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arXiv:2001.01318 · Physical review. B./Physical review. B

Ground-state cooling enabled by critical coupling and dark entangled states

Cristian L. Cortes, Matthew Otten, Stephen K. Gray

Published Jan 14, 2019• 10 citations
arXivHTMLPDF

Abstract

We analyze the cooling of a mechanical resonator coupled to an ensemble of interacting two-level systems via an open quantum systems approach. Using an exact analytical result, we find optimal cooling occurs when the phonon mode is critically coupled $(\ensuremath{\gamma}\ensuremath{\sim}g)$ to the two-level system ensemble. Typical systems operate in suboptimal cooling regimes due to the intrinsic parameter mismatch $(\ensuremath{\gamma}\ensuremath{\gg}g)$ between the dissipative decay rate $\ensuremath{\gamma}$ and the coupling factor $g$. To overcome this obstacle, we show that carefully engineering the coupling parameters through the strain profile of the mechanical resonator allows phonon cooling to proceed through the dark (subradiant) entangled states of an interacting ensemble, thereby resulting in optimal phonon cooling. Our results provide an avenue for ground-state cooling and should be accessible for experimental demonstrations.

DOI
10.1103/physrevb.99.014107

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We analyze the cooling of a mechanical resonator coupled to an ensemble of interacting two-level systems via an open quantum systems approach. Using an exact analytical result, we find optimal cooling occurs when the phonon mode is critically coupled (\ensuremathγ\ensuremath∼g)(\ensuremath{\gamma}\ensuremath{\sim}g)(\ensuremathγ\ensuremath∼g) to the two-level system ensemble. Typical systems operate in suboptimal cooling regimes due to the intrinsic parameter mismatch (\ensuremathγ\ensuremath≫g)(\ensuremath{\gamma}\ensuremath{\gg}g)(\ensuremathγ\ensuremath≫g) between the dissipative decay rate \ensuremathγ\ensuremath{\gamma}\ensuremathγ and the coupling factor ggg. To overcome this obstacle, we show that carefully engineering the coupling parameters through the strain profile of the mechanical resonator allows phonon cooling to proceed through the dark (subradiant) entangled states of an interacting ensemble, thereby resulting in optimal phonon cooling. Our results provide an avenue for ground-state cooling and should be accessible for experimental demonstrations.
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Phonon modes within pristine crystalline resonators now routinely reach the quantum ground state. Such systems are attractive for quantum information science applications, as advanced fabrication and processing can enable relatively long quantum coherence times, and precision control can be realized through optical, electrical, or qubit coupling. In many state-of-the-art systems, the phonon lifetime is limited by disorder. In particular, native oxides or damaged `dead layers' at surfaces can host two-level tunneling states that lead to a particularly problematic form of dissipation that increases at lower temperatures. As mechanical losses are driven down in systems such as micro-fabricated bulk acoustic wave resonators, tunneling states are expected to emerge as the dominant mechanism for phonon decoherence. A quantitative description of these mesoscopic systems therefore requires a framework that captures interactions between a selected phonon mode and a large ensemble of TLS. Here, we derive a quantum master equation for this coupled system, permitting the phonon decoherence produced by two-level tunneling states to be calculated. As an example, we estimate the lifetime of a variety of quantum states within quartz micro-resonators hosting a thin surface layer of tunneling states. We find that the phonon coherence time is maximized at low temperatures, in spite of increased mechanical dissipation, and that phonon-TLS coupling can be reduced for modes with strain nodes at the surfaces.
We develop a unified many-body theory of two-photon dark-state laser cooling, the workhorse for preparing trapped ions close to their motional quantum ground state. For ions with a ΛΛΛ level structure, driven by Raman lasers, we identify an ion-number-dependent crossover between weak and strong coupling where both the cooling rate and final temperature are simultaneously optimized. We obtain simple analytic results in both extremes: In the weak coupling limit, we show a Lorentzian spin-absorption spectrum determines the cooling rate and final occupation of the motional state, which are both independent of the number of ions. We also highlight the benefit of including an additional spin dependent force in this case. In the strong coupling regime, our theory reveals the role of collective dynamics arising from phonon exchange between dark and bright states, allowing us to explain the enhancement of the cooling rate with increasing ion number. Our analytic results agree closely with exact numerical simulations and provide experimentally accessible guidelines for optimizing cooling in large ion crystals, a key step toward scalable, high-fidelity trapped-ion quantum technologies.
We propose a ground state cooling scheme for an optomechanical resonator based on the system of one Λ-type three-level atom trapped in an optomechanical cavity. This cooling scheme works in a single-photon coupling, and strong atom-cavity coupling regimes. By investigating the cooling dynamics, we find that there is an EIT-like quantum coherent effect in this system which can suppress the undesired transitions for heating. Moreover, our study shows that the final average phonon number of the optomechanical resonator can be smaller than the one based on the sideband cooling. Furthermore, the ground state cooling of the resonator can still be achieved after thermal fluctuations included. In addition, in comparison with previous cooling methods, there are fewer limitations on the decay rates of both the cavity and the atom in this scheme. As a result, this scheme is very suitable to realize the ground cooling of an optomechanical resonator in the experiment.