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arXiv:0811.0857 · Physical Review A

Complete transfer of populations from a single state to a preselected superposition of states using piecewise adiabatic passage: Theory

Evgeny A. Shapiro, Valery Milner, Moshe Shapiro

Published Feb 26, 2009• 39 citations
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Abstract

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 ${\text{Na}}_{2}$ molecule.

DOI
10.1103/physreva.79.023422

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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 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.
This thesis is based upon the work published in the following two articles entitled: Robust Operation of a Universal Set of Logic Gates for Quantum Computation using Adiabatic Population Transfer between Molecular Levels [37], and Piecewise Adiabatic Passage with a Series of Femtosecond Pulses [54]. Both papers involve using the concept of a quantum control phenomenon, known as adiabatic passage in different manners, in order to achieve particular goals. In the first paper we present a robust construction of a set of logic gates operating on a system of qubits encoded in the ro-vibrational eigenstates of an Na₂ molecule using the optical Adiabatic Population Transfer (APT) method. We demonstrate the operation of a complete universal gate-set for quantum computation on a two-qubit system with gate fidelities approaching 99.99%. Like other APT-based processes, the method is robust against substantial fluctuations in the intensity of the laser pulse. Our construction is easily scalable to dealing with a larger number of qubits. The second line of research developed from the desire to merge the robustness of an adiabatic process, as presented in the previous paper, with the speed and additional level of control available by using pulse shaping techniques of broadband pulses. Therein we develop a method of executing complete population transfers between quantum states in a piecewise manner using a series of femtosecond laser pulses. The method can be applied to a large class of problems as it benefits from the high peak powers and large spectral bandwidths afforded by femtosecond pulses. The degree of population transfer is found to be robust to a wide variation in the absolute and relative intensities, durations, and time ordering of the pulses. The method is studied in detail for atomic sodium where piecewise adiabatic population transfer, as well as the induction of Ramsey-type interferences, is demonstrated.
We propose and experimentally demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The piecewise nature of the process suggests a possibility for the selective population transfer in complex quantum systems.
We develop a method of executing complete population transfers between quantum states in a piecewise manner using a series of femtosecond laser pulses. The method can be applied to a large class of problems as it benefits from the high peak powers and large spectral bandwidths afforded by femtosecond pulses. The degree of population transfer is robust to a wide variation in the absolute and relative intensities, durations, and time ordering of the pulses. The method is studied in detail for atomic sodium where piecewise adiabatic population transfer, as well as the induction of Ramsey-type interferences, is demonstrated.
We propose a class of schemes for robust population transfer between quantum states that utilize trains of coherent pulses, thus forming a generalized adiabatic passage via a wave packet. We study piecewise stimulated Raman adiabatic passage with pulse-to-pulse amplitude variation, and piecewise chirped Raman passage with pulse-to-pulse phase variation, implemented with an optical frequency comb. In the context of production of ultracold ground-state molecules, we show that with almost no knowledge of the excited potential, robust high-efficiency transfer is possible.
We introduce the ``shaped-adiabatic-passage'' method that allows one to realize a complete population transfer from a given state ∣1〉|1〉∣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.