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Journal of Physics B Atomic Molecular and Optical Physics

Non-adiabatic population transfer in coupled bosonic systems

T. C. H. Liew, Ivan Andreevich Shelykh

Published Nov 30, 2012• 3 citations
Publisher

Abstract

We study nonlinear Landau–Zener tunnelling in discrete Gross–Pitaevskii systems accounting for finite energy-level shifts generated by broadened pulse shapes in the non-adiabatic regime. Under these conditions, the tunnelling dynamics is generally sensitive to the pulse arrival time, however, we show that through variation of the pulse shape one can recover a case of rapid high fidelity population transfer independent of the pulse arrival time. We demonstrate how population transfer is possible in two-mode and three-mode systems. In large systems, we expect that population transfer between a pair of modes can be achieved through the application of a sequence of pulses that select pairs of neighbouring modes at each step.

DOI
10.1088/0953-4075/45/24/245003

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We study nonlinear Landau–Zener tunnelling in discrete Gross–Pitaevskii systems accounting for finite energy-level shifts generated by broadened pulse shapes in the non-adiabatic regime. Under these conditions, the tunnelling dynamics is generally sensitive to the pulse arrival time, however, we show that through variation of the pulse shape one can recover a case of rapid high fidelity population transfer independent of the pulse arrival time. We demonstrate how population transfer is possible in two-mode and three-mode systems. In large systems, we expect that population transfer between a pair of modes can be achieved through the application of a sequence of pulses that select pairs of neighbouring modes at each step.
Population inversion from an initial quantum state to a desired quantum state represents an exciting new frontier for quantum manipulation; that frontier is endowed with a strong interdisciplinary character and connections to other scientific fields, including atomic, molecular, and optical physics, as well as in solid-state devices, for fundamental studies, nuclear magnetic resonance and other spectroscopic techniques, metrology, interferometry, optical control of chemical reactions or quantum-information applications. Two-level systems are ubiquitous in these areas, and the driving of a population inversion is an important operation. So far various schemes for population transfer to a target state from an initial state have been proposed in theory and implemented in experiment. To be useful, such methods must, of course, be reliable, fast, and robust. Most literatures on two-level models investigated population inversion, which could be modelled by infinite-time processes. In this paper, by using a composite adiabatic passage (CAP) technique—in which the single pulse driving the quantum transition is replaced by a sequence of pulses with well-defined control phases, we investigate the population inversion problem of two-level quantum system with a finite duration. We take a sinusoidally varying pulse model that continuously vanishes at the beginning and the end of the finite duration as an example. The high-fidelity population inversion of the two-level system with finite duration is achieved. We discuss the effects of both coupling strength and detuning strength on the transition probability. It is found that this protocol could suppress the oscillations in the transition probability and reduce the admissible error bellow the 10 -4 quantum computation benchmark. The fidelity can arrive at 1, even with simple three- and five-composite pulse sequences. The protocol combines the advantages of adiabatic passage and composite pulses techniques. By choosing the composite phases appropriately, a high-fidelity, fast, stable and extremely robust complete population inversion is achieved for the finite-time two-level model. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp as long as the latter satisfy the symmetry property. Furthermore, the classical Hamiltonian is applied to describe the dynamic properties of the quantum system and further verify the effectiveness and feasibility of the proposed CAP technique. The results we present here are general and in principle apply to any two- and multi-level quantum systems. The accuracy of the CAP technique and its robustness against parameter variations make the protocol suitable for ultrahigh-fidelity quantum manipulation. We believe that the protocol can be widely used in many different areas of science, ranging from the quantum information, the quantum chemical, and the quantum optics to the ultracold atomic and molecular physics.
Abstract The Demkov-Kunike (DK) model, characterized by a hyperbolic tangent detuning and a hyperbolic secant coupling, serves as a universal framework for describing driven quantum systems. However, existing research has primarily focused on two-level systems, some gaps still persist in extending the model to three-level configurations to achieve coherent population transfer (CPT). This study constructs exact solutions for both two- and three-level DK models via a canonical transformation, providing a basis for the quantitative analysis of population transfer, and achieves effective regulation of CPT via a finite-time adiabatic driving mechanism under specific parameter constraints. Furthermore, we analyze the impact of pulse truncation—a common experimental constraint—as well as environmental dissipation on quantum state evolution. The results show that the proposed scheme achieves rapid, high-fidelity coherent population transfer not only under ideal conditions, but also in the presence of realistic pulse truncation and even when decoherence induced by system-environment coupling is included. This work achieves CPT in the three-level DK model, offering a promising approach for advancing quantum state control in practical applications.
We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.
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 investigate the problem of population transfer in a two-states system driven by an external electromagnetic field featuring a few cycles, until the extreme limit of two or one cycle. Taking the physical constraint of zero-area total field into account, we determine strategies leading to ultrahigh-fidelity population transfer despite the failure of the rotating wave approximation. We specifically implement adiabatic passage based on adiabatic Floquet theory for a number of cycles as low as 2.5 cycles, finding and making the dynamics follow an adiabatic trajectory connecting the initial and targeted states. Nonadiabatic strategies with shaped or chirped pulses, extending the π-pulse regime to two- or single-cycle pulses, are also derived.