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AIP conference proceedings

Non-Markovian optimal sideband cooling

Johan F. Triana, Leonardo A. Pachón

Published Jan 1, 2018• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.5031696

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 25, 2004•0 citations
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.
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.
The present state of the art in cooling mechanical resonators is a version of sideband cooling. Here we present a method that uses the same configuration as sideband cooling-coupling the resonator to be cooled to a second microwave (or optical) auxiliary resonator-but will cool significantly colder. This is achieved by varying the strength of the coupling between the two resonators over a time on the order of the period of the mechanical resonator. As part of our analysis, we also obtain a method for fast, high-fidelity quantum information transfer between resonators.
We show that in the regime of ground-state cooling, simple expressions can be derived for the performance of resolved-sideband cooling --- an example of coherent feedback control --- and optimal linear measurement-based feedback cooling for a harmonic oscillator. These results are valid to leading order in the small parameters that define this regime. They provide insight into the origins of the limitations of coherent and measurement-based feedback for linear systems, and the relationship between them. These limitations are not fundamental bounds imposed by quantum mechanics, but are due to the fact that both cooling methods are restricted to use only a linear interaction with the resonator. We compare the performance of the two methods on an equal footing --- that is, for the same interaction strength --- and confirm that coherent feedback is able to make much better use of the linear interaction than measurement-based feedback. We find that this performance gap is caused not by the back-action noise of the measurement but by the projection noise. We also obtain simple expressions for the maximal cooling that can be obtained by both methods in this regime, optimized over the interaction strength.
We propose a technique that allows to laser cool a nanomechanical resonator mode to its motional ground state. The method is based on resonant laser excitation of a phonon sideband of an embedded self-assembled quantum dot. The strength of this sideband coupling is determined directly by the difference between the electron-phonon couplings of the initial and final states of the quantum dot (QD) optical transition. When compared with the analogous sideband-cooling of a trapped-ion (TI), we find novel quantum interference effects in the cooling cycle and that the finite Q-value can lead to regimes where the final occupancy is proportional to the initial one -- with their ratio determined by the product of the "effective Lamb-Dicke" parameter and the Q-value. The interactions underlying this cooling scheme also provide a tool-box for quantum state engineering in these systems.