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Physical Review Letters

Pulse-shape-controlled tunneling in a laser field

Martin Holthaus

Published Sep 7, 1992• 94 citations
Publisher

Abstract

It is shown that appropriately shaped smooth pulses of an external oscillating force lead to population transfer in a bistable quantum system on a time scale that can be orders of magnitude shorter than the bare tunneling time. Those pulse shapes for which this phenomenon is achieved can accurately be determined from a tunneling functional ${\mathrm{\ensuremath{\Delta}}}_{\mathit{T}}$ which is constructed explicitly.

DOI
10.1103/physrevlett.69.1596

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It is shown that appropriately shaped smooth pulses of an external oscillating force lead to population transfer in a bistable quantum system on a time scale that can be orders of magnitude shorter than the bare tunneling time. Those pulse shapes for which this phenomenon is achieved can accurately be determined from a tunneling functional \ensuremathΔT{\mathrm{\ensuremath{\Delta}}}_{\mathit{T}}\ensuremathΔT​ which is constructed explicitly.
We consider the interaction of a two-state quantum system with a class of pulses of finite temporal duration. The pulse shape function f(t)f(t)f(t) of such a pulse is a nonanalytic function of time, with discontinuous derivatives at the turn-on and turn-off times. The excitation line width---the excited-state population versus the detuning---is determined primarily by the magnitude of the jumps of the derivative f(n)(t){f}^{(n)}(t)f(n)(t) at the points of nonanalyticity, where nnn is the order of the first discontinuous derivative; this nonanalyticity shows up in the nnnth superadiabatic basis. The excitation line width for such pulses exhibits weak power broadening---it scales up as ${\ensuremath{\Omega}}_{0}^{1/(n+1)}$, where ${\ensuremath{\Omega}}_{0}$ is the peak Rabi frequency of the transition: $\ensuremath{\Omega}(t)={\ensuremath{\Omega}}_{0}f(t)$. As a specific example, we consider the power-of-sine class $f(t)={\mathrm{sin}}^{n}(\ensuremath{\pi}t/T)$ ($0\ensuremath{\leqq}t\ensuremath{\leqq}T$) and a truncated Gaussian pulse, and we compare their excitation line widths with the well-known excitation profile of the rectangular pulse (the Rabi formula). We find that, because of the reduced power broadening, the sinn{\mathrm{sin}}^{n}sinn and truncated Gaussian pulses may accelerate manipulation of qubits compared to rectangular pulses. The reason is that the lower power broadening allows one to use higher Rabi frequency, and hence shorter pulse duration, without affecting significantly other closely lying states.
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.
In the previous paper on this topic it was shown how, for a pulse of arbitrary shape and duration, the drive frequency can be analytically optimized to maximize the amplitude of the population oscillations between the selected two levels in a general many level quantum system. It was shown how the standard Rabi theory can be extended beyond the simple two-level systems. Now, in order to achieve the quickest and as complete as possible population transfer between two pre-selected levels, driving pulse should be tailored so that it produces only a single half-oscillation of the population. In this paper, this second (and final) step towards the controlled population transfer using modified (i.e. many level system) Rabi oscillations is discussed. The results presented herein can be regarded as an extension of the standard πππ-pulse theory - also strictly valid only in the two level systems - to the coherently driven population oscillations in general many level systems.