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Physical Review E

Multiphoton population transfer in systems violating the classical twist condition: A comparative study of separatrix crossing in phase space

Türker Topçu, F. Robicheaux

Published Apr 27, 2011• 3 citations
Publisher

Abstract

Population transfer in Hamiltonian systems, such as between Rydberg states of atoms and vibrational modes in diatomic molecules, has been both experimentally and theoretically demonstrated. All these systems have the property that the classical frequency of the motion changes monotonically with energy. Referred to as the twist condition, this property makes it possible to transfer population both by chirping a driving field within a ladder climbing scheme and by adiabatically chirping through a multiphoton resonance connecting two bound states. In this paper, we demonstrate that the latter method for population transfer can still be made to work in a system which violates the classical twist condition. We use classical rigid rotor as an example system where the frequency changes monotonically with energy and compare the responsible separatrix crossing mechanism in phase space to that in a system which exhibits an extremum in the frequency-energy profile. We perform both one-dimensional classical and quantum simulations and find that the quantum phase-space distribution mirrors its corresponding classical counterpart.

DOI
10.1103/physreve.83.046607

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Population transfer in Hamiltonian systems, such as between Rydberg states of atoms and vibrational modes in diatomic molecules, has been both experimentally and theoretically demonstrated. All these systems have the property that the classical frequency of the motion changes monotonically with energy. Referred to as the twist condition, this property makes it possible to transfer population both by chirping a driving field within a ladder climbing scheme and by adiabatically chirping through a multiphoton resonance connecting two bound states. In this paper, we demonstrate that the latter method for population transfer can still be made to work in a system which violates the classical twist condition. We use classical rigid rotor as an example system where the frequency changes monotonically with energy and compare the responsible separatrix crossing mechanism in phase space to that in a system which exhibits an extremum in the frequency-energy profile. We perform both one-dimensional classical and quantum simulations and find that the quantum phase-space distribution mirrors its corresponding classical counterpart.
Efficient population transfer by adiabatically chirping through a multiphoton resonance in microwave driven and kicked Rydberg atoms has recently been reported both experimentally and theoretically. Here we report on our simulations in which we have exploited this mechanism to vibrationally excite a diatomic molecule up to |ν = 4, J from the ground state by chirping through a four-photon resonance condition. This is an efficient means of population transfer, which is an alternative to the ladder climbing scheme requiring chirping through a sequence of states in the correct order. We discuss and compare one-dimensional quantum and classical models where there is no rotational degree of freedom. This comparison suggests that for the lowest laser intensity we consider, the process is classically forbidden and the transition occurs through tunnelling. We show that for larger peak intensities, the transfer can be looked upon as a classical transition in phase space, similar to that observed in the atomic case. We extend our simulations to fully three-dimensional quantum calculations and investigate the effect of coupling between different rotational pathways. We finally discuss the effect of thermal averaging over the initial J-states using a temperature for which the first few rotational levels inside the ν = 0 manifold are populated.
Following an experimental observation, a recent simulation has shown that efficient population transfer can be achieved through adiabatic chirping of a microwave pulse through a 10-photon resonance connecting two Rydberg states with n = 72, ℓ = 1 and n ∼ 82. These simulations have revealed that this population transfer is essentially a classical transition caused by separatrix crossing in the classical phase space. Here, we present the results of our fully three-dimensional quantum and classical simulations of coherent multiphoton population transfer in a kicked Li atom in a Rydberg state. We were able to achieve ∼76% population transfer from the 40p to 46p state in Li through a 6-photon resonance and contrast our results with those when the transition is driven by microwaves. We further discuss the case when the atom starts out from a Stark state in conjunction with the ℓ-distribution of the transferred population. We use a one-dimensional classical model to investigate the classical processes taking place in the phase space and find that the same separatrix crossing mechanism observed in microwave transitions is also responsible for the transition when the atom is kicked.
The population of atoms in Rydberg states is efficiently transferred with a change in principal quantum number nnn of up to ten via multiphoton adiabatic rapid passage through a single multiphoton resonance using a frequency-chirped microwave pulse. A quantum-mechanical picture of multiphoton adiabatic rapid passage in a one-dimensional atom using a Floquet approach provides a good description of most, but not all, of the observed phenomena.
Coherent interactions between light fields and simple quantum systems, such as $\ensuremath{\pi}$-pulses and adiabatic passage through frequency chirps and stimulated Raman interactions, generally use one- or two-photon processes. This limits the use of such interactions to energy scales close to the photon energy of the control field. However, recent calculations have shown that a 3-level system, generic to ionized diatomic molecules, shows such a strong multiphoton coupling that $\ensuremath{\pi}$-pulses are possible on at least 12-photon transitions. In this paper, we show that adiabatic transfer of population is also possible on such high-order multiphoton transitions. Full one-dimensional quantum mechanical two-electron calculations confirm this effect even in a system with many excited states and an ionization continuum.
Coherent population transfer in an atom using a sequence of adiabatic rapid passages through single-photon resonances is well-known, but it requires that the frequency sweep match the changing frequencies of the atomic transitions. The same population transfer can be effected via a single multiphoton adiabatic rapid passage, which requires only a small frequency sweep, if it is possible to select the desired multiphoton transition from the many possible transitions. Here we report the observation of population transfer between Rydberg states by high order multiphoton adiabatic rapid passage.
Enhanced population transfer from the lowest to the highest level in the three-state ladder 5s->5p->5d of the rubidium atom by frequency swept ultra short laser pulses is observed if the frequency sweep first makes the pulse resonant with the 5s->5p transition, and later with the 5p->5d transition. With this intuitive scheme it is possible to achieve complete population inversion via the intermediate level by two successive adiabatic passages. Complete inversion is also obtained by a {open_quote}counterintuitive{close_quote} direction of the frequency-sweep, in which case population of the intermediate level during the pulse is strongly reduced. The atomic system can be seen as a model system for multistep vibrational excitation in an anharmonic molecular potential.