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Physical Review A

Complete adiabatic passage to arbitrarily sculpted superposition states

Petr Král, Moshe Shapiro

Published Apr 10, 2002• 14 citations
Publisher

Abstract

We introduce the ``shaped-adiabatic-passage'' method that allows one to realize a complete population transfer from a given state $|1〉$ to superpositions of energy eigenstates $|\ensuremath{\Psi}〉={\ensuremath{\sum}}_{k}{c}_{k}{e}^{\ensuremath{-}i{\ensuremath{\omega}}_{k}t}|k〉$ of any desired composition. This objective can be achieved by using a ``shaped'' (dump or Stokes) laser pulse, formed by simultaneous monochromatic pulses of the same smooth profile, resonantly coupling the states $|k〉$ with a single intermediate state $|2〉,$ followed by a (pump or anti-Stokes) pulse, coupling this intermediate state with the initial state $|1〉.$ The pulse shapes can be obtained from first-order perturbation theory, so the method can be used for efficient information coding in the form of superpositions of atomic Rydberg states or of molecular vibrational states.

DOI
10.1103/physreva.65.043413

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We introduce the shaped-adiabatic-passage'' method that allows one to realize a complete population transfer from a given state $|1〉$ to superpositions of energy eigenstates $|\ensuremath{\Psi}〉={\ensuremath{\sum}}_{k}{c}_{k}{e}^{\ensuremath{-}i{\ensuremath{\omega}}_{k}t}|k〉$ of any desired composition. This objective can be achieved by using a shaped'' (dump or Stokes) laser pulse, formed by simultaneous monochromatic pulses of the same smooth profile, resonantly coupling the states ∣k〉|k〉∣k〉 with a single intermediate state ∣2〉,|2〉,∣2〉, followed by a (pump or anti-Stokes) pulse, coupling this intermediate state with the initial state ∣1〉.|1〉.∣1〉. The pulse shapes can be obtained from first-order perturbation theory, so the method can be used for efficient information coding in the form of superpositions of atomic Rydberg states or of molecular vibrational states.
We discuss a simple scheme for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states. The technique, which we call fractional stimulated Raman adiabatic passage ({\it f-STIRAP}), is based upon (incomplete) adiabatic population transfer between an initial state ψ1ψ_1ψ1​ and state ψ3ψ_3ψ3​ through an intermediate state ψ2ψ_2ψ2​. As in STIRAP, the Stokes pulse arrives before the pump pulse, but unlike STIRAP, the two pulses terminate simultaneously while maintaining a constant ratio of amplitudes. The independence of f-STIRAP from details of pulse shape and pulse area makes it the analog of conventional STIRAP in the creation of coherent superpositions of states. We suggest a smooth realization of f-STIRAP which requires only two laser pulses (which can be derived from a single laser) and at the same time ensures the automatic fulfillment of the asymptotic conditions at early and late times. Furthermore, we provide simple analytic estimates of the robustness of f-STIRAP against variations in the pulse intensity, the pulse delay, and the intermediate-state detuning, and discuss its possible extension to multistate systems.
This paper discusses a generalization of stimulated Raman adiabatic passage (STIRAP) in which the single intermediate state is replaced by N intermediate states. Each of these states is connected to the initial state ${\ensuremath{\psi}}_{i}$ with a coupling proportional to the pump pulse and to the final state ${\ensuremath{\psi}}_{f}$ with a coupling proportional to the Stokes pulse, thus forming a parallel multi-\ensuremath{\Lambda} system. It is shown that the dark (trapped) state exists only when the ratio between each pump coupling and the respective Stokes coupling is the same for all intermediate states. We derive the conditions for existence of a more general adiabatic-transfer state that includes transient contributions from the intermediate states but still transfers the population from state ${\ensuremath{\psi}}_{i}$ to state ${\ensuremath{\psi}}_{f}$ in the adiabatic limit. We present various numerical examples for success and failure of multi-\ensuremath{\Lambda} STIRAP, which illustrate the analytic predictions. Our results suggest that in the general case of arbitrary couplings, it is most appropriate to tune the pump and Stokes lasers either just below or just above all intermediate states.
We demonstrate a method of adiabatic population transfer from a single quantum state into a coherent superposition of states. The transfer is executed with femtosecond pulses, spectrally shaped in a simple and intuitive manner, which does not require iterative feedback-controlled loops. In contrast to nonadiabatic methods of excitation, our approach is not sensitive to the exact value of laser intensity. We show that the population transfer is complete, and analyze the possibility of controlling the relative phases and amplitudes of the excited eigenstates. We discuss the limitations of the proposed control methods due to the dynamic level shifts and suggest ways of reducing their influence.
The manipulation of population transfer and the creation of an arbitrary superposition between two atomic states in the framework of a closed inverse Y-type four-level system driven by a series of pulse pairs and an external control field is reported. It is shown that when the laser fields are tuned to resonance with respective transitions, the non-adiabatic coupling between two degenerate adiabatic states can be reduced tremendously and complete population transfer from the initial state to the target state can be achieved in a piecewise manner. Moreover, an arbitrary superposition between the initial state and target state can be created by suitably tuning the Rabi frequency of the control laser field, inter-pair time delay, pulse number or intra-pair time delay between the pump and Stokes pulses. This scheme combines stimulated Raman adiabatic passage and temporal coherent control, and may be useful for quantum information processing and control of chemical reactions.
We develop a method for executing robust and selective transfer of populations between a single level and preselected superpositions of energy eigenstates. Viewed in the frequency domain, our method amounts to executing a series of simultaneous adiabatic passages into each component of the target superposition state. Viewed in the time domain, the method works by accumulating the wave function of the target wave packet as it revisits the transition region, in what amounts to an extension of the piecewise adiabatic passage technique [E. A. Shapiro et al., Phys. Rev. Lett. 99, 033002 (2007)] to the multistate regime. The viability of the method is verified by performing numerical tests for the Na2{\text{Na}}_{2}Na2​ molecule.
We show that the technique of Stark-chirped rapid adiabatic passage (SCRAP), hitherto used for complete population transfer between two quantum states, offers a simple and robust method for complete population transfer amongst three states in atoms and molecules. In this case SCRAP uses three laser pulses: a strong far-off-resonant pulse modifies the transition frequencies by inducing dynamic Stark shifts and thereby creating time-dependent level crossings amongst the three diabatic states, while near-resonant and moderately strong pump and Stokes pulses, appropriately offset in time, drive the population between the initial and final states via adiabatic passage. The population transfer efficiency is robust to variations in the intensities of the lasers, as long as these intensities are sufficiently large to enforce adiabatic evolution. With suitable pulse timings the population in the (possibly decaying) intermediate state can be minimized, as with stimulated Raman adiabatic passage (STIRAP). This technique applies to one-photon as well as multiphoton transitions and it is also applicable to media exhibiting inhomogeneous broadening; these features represent clear advantages over STIRAP by overcoming the inevitable dynamical Stark shifts that accompany multiphoton transitions as well as unwanted detunings, e.g., induced by Doppler shifts.