Ultimate conversion efficiency bound for the forward double-Λ atom–light coupling scheme

Stefanatos, Dionisis; Smponias, Athanasios; Hamedi, Hamid Reza; Paspalakis, Emmanuel

doi:10.1364/ol.404173

Cited by 9 publications

(7 citation statements)

References 29 publications

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“…The cases with 0 (red solid line) and / 0 = 1 (blue dashed line) almost coincide, as before, but the case with / 0 = 0.1 (green dashed-dotted line) now deviates substantially. Note that for pulses (35) the derivative of the mixing angle is where recall that T is normalized. Using the maximum value of this θ (for t = t 0 ) in the adiabaticity condition for the original system θ 0 /2 (neglecting dissipation), we obtain the condition 1 2 T 0 (37) which is not satisfied for T = 10 when / 0 = 0.1.…”

Section: Example and Discussionmentioning

confidence: 99%

“…Note that u = θ corresponds to the adiabatic gauge potential which represents nonadiabaticity, and optimal control theory allows us to determine how this control function should be varied in order to maximize the desired objective. The mathematical problem is similar to that of maximizing the conversion efficiency between light beams of different frequency or orbital angular momentum, propagating in a cloud of cold atoms characterized by a double-atom-light coupling scheme [35]. We present the detailed solution below.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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Optimal shape of STIRAP pulses for large dissipation at the intermediate level

Stefanatos

Paspalakis

2021

Quantum Inf Process

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We study the problem of maximizing population transfer efficiency in the STIRAP system for the case where the dissipation rate of the intermediate state is much higher than the maximum amplitude of the control fields. Under this assumption, the original three-level system can be reduced to a couple of equations involving the initial and target states only. We find the control fields which maximize the population transfer to the target state for a given duration T , without using any penalty involving the population of the lossy intermediate state, but under the constraint that the sum of the intensities of the pump and Stokes pulses is constant, so the total field has constant amplitude and the only control parameter is the mixing angle of the two fields. In the optimal solution the mixing angle changes in the bang-singular-bang manner, where the initial and final bangs correspond to equal instantaneous rotations, while the intermediate singular arc to a linear change with time. We show that the optimal angle of the initial and final rotations is the unique solution of a transcendental equation where duration T appears as a parameter, while the optimal slope of the intermediate linear change as well as the optimal transfer efficiency is expressed as functions of this optimal angle. The corresponding optimal solution recovers the counterintuitive pulse-sequence, with nonzero pump and Stokes fields at the boundaries. We also show with numerical simulations that transfer efficiency values close to the optimal derived using the approximate system can also be obtained with the original STIRAP system using dissipation rates comparable to the maximum control amplitude.

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Section: Example and Discussionmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

Optimal shape of STIRAP pulses for large dissipation at the intermediate level

Stefanatos

Paspalakis

2021

Quantum Inf Process

Self Cite

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show abstract

“…The cases with Γ ≫ Ω 0 (red solid line) and Γ/Ω 0 = 1 (blue dashed line) almost coincide, as before, but the case with Γ/Ω 0 = 0.1 (green dashed-dotted line) now deviates substantially. Note that for pulses (35) the derivative of the mixing angle is…”

Section: Example and Discussionmentioning

confidence: 99%

“…Note that u = θ corresponds to the adiabatic gauge potential which represents nonadiabaticity, and optimal control theory allows us to determine how this control function should be varied in order to maximize the desired objective. The mathematical problem is similar to that of maximizing the conversion efficiency between light beams of different frequency or orbital angular momentum, propagating in a cloud of cold atoms characterized by a double-Λ atom-light coupling scheme [35]. We present the detailed solution below.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Optimal shape of STIRAP pulses for large dissipation at the intermediate level

Stefanatos,

Paspalakis

2021

Preprint

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We study the problem of maximizing population transfer efficiency in the STIRAP system for the case where the dissipation rate of the intermediate state is much higher than the maximum amplitude of the control fields. Under this assumption, the original three-level system can be reduced to a couple of equations involving the initial and target states only. We find the control fields which maximize the population transfer to the target state for a given duration T , without using any penalty involving the population of the lossy intermediate state, but under the constraint that the sum of the intensities of the pump and Stokes pulses is constant, so the total field has constant amplitude and the only control parameter is the mixing angle of the two fields. In the optimal solution the mixing angle changes in the bang-singular-bang manner, where the initial and final bangs correspond to equal instantaneous rotations, while the intermediate singular arc to a linear change with time. We show that the optimal angle of the initial and final rotations is the unique solution of a transcendental equation where duration T appears as a parameter, while the optimal slope of the intermediate linear change as well as the optimal transfer efficiency are expressed as functions of this optimal angle. The corresponding optimal solution recovers the counterintuitive pulse-sequence, with nonzero pump and Stokes fields at the boundaries. We also show with numerical simulations that, transfer efficiency values close to the optimal derived using the approximate system, can also be obtained with the original STIRAP system using dissipation rates comparable to the maximum control amplitude.

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“…The usage of this protocol is also motivated by our recent work [34] in a different context, involving the double-Λ atom-light coupling scheme. We show there that the performance of the aforementioned protocol, when applied to the dynamical system (6) with R = q = δ = 0, approaches that of the optimal protocol, where the mixing 7).…”

Section: A Simple Sin-cos Control Protocolmentioning

confidence: 99%

Optimized pulses for population transfer via laser induced continuum structures

Stefanatos,

Paspalakis

2021

Preprint

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We use optimal control in order to find the optimal shapes of pulses maximizing the population transfer between two bound states which are coupled via a continuum of states. We find that the optimal bounded controls acquire the bang-interior and interior-bang form, with the bang part corresponding to the maximum allowed control value and the interior part to values between zero and the maximum. Then, we use numerical optimal control to obtain the switching times and the interior control values. We compare our results with those obtained using Gaussian STIRAP pulses, and find that the optimal method performs better, with the extent of improvement depending on the effective two-photon detuning and the size of incoherent losses. When we consider effective twophoton resonance, the improvement is more dramatic for larger incoherent losses, while when we take into account the effective two-photon detuning, the improvement is better for smaller incoherent losses. We also obtain how the transfer efficiency increases with increasing absolute value of the Fano factor. The present work is expected to find application in areas where the population transfer between two bound states through a continuum structure plays an important role, for example coherence effects, like population trapping and electromagnetically induced transparency, optical analogs for light waves propagating in waveguide-based photonic structures, and qubits coupled via a continuum of bosonic or waveguide modes.

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Ultimate conversion efficiency bound for the forward double-Λ atom–light coupling scheme

Cited by 9 publications

References 29 publications

Optimal shape of STIRAP pulses for large dissipation at the intermediate level

Optimal shape of STIRAP pulses for large dissipation at the intermediate level

Optimal shape of STIRAP pulses for large dissipation at the intermediate level

Optimized pulses for population transfer via laser induced continuum structures

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