Minimum-Time Transitions Between Thermal Equilibrium States of the Quantum Parametric Oscillator

Stefanatos, Dionisis

doi:10.1109/tac.2017.2684083

Cited by 31 publications

(42 citation statements)

References 38 publications

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“…Suppose we want to open the trap in such a way that, at time t = T , its frequency is ω(T ) = ω T < ω 0 while the initial and final occupation numbers are the same (as defined from the initial and final Fock basis respectively). These protocols are particularly important in the design of quantum thermal machines [27][28][29][30][31].…”

Section: Model and Control Problemmentioning

confidence: 99%

Exploiting landscape geometry to enhance quantum optimal control

2020

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The successful application of Quantum Optimal Control (QOC) over the past decades unlocked the possibility of directing the dynamics of quantum systems. Nevertheless, solutions obtained from QOC algorithms are usually highly irregular, making them unsuitable for direct experimental implementation. In this paper, we propose a method to reshape those unattractive optimal controls. The approach is based on the fact that solutions to QOC problems are not isolated policies but constitute multidimensional submanifolds of control space. This was originally shown for finitedimensional systems. Here, we analytically prove that this property is still valid in a continuous variable system. The degenerate subspace can be effectively traversed by moving in the null subspace of the hessian of the cost function, allowing for the pursuit of secondary objectives. To demonstrate the usefulness of this procedure, we apply the method to smooth and compress optimal protocols in order to meet laboratory demands.

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Section: Model and Control Problemmentioning

confidence: 99%

Exploiting landscape geometry to enhance quantum optimal control

2020

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“…We start by presenting the minimum-time solution given in [7]. If we define the dimensionless variable b through the relations…”

Section: Implications Of the Minimum-time Solutionmentioning

confidence: 99%

“…In our recent work [7], we solved this problem for the more general case where u 1 ≤ 1/γ 4 and u 2 ≥ 1. Here we present the solution when the control bounds are fixed as in (27), corresponding to the bounds in (2).…”

Section: Implications Of the Minimum-time Solutionmentioning

confidence: 99%

“…For u 2 = 1, the starting point (1, 0) is an equilibrium point for system (24), (25), thus the candidate optimal trajectories (extremals) should start with u = u 1 . The solution of the transcendental equation in Theorem 2 from [7] is restricted in the interval 0 < s ≤ Min{(1 − u 1 ) 2 /4, (u 2 γ 2 − 1/γ 2 ) 2 /4}, which is simplified to 0 < s ≤ (1 − u 1 ) 2 /4 for the control bounds given in (27). Remark 1.…”

Section: Implications Of the Minimum-time Solutionmentioning

confidence: 99%

“…In the present article, we use our recent complete solution for the optimal control problem of the quantum parametric oscillator [7] and derive an exponential bound on the minimum achievable temperature with this system. Note that such a bound has been previously obtained for this system, but in the more general case where the harmonic potential can become repulsive [3].…”

Section: Introductionmentioning

confidence: 99%

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Exponential bound in the quest for absolute zero

Stefanatos

2017

Phys. Rev. E

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In most studies for the quantification of the third thermodynamic law, the minimum temperature which can be achieved with a long but finite-time process scales as a negative power of the process duration. In this article, we use our recent complete solution for the optimal control problem of the quantum parametric oscillator to show that the minimum temperature which can be obtained in this system scales exponentially with the available time. The present work is expected to motivate further research in the active quest for absolute zero.

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