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Physical Review A

Optimal adiabatic passage by shaped pulses: Efficiency and robustness

S. Guérin, Vagharshak Hakobyan, Hans Rudolf Jauslin

Published Jul 27, 2011• 64 citations
Publisher

Abstract

We explore the efficiency and robustness of population transfer in two-state systems by adiabatic passage (i) when the driving pulse is optimally designed in order to lead to parallel adiabatic passage or (ii) with a linear chirping. We show how one could practically implement the corresponding designs of the pulses in the spectral domain. We analyze the robustness of the two shapings taking into account fluctuations of the phase, amplitude, and the area of the pulse. We show the overall superiority of the parallel adiabatic passage especially when one faces the issue of a pulse area that is not well known. We show that the robustness of parallel adiabatic passage is not improved when it is complemented by a correcting field that cancels out the nonadiabatic losses.

DOI
10.1103/physreva.84.013423

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We explore the efficiency and robustness of population transfer in two-state systems by adiabatic passage (i) when the driving pulse is optimally designed in order to lead to parallel adiabatic passage or (ii) with a linear chirping. We show how one could practically implement the corresponding designs of the pulses in the spectral domain. We analyze the robustness of the two shapings taking into account fluctuations of the phase, amplitude, and the area of the pulse. We show the overall superiority of the parallel adiabatic passage especially when one faces the issue of a pulse area that is not well known. We show that the robustness of parallel adiabatic passage is not improved when it is complemented by a correcting field that cancels out the nonadiabatic losses.
We present a general and versatile technique of population transfer based on parallel adiabatic passage by femtosecond shaped pulses. Their amplitude and phase are specifically designed to optimize the adiabatic passage corresponding to parallel eigenvalues at all times. We show that this technique allows the robust adiabatic population transfer in a Raman system with the total pulse area as low as $3\ensuremath{\pi}$, corresponding to a fluence of one order of magnitude below the conventional stimulated Raman adiabatic passage process. This process of short duration, typically picosecond and subpicosecond, is easily implementable with the modern pulse shaper technology and opens the possibility of ultrafast robust population transfer with interesting applications in quantum information processing.
This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be set in the framework of adiabatic passage, which is known to facilitate ensemble control of quantum systems. Building on this insight, we present a mathematical proof of robustness for a control protocol—chirped pulse—practised by experimentalists to drive an ensemble of quantum systems from the ground state to the most excited state. We then propose new adiabatic control protocols using a single chirped and amplitude-shaped pulse, to robustly perform any permutation of eigenstate populations, on an ensemble of systems with unknown coupling strengths. These adiabatic control protocols are illustrated by simulations on a four-level ladder.
We present a method for optimization of the technique of adiabatic passage between two quantum states by composite sequences of frequency-chirped pulses with specific relative phases: composite adiabatic passage (CAP). By choosing the composite phases appropriately the nonadiabatic losses can be canceled to any desired order with sufficiently long sequences, regardless of the nonadiabatic coupling. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp. The accuracy of the CAP technique and its robustness against parameter variations make CAP suitable for high-fidelity quantum information processing.
We examine the adiabatic limit of population transfer in two-level models driven by a chirped laser field. We show that the nonadiabatic correction is minimized when the adiabatic eigenenergies associated to the dynamics are parallel. In the diagram of the difference of the eigenenergy surfaces as a function of the parameters, this corresponds to an adiabatic passage along a level line. The analytical arguments are based on the Dykhne-Davis-Pechukas treatment. We illustrate this behavior with various examples.
Adiabatic rapid passage (ARP) is extensively used to achieve efficient transfer or inversion of populations in quantum systems. Landau and Zener accurately estimated the transfer probability of ARP for a closed system and showed that this probability improved with higher drive amplitude. Recently, we found that, in open quantum systems, applying a strong drive can give rise to significant drive-induced dissipation (DID). Here, we investigate the effect of DID on the performance of ARP that is implemented using a linearly chirped pulse on a two-level system. From the Landau-Zener formula, the population transfer was known to be enhanced with increasing drive amplitude. However, here we show that, beyond a threshold value of the drive amplitude, the transfer probability is reduced because of the detrimental effect of DID. We show that the competition between the two processes results in an optimal behavior of the population transfer. We also propose a phenomenological model that helps explain such nonmonotonic behavior of the transfer. Using this model, we estimate the optimum time at which the maximum population transfer occurs. We extend the analysis for rectangular as well as Gaussian pulse profiles and conclude that a Gaussian pulse outperforms a rectangular pulse.
We propose a pulse-shaping method for improving population transfer in multistate stimulated Raman adiabatic passage (STIRAP) with nearest-neighbour couplings only. The method extends the quasiparallel-eigenenergy approach, previously used for two- and three-state systems, to multistate chains without introducing additional shortcut fields. The pump and Stokes fields are shaped so that the eigenenergies closest to the dark state remain nearly parallel to it during the central part of the interaction, where nonadiabatic transitions are most likely to occur. We derive analytic prescriptions for the required pulse shapes and apply them to five-, seven-, and nine-state chains formed by magnetic sublevels of degenerate manifolds with angular momenta Jg→Je=JgJ_g\rightarrow J_e=J_gJg​→Je​=Jg​ and Jg→Je=Jg−1J_g\rightarrow J_e=J_g-1Jg​→Je​=Jg​−1 driven by a pair of right- and left-circularly polarized pulses. Numerical simulations show that the optimized pulses can reduce the population transfer error by several orders of magnitude compared to standard Gaussian pulses. The same shapes also improve robustness against variations of the peak Rabi frequency, the single-photon detuning, and the multiphoton detuning. The comparison between the two angular-momentum families shows that the Jg→JgJ_g\rightarrow J_gJg​→Jg​ chains are generally more favourable, because their Clebsch-Gordan coefficients keep the relevant bright-state gap larger in the region where the dark state changes most rapidly. Finally, simulations with spontaneous emission show that the optimized resonant pulses remain advantageous in the lossy regime as well.