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arXiv:2002.03345 · New Journal of Physics

Stationary quantum entanglement between a massive mechanical membrane and a low frequency LC circuit

Jie Li, Simon Gröblacher

Published May 6, 2020• 17 citations
arXivHTMLPDF

Abstract

Abstract We study electro-mechanical entanglement in a system where a massive membrane is capacitively coupled to a low frequency LC resonator. In opto- and electro-mechanics, the entanglement between a megahertz (MHz) mechanical resonator and a gigahertz (GHz) microwave LC resonator has been widely and well explored, and recently experimentally demonstrated. Typically, coupling is realized through a radiation pressure-like interaction, and entanglement is generated by adopting an appropriate microwave drive. Through this approach it is however not evident how to create entanglement in the case where both the mechanical and LC oscillators are of low frequency, e.g., around 1 MHz. Here we provide an effective approach to entangling two low-frequency resonators by further coupling the membrane to an optical cavity. The cavity is strongly driven by a red-detuned laser, sequentially cooling the mechanical and electrical modes, which results in stationary electro-mechanical entanglement at experimentally achievable temperatures. The entanglement directly originates from the electro-mechanical coupling itself and due to its quantum nature will allow testing quantum theories at a more macroscopic scale than currently possible.

DOI
10.1088/1367-2630/ab90d2

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Abstract We study electro-mechanical entanglement in a system where a massive membrane is capacitively coupled to a low frequency LC resonator. In opto- and electro-mechanics, the entanglement between a megahertz (MHz) mechanical resonator and a gigahertz (GHz) microwave LC resonator has been widely and well explored, and recently experimentally demonstrated. Typically, coupling is realized through a radiation pressure-like interaction, and entanglement is generated by adopting an appropriate microwave drive. Through this approach it is however not evident how to create entanglement in the case where both the mechanical and LC oscillators are of low frequency, e.g., around 1 MHz. Here we provide an effective approach to entangling two low-frequency resonators by further coupling the membrane to an optical cavity. The cavity is strongly driven by a red-detuned laser, sequentially cooling the mechanical and electrical modes, which results in stationary electro-mechanical entanglement at experimentally achievable temperatures. The entanglement directly originates from the electro-mechanical coupling itself and due to its quantum nature will allow testing quantum theories at a more macroscopic scale than currently possible.
Cavity electro-(opto-)mechanics allows us to access not only single isolated but also multiple mechanical modes in a massive object. Here we develop a multi-mode electromechanical system in which a several membrane vibrational modes are coupled to a three-dimensional loop-gap superconducting microwave cavity. The tight confinement of the electric field across a mechanically-compliant narrow-gap capacitor brings the system into the quantum strong coupling regime under a red-sideband pump field. We demonstrate strong coupling between two mechanical modes, which is induced by two-tone parametric drives and mediated by a virtual photon in the cavity. The tunable inter-mechanical-mode coupling can be used to generate entanglement between the mechanical modes.
Quantum entanglement in mechanical systems is not only a key signature of macroscopic quantum effects but has wide applications in quantum technologies. Here we propose an effective approach for creating strong steady-state entanglement between two directly coupled mechanical oscillators (or a mechanical oscillator and a microwave resonator) in a modulated optomechanical system. The entanglement is achieved by combining the processes of a cavity cooling and the two-mode parametric interaction, which can surpass the bound on the maximal stationary entanglement from the two-mode parametric interaction. In principle, our proposal allows one to cool the system from an initial thermal state to an entangled state with high purity by a monochromatic driving laser. Also, the obtained entangled state can be used to implement the continuous-variable teleportation with high fidelity. Moreover, our proposal is robust against the thermal fluctuations of the mechanical modes under the condition of strong optical pumping.
We theoretically investigate the steady-state bipartite entanglements, mechanical ground-state cooling, and mechanical quadrature squeezing in a hybrid electro-optomechanical system where a moving membrane is linearly coupled to the microwave field mode of an LC circuit, while it simultaneously interacts both linearly and quadratically with the radiation pressure of a single-mode optical cavity. We show that by choosing a suitable sign and amplitude for the quadratic optomechanical coupling (QOC), one can achieve enhanced and thermally robust stationary bipartite entanglement between the subsystems, improved mechanical ground-state cooling, and QQQ-quadrature squeezing of the mechanical mode beyond the 3-dB limit of squeezing. In particular, we find that in the presence of QOC with negative sign and in the resolved sideband regime the bipartite optical-mechanical entanglement can be increased by about 2 orders of magnitude around the temperature of 1 mK, and it can be preserved against thermal noise up to the ambient temperature of 0.1 K. Furthermore, the QOC with positive sign can give rise to the enhancement of the mechanical ground-state cooling by about 1 order of magnitude in the optical and microwave red-detuned regime. We also find that for the positive sign of QOC and near the microwave resonance frequency the squeezing degree of the QQQ quadrature of the mechanical mode can be amplified up to 15 dB. Such a hybrid electro-optomechanical system can serve as a promising platform to engineer an improved entangled source for quantum sensing as well as quantum information processing.
We present a complete theory for laser cooling of a macroscopic radio-frequency LC electrical circuit by means of an optoelectromechanical system, consisting of an optical cavity dispersively coupled to a nanomechanical oscillator, which is in turn capacitively coupled to the LC circuit of interest. We determine the optimal parameter regime where the LC resonator can be cooled down to its quantum ground state, which requires a large optomechanical cooperativity, and a larger electromechanical cooperativity. Moreover, comparable optomechanical and electromechanical coupling rates are preferable for reaching the quantum ground state.
Abstract Quantum entanglement in the motion of macroscopic objects is of significance to both fundamental studies and quantum technologies. Here we show how to entangle the mechanical vibration modes of two massive ferrimagnets that are placed in the same microwave cavity. Each ferrimagnet supports a magnon mode and a low-frequency vibration mode coupled by the magnetostrictive force. The two magnon modes are, respectively, coupled to the microwave cavity by the magnetic dipole interaction. We first generate a stationary nonlocal entangled state between the vibration mode of the ferrimagnet-1 and the magnon mode of the ferrimagnet-2. This is realized by continuously driving the ferrimagnet-1 with a strong red-detuned microwave field and the entanglement is achieved by exploiting the magnomechanical parametric down-conversion and the cavity–magnon state-swap interaction. We then switch off the pump on the ferrimagnet-1 and, simultaneously, turn on a red-detuned pulsed drive on the ferrimagnet-2. The latter drive is used to activate the magnomechanical beamsplitter interaction, which swaps the magnonic and mechanical states of the ferrimagnet-2. Consequently, the previously generated phonon–magnon entanglement is transferred to the mechanical modes of two ferrimagnets. The work provides a scheme to prepare entangled states of mechanical motion of two massive objects, which may find applications in various studies exploiting macroscopic entangled states.
Einstein–Podolski–Rosen (EPR) entanglement state is achievable by combining two single-mode position and momentum squeezed states at a 50:50 beam-splitter (BS). We investigate the generation of the EPR entangled state of two vibrating membranes in a ring resonator, where clockwise (CW) and counter-clockwise (CCW) travelling-wave modes are driven by lasers and finite-bandwidth squeezed lights. Since the optomechanical coupling depends on the location of the membranes, CW and CCW can couple to the symmetric and antisymmetric combination of mechanical modes for a suitable arrangement, which corresponds to a 50:50 BS mixing. Moreover, by employing the red-detuned driving laser and tuning the central frequency of squeezing field blue detuned from the driving laser with a mechanical frequency, the squeezing property of squeezed light can be perfectly transferred to the mechanical motion in the weak coupling regime. Thus, the BS mixing modes can be position and momentum squeezed by feeding the appropriate squeezed lights respectively, and the EPR entangled mechanical state is obtained. Moreover, cavity-induced mechanical cooling can further suppress the influence of thermal noise on the entangled state.