Christiane P. Koch

Stabilization of ultracold molecules using optimal control theory

In recent experiments on ultracold matter, molecules have been produced from ultracold atoms by photoassociation, Feshbach resonances, and three-body recombination. The created molecules are translationally cold, but vibrationally highly excited. This will eventually lead them to be lost from the trap due to collisions. We propose shaped laser pulses to transfer these highly excited molecules to their ground vibrational level. Optimal control theory is employed to find the light field that will carry out this task with minimum intensity. We present results for the sodium dimer. The final target can be reached to within 99% provided the initial guess field is physically motivated. We find that the optimal fields contain the transition frequencies required by a good Franck-Condon pumping scheme. The analysis identifies the ranges of intensity and pulse duration which are able to achieve this task before any other competing processes take place. Such a scheme could produce stable ultracold molecular samples or even stable molecular Bose-Einstein condensates.

A complete quantum description of an ultrafast pump-probe charge transfer event in condensed phase

An ultrafast photoinduced charge transfer event in condensed phase is simulated. The interaction with the field is treated explicitly within a time-dependent framework. The description of the interaction of the system with its environment is based on the surrogate Hamiltonian method where the infinite number of degrees of freedom of the environment is approximated by a finite set of two-level modes for a limited time. This method is well suited to ultrafast events, since it is not limited by weak coupling between system and environment. Moreover, the influence of the external field on the system-bath coupling is included naturally. The surrogate Hamiltonian method is generalized to incorporate two electronic states including all possible system-bath interactions. The method is applied to a description of a pump-probe experiment where every step of the cycle is treated consistently. Dynamical variables are considered which go beyond rates of charge transfer such as the transient absorption spectrum. The pa...

Making ultracold molecules in a two-color pump-dump photoassociation scheme using chirped pulses

This theoretical paper investigates the formation of ground state molecules from ultracold cesium atoms in a two-color scheme. Following previous work on photoassociation with chirped picosecond pulses [Luc-Koenig et al., Phys. Rev. A, 70, 033414 (2004)], we investigate stabilization by a second (dump) pulse. By appropriately choosing the dump pulse parameters and time delay with respect to the photoassociation pulse, we show that a large number of deeply bound molecules are created in the ground triplet state. We discuss (i) broad-bandwidth dump pulses which maximize the probability to form molecules while creating a broad vibrational distribution as well as (ii) narrow-bandwidth pulses populating a single vibrational ground state level, bound by 113 cm{sup -1}. The use of chirped pulses makes the two-color scheme robust, simple, and efficient.

Dissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin and harmonic baths

The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the surrogate Hamiltonian approach. This method is based on constructing a system-bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results are compared to calculations that include a finite number of harmonic modes carried out by using the multiconfiguration time-dependent Hartree method of Nest and Meyer [J. Chem. Phys. 119, 24 (2003)]. In the weak coupling regime, at zero temperature and for small excitations of the primary system, both methods converge to the Markovian limit. When initially the primary system is significantly excited, the spin bath can saturate restricting the energy acceptance. An interaction term between bath modes that spreads the excitation eliminates the saturation. The loss of phase between two cat states has been analyzed and the results for the spin and harmonic baths are almost identical. For stronger couplings, the dynamics induced by the two types of baths deviate. The accumulation and degree of entanglement between the bath modes have been characterized. Only in the spin bath the dynamics generate entanglement between the bath modes.

Surrogate Hamiltonian study of electronic relaxation in the femtosecond laser induced desorption of NO/NiO(100)

A microscopic model for electronic quenching in the photodesorption of NO from NiO(100) is developed. The quenching is caused by the interaction of the excited adsorbate–substrate complex with electron hole pairs (O 2p→Ni 3d states) in the surface. The electron hole pairs are described as a bath of two level systems which are characterized by an excitation energy and a dipole charge. The parameters are connected to estimates from photoemission spectroscopy and configuration interaction calculations. Due to the localized electronic structure of NiO a direct optical excitation mechanism can be assumed, and a reliable potential energy surface for the excited state is available. Thus a treatment of all steps in the photodesorption event from first principles becomes possible for the first time. The surrogate Hamiltonian method, which allows one to monitor convergence, is employed to calculate the desorption dynamics. Desorption probabilities of the right order of magnitude and velocities in the experimentally...

Protecting coherence in optimal control theory: State-dependent constraint approach

Optimal control theory is developed for the task of obtaining an objective in a subspace of the Hilbert space while avoiding population transfer to other subspaces. The objective, a state-to-state transition or a unitary transformation, is carried out without loss of coherence, provided the system in the allowed subspace is decoupled from its environment. An optimization functional is introduced that leads to monotonic convergence of the algorithm. This approach becomes necessary for molecular systems which are subject to processes implying loss of coherence such as ionization or predissociation. In the subspaces corresponding to lossy channels, controllability is hampered or even completely lost. A functional constraint that depends on the state of the system at each instant in time keeps the system out of the lossy channels. We outline the resulting algorithm and discuss its convergence properties. The functionality of the algorithm is demonstrated for the examples of a state-to-state transition and of a unitary transformation for a model of cold Rb2.

Short-pulse photoassociation in rubidium below the D1 line

Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the 5S +5 P1/2 asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range 1 / R 3 potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the 0 u states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.

Stimulating the production of deeply bound RbCs molecules with laser pulses: the role of spin?orbit coupling in forming ultracold molecules

We investigate the possibility of forming deeply bound ultracold RbCs molecules by a two-color photoassociation experiment. We compare the results with those for Rb2 in order to understand the characteristic differences between heteronuclear and homonuclear molecules. The major differences arise from the different long-range potential for excited states. Ultracold 85Rb and 133Cs atoms colliding on the X 1Σ+ potential curve are initially photoassociated to form excited RbCs molecules in the region below the Rb(5S)+Cs(6P1/2) asymptote. We explore the nature of the Ω=0+ levels in this region, which have mixed A 1Σ+ and b 3Π character. We then study the quantum dynamics of RbCs by a time-dependent wavepacket (TDWP) approach. A wavepacket is formed by exciting a few vibronic levels and is allowed to propagate on the coupled electronic potential energy curves. We calculate the time dependence of the overlap between the wavepacket and ground-state vibrational levels. For a detuning of 7.5 cm−1 from the atomic line, the wavepacket for RbCs reaches the short-range region in about 13 ps, which is significantly faster than for the homonuclear Rb2 system; this is mostly because of the absence of an R−3 long-range tail in the excited-state potential curves for heteronuclear systems. We give a simple semiclassical formula that relates the time taken to the long-range potential parameters. For RbCs, in contrast to Rb2, the excited-state wavepacket shows a substantial peak in singlet density near the inner turning point, and this produces a significant probability of de-excitation to form ground-state molecules bound by up to 1500 cm−1. The short-range peak depends strongly on non-adiabatic coupling and is reduced if the strength of the spin–orbit coupling is increased. Our analysis of the role of spin–orbit coupling concerns the character of the mixed states in general and is important for both photoassociation and stimulated Raman de-excitation.

A Chebychev propagator for inhomogeneous Schrödinger equations

A propagation scheme for time-dependent inhomogeneous Schrödinger equations is presented. Such equations occur in time dependent optimal control theory and in reactive scattering. A formal solution based on a polynomial expansion of the inhomogeneous term is derived. It is subjected to an approximation in terms of Chebychev polynomials. Different variants for the inhomogeneous propagator are demonstrated and applied to two examples from optimal control theory. Convergence behavior and numerical efficiency are analyzed.

A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians

A propagation method for time-dependent Schrodinger equations with an explicitly time-dependent Hamiltonian is developed where time ordering is achieved iteratively. The explicit time dependence of the time-dependent Schrodinger equation is rewritten as an inhomogeneous term. At each step of the iteration, the resulting inhomogeneous Schrodinger equation is solved with the Chebychev propagation scheme presented in the work of M. Ndong et al. [J. Chem. Phys. 130, 124108 (2009)]. The iteratively time-ordering Chebychev propagator is shown to be robust, efficient, and accurate and compares very favorably with all other available propagation schemes.