Dynamical Suppression of Unwanted Transitions in Multistate Quantum Systems

Genko T. Genov and Nikolay V. Vitanov

Phys. Rev. Lett. 110, 133002 – Published 26 March 2013

Abstract

We propose a method to suppress unwanted transition channels and achieve perfect population transfer in multistate quantum systems by using composite pulse sequences. Unwanted transition paths may be present due to imperfect light polarization, misalignment of the quantization axis, spatial inhomogeneity of the trapping fields, off-resonant couplings, etc., or they may be merely unavoidable, e.g., due to perturbing excitations in molecules and solids. Compensation of separate or simultaneous deviations in polarization, pulse area, and detuning is demonstrated, even when these deviations are unknown, in three-state $V$ and $Ξ$ (ladder) systems and in a four-state $Y$ system.

Received 3 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.133002

Authors & Affiliations

Genko T. Genov and Nikolay V. Vitanov

Department of Physics, Sofia University, 5 James Bourchier Boulevard, 1164 Sofia, Bulgaria

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Vol. 110, Iss. 13 — 29 March 2013

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Images

Figure 1
$V$ , $Ξ$ (ladder), and $Y$ systems.Reuse & Permissions
Figure 2
Transition probabilities $P_{1 \to 2}$ (solid lines) and $P_{1 \to 3}$ (dashed lines) vs the mixing angle $θ$ for a single resonant pulse with rms area $A = π$ and for composite sequences of $n$ pulses (each with rms area $π$ ). Upper frame: $V$ system with phases $ϕ_{12} = (0, 2 / 3, 0) π$ and $ϕ_{13} = (0, 1, 1 / 3) π$ for three pulses and $ϕ_{12} = (0, 1.411, 0.249, - 0.432, - 0.935) π$ and $ϕ_{13} = (0, 0.454, - 0.632, 0.14, - 0.514) π$ for five pulses. Lower frame: $Ξ$ system with phases $ϕ_{12} = (0, 2 / 3, 1 / 6) π$ and $ϕ_{23} = (0, - 2 / 3, 1 / 6) π$ for three pulses and $ϕ_{12} = (0, - 4, - 1, 7, - 4) π / 10$ and $ϕ_{23} = (0, 4, 3, - 5, 0) π / 10$ for five pulses. The ( $3 e$ ) curves in both frames show the transition probabilities for three pulses when their phases experience random errors with a Gaussian distribution with a standard deviation of $0.05 π$ .Reuse & Permissions
Figure 3
Transition probability $P_{1 \to 2}$ in a $V$ system. Upper frames: $P_{1 \to 2}$ vs the mixing angle $θ$ and the rms pulse area $A$ for a single resonant pulse (upper left) and a composite sequence of three resonant pulses (upper right) with phases $ϕ_{12} = (0, 2 / 3, 0) π$ and $ϕ_{13} = (0, 1, 1 / 3) π$ . Lower frames: $P_{1 \to 2}$ vs the mixing angle $θ$ and the single-photon detuning $Δ$ for a single rectangular pulse of duration $T$ and rms area $A = π$ (lower left) and a composite sequence of three rectangular pulses, each with duration $T$ and rms area $π$ and phases $ϕ_{12} = (0, 1 / 3, 0) π$ and $ϕ_{13} = (0, 2 / 3, 0) π$ (lower right).Reuse & Permissions
Figure 4
Transition probabilities $P_{0 \to 2}$ (solid lines) and $P_{0 \to 3}$ (dashed lines) in a $Y$ system vs the mixing angle $θ$ for a single pulse pair with rms area $2 π$ and for composite sequences of two and six pulse pairs (each with rms area $A = π$ ), with phases $ϕ_{01} = ϕ_{12} = (0, 0)$ and $ϕ_{13} = (0, 1) π$ for two pairs and $ϕ_{01} = (0, 0, - 0.181, - 0.181, - 0.033, - 0.033) π$ , $ϕ_{12} = (0, 0, - 0.517, - 0.517, - 0.398, - 0.398) π$ , and $ϕ_{13} = (0, 0.562, 0.026, - 1.554, 0.393, 0.238) π$ for six pairs. The ( $2 d$ ) curve shows the transition probabilities for the two pulse pairs when there is a random time delay of the $| 0 ⟩ \to | 1 ⟩$ coupling, i.e., $Ω_{01} (t) \to Ω_{01} (t + τ)$ , where $τ$ has a Gaussian distribution with a standard deviation of $0.1 T$ , where $A (T) = π$ .Reuse & Permissions
Figure 5
Transition probability $P_{0 \to 2}$ for a $Y$ system. Upper frames: $P_{0 \to 2}$ vs the mixing angle $θ$ and the rms pulse area $A$ for a single resonant pulse pair (upper left) and a composite sequence of three resonant pulse pairs (upper right), with phases $ϕ_{01} = (0, 1, - 1 / 3) π$ , $ϕ_{12} = (0, - 2 / 3, 1 / 3) π$ , and $ϕ_{13} = (0, 1, 0) π$ . Lower frames: $P_{0 \to 2}$ vs the mixing angle $θ$ and the single-photon detuning $Δ$ for a single pair of rectangular pulses with rms area $A = 2 π$ (lower left) and a composite sequence of three pairs of rectangular pulses, each with rms area $2 π$ and phases $ϕ_{01} = ϕ_{12} = (0, 2 / 3, 0) π$ and $ϕ_{13} = (0, 1, 0) π$ .Reuse & Permissions

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