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arXiv:1508.04869 · Physical Review Letters

Ultrafast Optimal Sideband Cooling under Non-Markovian Evolution

Johan F. Triana, Andres Estrada, Leonardo A. Pachón

Published May 2, 2016• 47 citations
arXivHTMLPDF

Abstract

A sideband cooling strategy that incorporates (i) the dynamics induced by structured (non-Markovian) environments in the target and auxiliary systems and (ii) the optimally time-modulated interaction between them is developed. For the context of cavity optomechanics, when non-Markovian dynamics are considered in the target system, ground state cooling is reached at much faster rates and at a much lower phonon occupation number than previously reported. In contrast to similar current strategies, ground state cooling is reached here for coupling-strength rates that are experimentally accessible for the state-of-the-art implementations. After the ultrafast optimal-ground-state-cooling protocol is accomplished, an additional optimal control strategy is considered to maintain the phonon number as close as possible to the one obtained in the cooling procedure. Contrary to the conventional expectation, when non-Markovian dynamics are considered in the auxiliary system, the efficiency of the cooling protocol is undermined.

DOI
10.1103/physrevlett.116.183602

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A sideband cooling strategy that incorporates (i) the dynamics induced by structured (non-Markovian) environments in the target and auxiliary systems and (ii) the optimally time-modulated interaction between them is developed. For the context of cavity optomechanics, when non-Markovian dynamics are considered in the target system, ground state cooling is reached at much faster rates and at a much lower phonon occupation number than previously reported. In contrast to similar current strategies, ground state cooling is reached here for coupling-strength rates that are experimentally accessible for the state-of-the-art implementations. After the ultrafast optimal-ground-state-cooling protocol is accomplished, an additional optimal control strategy is considered to maintain the phonon number as close as possible to the one obtained in the cooling procedure. Contrary to the conventional expectation, when non-Markovian dynamics are considered in the auxiliary system, the efficiency of the cooling protocol is undermined.
An optimized sideband cooling in the presence of initial system correlations is investigated for a standard optomechanical system coupled to a general mechanical non-Markovian reservoir. We study the evolution of phonon number by incorporating the effects of initial correlations into the time-dependent coefficients in the Heisenberg equation. We introduce the concept of cooling rate and define an average phonon reduction function to describe the sideband cooling effect in non-Markovian regime. Our results show that the instantaneous phonon number can be significantly reduced by introducing either the parametric-amplification type or the beam-splitter type initial correlations. In addition, the ground state cooling rate can be accelerated by enhancing the initial correlation of beam-splitter type. By optimizing the initial state of the system and utilizing Q-modulation technology, a stable mechanical ground state can be obtained in a very short time. Our optimized cooling protocol provides an appealing platform for phonon manipulation and quantum information processing in solid-state systems.
Abstract We propose an optimized sideband cooling protocol for an optomechanical system coupled to a mechanical non-Markovian reservoir, considering the presence of initial system correlations. By incorporating the effect of initial correlations in the Heisenberg equations, we derive a more stringent dependence on the initial conditions and time-dependent evolution of the phonon numbers. Our findings demonstrate that considering the initial correlations can significantly reduce the number of phonons during the cooling process. Moreover, by adjusting the strength and phase of the initial correlation, the ground-state cooling process can be accelerated. We observe a characterization of this cooling optimization process that resembles the phenomenon of entanglement death and revival. This work provides a promising platform for effectively manipulating phonons and facilitating quantum information processing in optomechanical systems.
Optimal control theory is applied to sideband cooling of nano-mechanical resonators. The formulation described here makes use of exact results derived by means of the path-integral approach of quantum dynamics, so that no approximation is invoked. It is demonstrated that the intricate interplay between time-dependent fields and structured thermal bath may lead to improve results of the sideband cooling by an order of magnitude. Cooling is quantified by means of the mean number of phonons of the mechanical modes as well as by the von Neumann entropy. Potencial extension to non-linear systems, by means of semiclassical methods, is briefly discussed.
Cooling down a trapped ion into its motional ground state is a central step for trapped-ion-based quantum information processing. State-of-the-art cooling schemes often work under a set of optimal cooling conditions derived analytically using a perturbative approach, in which the sideband coupling is assumed to be the weakest of all the relevant transitions. As a result, the cooling rate is severely limited. Here we propose to use a quantum control technique powered with automatic differentiation to speed up the classical cooling schemes. We demonstrate the efficacy of our approach by applying it to find the optimal cooling conditions for classical sideband cooling and electromagnetically induced transparency cooling schemes, which are in general beyond the weak-sideband-coupling regime. Based on those numerically found optimal cooling conditions, we show that faster cooling can be achieved while at the same time a low average phonon occupation can be retained.
Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme, which is particularly well suited for systems in the sideband-unresolved regime, based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. We find that, by introducing an additional passive element – either a narrow linewidth cavity or a mirror with a delay line – an optomechanical system in the deeply sideband-unresolved regime will exhibit dynamics similar to one that is sideband-resolved. With this new approach, the experimental realization of groundstate cooling and optomechanical entanglement is well within reach of current integrated state-of-the-art high-Q mechanical resonators.
We study optimal control strategies to optimize the relaxation rate towards the fixed point of a quantum system in the presence of a non-Markovian (NM) dissipative bath. Contrary to naive expectations that suggest that memory effects might be exploited to improve optimal control effectiveness, NM effects influence the optimal strategy in a non trivial way: we present a necessary condition to be satisfied so that the effectiveness of optimal control is enhanced by NM subject to suitable unitary controls. For illustration, we specialize our findings for the case of the dynamics of single qubit amplitude damping channels. The optimal control strategy presented here can be used to implement optimal cooling processes in quantum technologies and may have implications in quantum thermodynamics when assessing the efficiency of thermal micro-machines.