Amplification of the parametric dynamical Casimir effect via optimal control

Fabian Hoeb, Fabrizio Angaroni, Jonathan Zoller, Tommaso Calarco, Giuliano Strini, Simone Montangero, and Giuliano Benenti

Phys. Rev. A 96, 033851 – Published 27 September 2017

Abstract

We introduce different strategies to enhance photon generation in a cavity within the Rabi model in the ultrastrong coupling regime. We show that a bang-bang strategy allows one to enhance the effect up to 1 order of magnitude with respect to simply driving the system in resonance for a fixed time. Moreover, up to about another order of magnitude can be gained by exploiting quantum optimal control strategies. Finally, we show that such optimized protocols are robust with respect to systematic errors and noise, paving the way to future experimental implementations of such strategies.

Received 2 June 2017

DOI:https://doi.org/10.1103/PhysRevA.96.033851

Physics Subject Headings (PhySH)

Machine learning Quantum algorithms Quantum control Quantum gates Quantum simulation

Quantum Information, Science & Technology

Authors & Affiliations

Fabian Hoeb¹, Fabrizio Angaroni^2,3, Jonathan Zoller¹, Tommaso Calarco¹, Giuliano Strini⁴, Simone Montangero^1,5, and Giuliano Benenti^2,3,6

¹Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technology (IQST), Ulm University, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
²Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
³Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
⁴Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy
⁵Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
⁶NEST, Istituto Nanoscienze-CNR, 56126 Pisa, Italy

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Issue

Vol. 96, Iss. 3 — September 2017

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Images

Figure 1
Results for the on-off protocol. Top: Dynamical evolution of the mean number of photons $〈 n 〉$ at interaction strength $λ = 0.80$ (solid green line) and $λ = 0.83$ (dashed green line). Bottom: Figure of merit $f$ as a function of the coupling strength $λ$ . For both figures, the initial and final off-resonance periods, as indicated by the vertical black lines, are set to $τ = 4 τ_{s}$ .
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Figure 2
Expected photon number $〈 n 〉$ versus time for bang-bang strategy (left, blue solid lines) and dCRAB (right, red solid lines) for coupling strengths $λ = 0.17$ (a, c) and $λ = 0.83$ (b, d). On the secondary $y$ axis, the control pulses (dashed lines, colors, respectively) are displayed. Note that there is an initial and final time interval equally out of resonance for both strategies, used to compute the figure of merit $f$ [see Eq. (5)].
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Figure 3
Created photon number $f$ versus coupling strength $λ$ after application of three different control strategies: dCRAB optimization (red circles), bang-bang strategy (blue squares), and unoptimized on- and off-resonance sweeps (green diamonds). Note that the dCRAB optimized solutions improve significantly compared to the other two strategies and hence pave the way towards optimal amplification of the DCE.
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Figure 4
Figure of merit for the dCRAB pulse computed for the unperturbed $λ = 0.83$ case when the system is exposed either to a systematic (top) or statistical (bottom) errors. In the former case, the actual value of $λ$ set for the propagation ranges in (0.80, 0.86). In the latter, the qubit frequency $ω_{q} (t)$ is affected by random noise uniformly distributed in the interval $[- \frac{δ ω_{q}}{ω}, \frac{δ ω_{q}}{ω}]$ , with correlation time $τ_{c} \approx 0.03 T$ . That is, $ξ (t)$ is reset at every time interval $τ_{c}$ . Error bars denote statistical errors for 100 realizations of noise per point, while the red straight line shows the outcome from a quadratic fit.
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Figure 5
Working principle of the bang-bang strategy shown for an initial pulse (a) and the first iteration of the algorithm (b), for $λ = 0.5$ and $τ_{O} / τ_{s} = 1.5$ . During the time on resonance of the pulse [dashed line in (a)], $〈n〉 (t)$ oscillates around an average value [solid line in (a)]. Upon switching back out of resonance at the maximum of the first oscillation [the corresponding pulse is the dashed line in (b)], the values of $〈n〉$ remain almost frozen around this maximum [solid line in (b)]. Reverting back to the resonance regime leads to the oscillatory behavior of $〈n〉$ . The initial fast increase after each switch on resonance results in the overall population increase of the cavity.
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