, of arbitrary shape and frequency, minimizing the pulse energy. For n = 3, we prove that the Hamiltonian system given by the Pontryagin Maximum Principle is completely integrable, since this problem can be stated as a "k ⊕ p problem" on a simple Lie group. Optimal trajectories and controls are exhausted. The main result is that optimal controls correspond to lasers that are "in resonance". For n ≥ 4 the integrability of the Hamiltonian system given by the Pontryagin Maximum Principle is an open question, but is possible to prove that optimal trajectories are still in resonance even without finding the explicit expressions for trajectories and controls. The amplitude of optimal controls is computed numerically for n = 4

Optimal control in laser-induced population transfer for two- and three-level quantum systems

We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two- and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the well-known technique of “π-pulse transfer” in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the “π-pulse transfer.” This geometrical picture also allows one to analyze the population transfer by adiabatic passage.

On the K + P Problem for a Three-Level Quantum System: Optimality Implies Resonance

We apply techniques of subriemannian geometry on Lie groups to laser-induced population transfer in a three-level quantum system. The aim is to induce transitions by two laser pulses, of arbitrary shape and frequency, minimizing the pulse energy. We prove that the Hamiltonian system given by the Pontryagin maximum principle is completely integrable, since this problem can be stated as a “k ⊕ p problem” on a simple Lie group. Optimal trajectories and controls are exhausted. The main result is that optimal controls correspond to lasers that are “in resonance”.

Laser-induced population transfer in multistate systems: A comparative study.

We examine similarities and differences in three schemes that are capable of producing complete population transfer in multistate systems: generalized \ensuremath{\pi} pulses, adiabatic passage by pulse chirping, and counterintuitive pulses or stimulated Raman adiabatic passage. We use the picture of adiabatic following through avoided crossings of instantaneous eigenvalues to exhibit the essential differences between the latter two procedures.