Michael J. Hartmann, Martin B. Plenio
We consider two dielectric membranes suspended inside a Fabry-Perot-cavity, which are cooled to a steady state via a drive by suitable classical lasers. We show that the vibrations of the membranes can be entangled in this steady state. They thus form two mechanical, macroscopic degrees of freedom that share steady state entanglement.
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We formulate a non-relativistic Hamiltonian in order to describe the interaction between a moving dielectric membrane and radiation pressure. Such a Hamiltonian is derived without making use of the single-mode adiabatic approximation, and hence it enables us to incorporate multi-mode effects in cavity optomechanics. By performing second quantization, we show how a set of generalized Fock states can be constructed to represent quantum states of the membrane and cavity field. In addition, we discuss examples showing how photon scattering among different cavity modes would modify the interaction …
We perform a theoretical investigation into the classical and quantum dynamics of an optical field in a cavity containing a moving membrane ("membrane-in-the-middle" set-up). Our approach is based on the Maxwell wave equation, and complements previous studies based on an effective Hamiltonian. The analysis shows that for slowly moving and weakly reflective membranes the dynamics can be approximated by unitary, first-order-in-time evolution given by an effective Schrödinger-like equation with a Hamiltonian that does not depend on the membrane speed. This approximate theory is the one typically …
Optomechanical arrays made of structured flexible dielectrics are a promising system for exploring quantum and many-body optomechanical phenomena. We generalize investigations of the optomechanical properties of periodic arrays of one-dimensional scatterers in optical resonators to the case of vibrating membranes whose thickness is not necessarily small with respect to the optical wavelength of interest. The array optical transmission spectrum and its optomechanical coupling with a linear Fabry-Perot cavity field are investigated both analytically and numerically.
The interaction between a high-frequency dilational mode of a thin dielectric film and an optical cavity field is studied theoretically in the membrane-in-the-middle setup. A derivation from first principles leads to a multi-mode optomechanical Hamiltonian where multiple cavity modes are coupled by the thickness variation of the membrane. For membrane thicknesses on the order of one micron, the frequency of this dilational mode is in the GHz range. This can be matched to the free spectral range of the optical cavity, such that the mechanical oscillator will resonantly couple cavity modes at di…
Casimir forces on suspended thin dielectric membranes covered with graphene
该研究从理论和实验探究覆盖石墨烯的悬浮薄电介质膜的卡西米尔力，发现用薄电介质膜替代石墨烯下的固体衬底可部分恢复卡西米尔力的强热依赖性，室温实验测得的力梯度与理论预测一致。
Fast, large area patterning of arbitrary structures down to the nanometre scale is of great interest for a range of applications including the semiconductor industry, quantum electronics, nanophotonics and others. It was recently proposed that nanometre-resolution mask lithography can be realised by sending metastable helium atoms through a binary holography mask consisting of a pattern of holes. However, these first calculations were done using a simple scalar wave approach, which did not consider the dispersion force interaction between the atoms and the mask material. To access the true pot…
Spin-induced multipartite steady-state entanglement of motional modes in hexagonal boron nitride membranes
研究六方氮化硼薄膜中自旋诱导运动模式多体稳态纠缠，通过三个机械模式与自旋缺陷耦合，推导运动方程分析参数范围及耦合强度影响，结果表明能在广泛参数下实现不同振动模式间二分和三分稳态纠缠，利于二维连续变量簇态生成用于量子计算。
Sympathetic cooling with ultracold atoms and atomic ions enables ultralow temperatures in systems where direct laser or evaporative cooling is not possible. It has so far been limited to the cooling of other microscopic particles, with masses up to $90$ times larger than that of the coolant atom. Here we use ultracold atoms to sympathetically cool the vibrations of a Si$_3$N$_4$ nanomembrane, whose mass exceeds that of the atomic ensemble by a factor of $10^{10}$. The coupling of atomic and membrane vibrations is mediated by laser light over a macroscopic distance and enhanced by placing the m…
We have realized a hybrid optomechanical system by coupling ultracold atoms to a micromechanical membrane. The atoms are trapped in an optical lattice, which is formed by retro-reflection of a laser beam from the membrane surface. In this setup, the lattice laser light mediates an optomechanical coupling between membrane vibrations and atomic center-of-mass motion. We observe both the effect of the membrane vibrations onto the atoms as well as the backaction of the atomic motion onto the membrane. By coupling the membrane to laser-cooled atoms, we engineer the dissipation rate of the membrane.…
We study the optomechanical behaviour of a driven Fabry-Pérot cavity containing two vibrating dielectric membranes. We characterize the cavity-mode frequency shift as a function of the two-membrane positions, and report a $\sim 2.47$ gain in the optomechanical coupling strength of the membrane relative motion with respect to the single membrane case. This is achieved when the two membranes are properly positioned to form an inner cavity which is resonant with the driving field. We also show that this two-membrane system has the capability to tune the single-photon optomechanical coupling on de…
Membrane-in-the-middle optomechanics with a soft-clamped membrane at milliKelvin temperatures
本文提出无致动器光学腔与机械谐振器设计，解决毫开尔文温度下软钳位氮化硅薄膜光力学中的振动与吸收加热问题，并测得相干时间随腔内功率的标度关系。
We present an experimental study of dynamical back-action cooling of the fundamental vibrational mode of a thin semitransparent membrane placed within a high-finesse optical cavity. We study how the radiation pressure interaction modifies the mechanical response of the vibrational mode, and the experimental results are in agreement with a Langevin equation description of the coupled dynamics. The experiments are carried out in the resolved sideband regime, and we have observed cooling by a factor 350 We have also observed the mechanical frequency shift associated with the quadratic term in the…
We present the results of theoretical and experimental studies of dispersively coupled (or "membrane in the middle") optomechanical systems. We calculate the linear optical properties of a high finesse cavity containing a thin dielectric membrane. We focus on the cavity's transmission, reflection, and finesse as a function of the membrane's position along the cavity axis and as a function of its optical loss. We compare these calculations with measurements and find excellent agreement in cavities with empty-cavity finesses in the range 10^4 to 10^5. The imaginary part of the membrane's index o…
We report on the optical and mechanical characterization of arrays of parallel micromechanical membranes. Pairs of high-tensile stress, 100 nm-thick silicon nitride membranes are assembled parallel with each other with separations ranging from 8.5 to 200 $μ$m. Their optical properties are accurately determined using a combination of broadband and monochromatic illuminations and the lowest vibrational mode frequencies and mechanical quality factors are determined interferometrically. The results and techniques demonstrated are promising for investigations of collective phenomena in optomechanic…
We consider long-wave phonon-polaritons and longitudinal optical phonons in alkali-halide ionic crystals. The model of point charges that are polarized in the self-consistent electromagnetic field in a dielectric environment is used. The standard dispersion laws for both branches of phonon-polaritons and longitudinal optical phonons are obtained. The transversal optical phonon frequency is found from the electrostatic equilibrium condition. It is proved by comparison with tabular data that the found frequency coincides with the ion plasma frequency multiplied on the relation $\sqrt{(\varepsilo…
The radiation pressure of light can act to damp and cool the vibrational motion of a mechanical resonator. In understanding the quantum limits of this cooling, one must consider the effect of shot noise fluctuations on the final thermal occupation. In optomechanical sideband cooling in a cavity, the finite Stokes Raman scattering defined by the cavity linewidth combined with shot noise fluctuations dictates a quantum backaction limit, analogous to the Doppler limit of atomic laser cooling. In our work we sideband cool to the quantum backaction limit by using a micromechanical membrane precoole…
Membrane-in-the-middle optomechanical system and structural frequencies
针对含可移动介电膜的一维膜居中光机械腔，本文提出与膜位置无关的结构角频率，给出薄膜近似公式，并用多尺度解准确描述电磁势。
Full dynamics of two-membrane cavity optomechanics
本文研究了双膜腔光力学系统中非线性相互作用对动力学的影响，发现传统线性处理在某些参数域下无法准确描述膜的同步和纠缠特性。
We study the cavity mode frequencies of a Fabry-Pérot cavity containing two vibrating dielectric membranes. We derive the equations for the mode resonances and provide approximate analytical solutions for them as a function of the membrane positions, which act as an excellent approximation when the relative and center-of-mass position of the two membranes are much smaller than the cavity length. With these analytical solutions, one finds that extremely large optomechanical coupling of the membrane relative motion can be achieved in the limit of highly reflective membranes when the two membrane…
We study the non-linear dynamics of a multimode optomechanical system constituted of a driven high-finesse Fabry-Pérot cavity containing two vibrating dielectric membranes. The analytical study allows to derive a full and consistent description of the displacement detection by a probe beam in the non-linear regime, enabling the faithful detection of membrane displacements well above the usual sensing limit corresponding to the cavity linewidth. In the weak driving regime where the system is in a pre-synchronized situation, the unexcited oscillator has a small, synchronized component at the fre…
Two-membrane etalon
本文通过理论与实验研究由两片平行半透明薄膜构成的低精细度光学腔，建立可复现实验结果的解析模型，为多振子“中间薄膜”光力学提供完整建模基础。
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