Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode

Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7?±?0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.     

Circuit cavity electromechanics in the strong-coupling regime

Demonstrating and exploiting the quantum nature of macroscopic mechanical objects would help us to investigate directly the limitations of quantum-based measurements and quantum information protocols, as well as to test long-standing questions about macroscopic quantum coherence. Central to this effort is the necessity of long-lived mechanical states. Previous efforts have witnessed quantum behaviour, but for a low-quality-factor mechanical system. The field of cavity optomechanics and electromechanics, in which a high-quality-factor mechanical oscillator is parametrically coupled to an electromagnetic cavity resonance, provides a practical architecture for cooling, manipulation and detection of motion at the quantum level. One requirement is strong coupling, in which the interaction between the two systems is faster than the dissipation of energy from either system. Here, by incorporating a free-standing, flexible aluminium membrane into a lumped-element superconducting resonant cavity, we have increased the single-photon coupling strength between these two systems by more than two orders of magnitude, compared to previously obtained coupling strengths. A parametric drive tone at the difference frequency between the mechanical oscillator and the cavity resonance dramatically increases the overall coupling strength, allowing us to completely enter the quantum-enabled, strong-coupling regime. This is evidenced by a maximum normal-mode splitting of nearly six bare cavity linewidths. Spectroscopic measurements of these 'dressed states' are in excellent quantitative agreement with recent theoretical predictions. The basic circuit architecture presented here provides a feasible path to ground-state cooling and subsequent coherent control and measurement of long-lived quantum states of mechanical motion.     

Laser cooling of a nanomechanical oscillator into its quantum ground state

The simple mechanical oscillator, canonically consisting of a coupled mass-spring system, is used in a wide variety of sensitive measurements, including the detection of weak forces and small masses. On the one hand, a classical oscillator has a well-defined amplitude of motion; a quantum oscillator, on the other hand, has a lowest-energy state, or ground state, with a finite-amplitude uncertainty corresponding to zero-point motion. On the macroscopic scale of our everyday experience, owing to interactions with its highly fluctuating thermal environment a mechanical oscillator is filled with many energy quanta and its quantum nature is all but hidden. Recently, in experiments performed at temperatures of a few hundredths of a kelvin, engineered nanomechanical resonators coupled to electrical circuits have been measured to be oscillating in their quantum ground state. These experiments, in addition to providing a glimpse into the underlying quantum behaviour of mesoscopic systems consisting of billions of atoms, represent the initial steps towards the use of mechanical devices as tools for quantum metrology or as a means of coupling hybrid quantum systems. Here we report the development of a coupled, nanoscale optical and mechanical resonator formed in a silicon microchip, in which radiation pressure from a laser is used to cool the mechanical motion down to its quantum ground state (reaching an average phonon occupancy number of 0.85 ± 0.08). This cooling is realized at an environmental temperature of 20?K, roughly one thousand times larger than in previous experiments and paves the way for optical control of mesoscale mechanical oscillators in the quantum regime.     

Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane

Macroscopic mechanical objects and electromagnetic degrees of freedom can couple to each other through radiation pressure. Optomechanical systems in which this coupling is sufficiently strong are predicted to show quantum effects and are a topic of considerable interest. Devices in this regime would offer new types of control over the quantum state of both light and matter, and would provide a new arena in which to explore the boundary between quantum and classical physics. Experiments so far have achieved sufficient optomechanical coupling to laser-cool mechanical devices, but have not yet reached the quantum regime. The outstanding technical challenge in this field is integrating sensitive micromechanical elements (which must be small, light and flexible) into high-finesse cavities (which are typically rigid and massive) without compromising the mechanical or optical properties of either. A second, and more fundamental, challenge is to read out the mechanical element's energy eigenstate. Displacement measurements (no matter how sensitive) cannot determine an oscillator's energy eigenstate, and measurements coupling to quantities other than displacement have been difficult to realize in practice. Here we present an optomechanical system that has the potential to resolve both of these challenges. We demonstrate a cavity which is detuned by the motion of a 50-nm-thick dielectric membrane placed between two macroscopic, rigid, high-finesse mirrors. This approach segregates optical and mechanical functionality to physically distinct structures and avoids compromising either. It also allows for direct measurement of the square of the membrane's displacement, and thus in principle the membrane's energy eigenstate. We estimate that it should be practical to use this scheme to observe quantum jumps of a mechanical system, an important goal in the field of quantum measurement.     

失谐力光系统中的光子-声子转换和基态冷却

研究由辐射压力引起Fabry-Perot力光腔中动力学行为.从力光系统哈密顿量出发,探讨在失谐条件下力光腔中量子现象.引入散射矩阵方案来论证光子和声子以有效并且可逆方转换.这对于光学光子和微械阵子之间量子态转变提供了一个可行方案.光声转变预着一可行量子光学器件.同我们用量子郎之万方法和主方程方法这两方法推导最声子占有数来研究械振子态冷却,并且对这两方法进行了参数比较.出在么条件下哪方法更实用.     

声子之间相互作用对量子点中激子性质的影响

本文采用线性组合算符和幺正变换方法研究了抛物型量子点中强耦合激子的性质．当计及电子在反冲效应中发射和吸收不同波矢的声子之间的相互作用时,讨论了量子点中激子的基态能量的影响．以氯化铊半导体为例进行了数值计算,结果表明：激子的基态能量随量子点半径的增大而减小,随量子点受限强度的增大而增大．     

Radiation-pressure cooling and optomechanical instability of a micromirror

Recent table-top optical interferometry experiments and advances in gravitational-wave detectors have demonstrated the capability of optical interferometry to detect displacements with high sensitivity. Operation at higher powers will be crucial for further sensitivity enhancement, but dynamical effects caused by radiation pressure on the interferometer mirrors must be taken into account, and the appearance of optomechanical instabilities may jeopardize the stable operation of the next generation of interferometers. These instabilities are the result of a nonlinear coupling between the motion of the mirrors and the optical field, which modifies the effective dynamics of the mirror. Such 'optical spring' effects have already been demonstrated for the mechanical damping of an electromagnetic waveguide with a moving wall, the resonance frequency of a specially designed flexure oscillator, and the optomechanical instability of a silica microtoroidal resonator. Here we present an experiment where a micromechanical resonator is used as a mirror in a very high-finesse optical cavity, and its displacements are monitored with unprecedented sensitivity. By detuning the laser frequency with respect to the cavity resonance, we have observed a drastic cooling of the microresonator by intracavity radiation pressure, down to an effective temperature of 10 kelvin. For opposite detuning, efficient heating is observed, as well as a radiation-pressure-induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a micromechanical resonator, either by passive or active cooling techniques.     

量子阱中极化子基态自陷能的耦合求解方法

用一种新的变分方法研究准二维量子阱中极化子系统的自陷能等问题．只有纵光学声子和表面声子的对称模对极化子的基态能量有贡献．作为例子,对ＧｓＡｓ／ＡｌＡｓ量子阱中极化子的基态波函数和自陷能进行了数值分析．与先前的结果相比,当有效耦合常数稍大时极化子具有更低的自陷能．     

Self-cooling of a micromirror by radiation pressure

Cooling of mechanical resonators is currently a popular topic in many fields of physics including ultra-high precision measurements, detection of gravitational waves and the study of the transition between classical and quantum behaviour of a mechanical system. Here we report the observation of self-cooling of a micromirror by radiation pressure inside a high-finesse optical cavity. In essence, changes in intensity in a detuned cavity, as caused by the thermal vibration of the mirror, provide the mechanism for entropy flow from the mirror's oscillatory motion to the low-entropy cavity field. The crucial coupling between radiation and mechanical motion was made possible by producing free-standing micromirrors of low mass (m approximately 400 ng), high reflectance (more than 99.6%) and high mechanical quality (Q approximately 10,000). We observe cooling of the mechanical oscillator by a factor of more than 30; that is, from room temperature to below 10 K. In addition to purely photothermal effects we identify radiation pressure as a relevant mechanism responsible for the cooling. In contrast with earlier experiments, our technique does not need any active feedback. We expect that improvements of our method will permit cooling ratios beyond 1,000 and will thus possibly enable cooling all the way down to the quantum mechanical ground state of the micromirror.     

Rashba效应影响下InAs/GaAs自组织量子点中极化子性质

考虑Rashab自旋-轨道相互作用对半导体量子点中极化子基态能量的影响．采用LLP中耦合的方法处理了电子-声子相互作用．结果表明由于Rashba效应的影响使得极化子的基态能量分列为上下两支而且Rashba自旋-轨道相互作用能与总的基态能及其它能量成分间的比例关系，随电子波矢K变化非常显著．Rashba自旋-轨道相互用作使得量子点中极化子基态能量在无任何外磁场的情况下发生分裂，所以完全不同于强磁场影响下的简单Zeeman效应，然而，自旋-轨道相互作用引起的分裂有时掺杂着Zeeman分裂。因此它引起的分裂属于复杂分裂．声子对总能量的贡献为负，由于声子的存在极化子争裂能较裸电子更为稳定．     

Sub-kelvin optical cooling of a micromechanical resonator

Micromechanical resonators, when cooled down to near their ground state, can be used to explore quantum effects such as superposition and entanglement at a macroscopic scale. Previously, it has been proposed to use electronic feedback to cool a high frequency (10 MHz) resonator to near its ground state. In other work, a low frequency resonator was cooled from room temperature to 18 K by passive optical feedback. Additionally, active optical feedback of atomic force microscope cantilevers has been used to modify their response characteristics, and cooling to approximately 2 K has been measured. Here we demonstrate active optical feedback cooling to 135 +/- 15 mK of a micromechanical resonator integrated with a high-quality optical resonator. Additionally, we show that the scheme should be applicable at cryogenic base temperatures, allowing cooling to near the ground state that is required for quantum experiments--near 100 nK for a kHz oscillator.     

Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip

An optical cavity enhances the interaction between atoms and light, and the rate of coherent atom-photon coupling can be made larger than all decoherence rates of the system. For single atoms, this 'strong coupling regime' of cavity quantum electrodynamics has been the subject of many experimental advances. Efforts have been made to control the coupling rate by trapping the atom and cooling it towards the motional ground state; the latter has been achieved in one dimension so far. For systems of many atoms, the three-dimensional ground state of motion is routinely achieved in atomic Bose-Einstein condensates (BECs). Although experiments combining BECs and optical cavities have been reported recently, coupling BECs to cavities that are in the strong-coupling regime for single atoms has remained an elusive goal. Here we report such an experiment, made possible by combining a fibre-based cavity with atom-chip technology. This enables single-atom cavity quantum electrodynamics experiments with a simplified set-up and realizes the situation of many atoms in a cavity, each of which is identically and strongly coupled to the cavity mode. Moreover, the BEC can be positioned deterministically anywhere within the cavity and localized entirely within a single antinode of the standing-wave cavity field; we demonstrate that this gives rise to a controlled, tunable coupling rate. We study the heating rate caused by a cavity transmission measurement as a function of the coupling rate and find no measurable heating for strongly coupled BECs. The spectrum of the coupled atoms-cavity system, which we map out over a wide range of atom numbers and cavity-atom detunings, shows vacuum Rabi splittings exceeding 20 gigahertz, as well as an unpredicted additional splitting, which we attribute to the atomic hyperfine structure. We anticipate that the system will be suitable as a light-matter quantum interface for quantum information.     

Coupled quantized mechanical oscillators

The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models. Realizations of harmonic oscillators in the quantum regime include electromagnetic fields in a cavity and the mechanical modes of a trapped atom or macroscopic solid. Quantized interaction between two motional modes of an individual trapped ion has been achieved by coupling through optical fields, and entangled motion of two ions in separate locations has been accomplished indirectly through their internal states. However, direct controllable coupling between quantized mechanical oscillators held in separate locations has not been realized previously. Here we implement such coupling through the mutual Coulomb interaction of two ions held in trapping potentials separated by 40?μm (similar work is reported in a related paper). By tuning the confining wells into resonance, energy is exchanged between the ions at the quantum level, establishing that direct coherent motional coupling is possible for separately trapped ions. The system demonstrates a building block for quantum information processing and quantum simulation. More broadly, this work is a natural precursor to experiments in hybrid quantum systems, such as coupling a trapped ion to a quantized macroscopic mechanical or electrical oscillator.     

Laser cooling and real-time measurement of the nuclear spin environment of a solid-state qubit

Control over quantum dynamics of open systems is one of the central challenges in quantum science and engineering. Coherent optical techniques, such as coherent population trapping involving dark resonances, are widely used to control quantum states of isolated atoms and ions. In conjunction with spontaneous emission, they allow for laser cooling of atomic motion, preparation and manipulation of atomic states, and rapid quantum optical measurements that are essential for applications in metrology. Here we show that these techniques can be applied to monitor and control individual atom-like impurities, and their local environment, in the solid state. Using all-optical manipulation of the electronic spin of an individual nitrogen-vacancy colour centre in diamond, we demonstrate optical cooling, real-time measurement and conditional preparation of its nuclear spin environment by post-selection. These methods offer potential applications ranging from all-optical nanomagnetometry to quantum feedback control of solid-state qubits, and may lead to new approaches for quantum information storage and processing.     

Rashba效应影响下半导体量子点中强耦合极化子的声子平均数

采用改进的线性组合算符方法，研究了Rashba效应影响下半导体量子点中强耦合极化子的光学声子平均数．导出在电子-体纵光学声子（LO）强耦合时抛物量子点中极化子的光学声子平均数、振动频率、相互作用能和有效质量随受限强度和Rashba自旋-轨道耦合常数的变化．数值计算结果表明Rashba自旋-轨道相互作用使极化子的有效质量、基态能分裂为上下两支，随耦合常数的增加极化子基态能量、有效质量表现为增加和较少两种截然相反的情形；Rashba自旋-轨道相互作用影响下强耦合极化子的光学声子平均数随量子点的受限强度、电子声子耦合强度增大而增大，极化子的相互作用能随受限强度的增加先急剧增加，当达到极值后随受限强度的增加而急剧减少．     

声子之间相互作用对弱耦合量子点中极化子内声子平均数的影响

采用线性组合算符和幺正变换方法,研究了量子点中弱耦合极化子的性质。在考虑声子之间相互作用时,讨论了极化子的基态能量随量子点受限长度和平均声子数的变化关系。数值计算结果表明：极化子的基态能量和平均声子数都随量子点受限长度的增加而减少,平均声子数随基态能量的增加而增加。在基态能量相同时,考虑声子之间相互作用时的平均声子数比不考虑声子相互作用时的平均声子数要小一些,即声子之间的相互作用对量子点中平均声子数影响不能忽略。     

Microwave quantum logic gates for trapped ions

Control over physical systems at the quantum level is important in fields as diverse as metrology, information processing, simulation and chemistry. For trapped atomic ions, the quantized motional and internal degrees of freedom can be coherently manipulated with laser light. Similar control is difficult to achieve with radio-frequency or microwave radiation: the essential coupling between internal degrees of freedom and motion requires significant field changes over the extent of the atoms' motion, but such changes are negligible at these frequencies for freely propagating fields. An exception is in the near field of microwave currents in structures smaller than the free-space wavelength, where stronger gradients can be generated. Here we first manipulate coherently (on timescales of 20 nanoseconds) the internal quantum states of ions held in a microfabricated trap. The controlling magnetic fields are generated by microwave currents in electrodes that are integrated into the trap structure. We also generate entanglement between the internal degrees of freedom of two atoms with a gate operation suitable for general quantum computation; the entangled state has a fidelity of 0.76(3), where the uncertainty denotes standard error of the mean. Our approach, which involves integrating the quantum control mechanism into the trapping device in a scalable manner, could be applied to quantum information processing, simulation and spectroscopy.     

高斯脉冲冷却机械振子

光力学系统常被用来实现机械振子的基态冷却,进而实现宏观量子态制备.如何获得更好的冷却效果是光力冷却的核心问题.然而理论证明,采用单束连续光来驱动机械振子存在冷却极限,即无法通过提高驱动强度或振子频率来获得更低的冷却比率,因而需要发展新的动力学理论.我们探讨采用高斯脉冲来驱动机械振子,这一光力学系统在绝大多数情况下不存在稳态,无法使用常用的线性化展开来处理.我们采用新的线性化方法获得有效哈密顿量,由此可以获得光力学系统的动力学演化,进而直接得到系统热声子数的变化.通过详细分析脉冲波形、脉冲强度以及脉冲宽度对热声子数演化的影响,证明选择合适的驱动强度、脉冲宽度,机械振子可以被单个脉冲冷却到基态,并通过多个脉冲来保持在基态.甚至利用脉冲波形中驱动强度的增、减,可以延缓压缩效应对光力系统造成的加热.由此可以突破单束连续驱动的冷却极限,甚至通过强、短高斯脉冲可以将冷却极限降低1/2,展现出脉冲驱动冷却光力学系统的优势.     

Climbing the Jaynes-Cummings ladder and observing its nonlinearity in a cavity QED system

The field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has gained new momentum by recent reports of quantum optical experiments with solid-state semiconducting and superconducting systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter-light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set-up, in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high-quality on-chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits (photons) and stationary qubits for applications in quantum information processing and communication.     

考虑Rashba效应自组织量子点中极化子性质

在对半导体量子点的研究中考虑自旋一轨道相互作用对极化子基态能量的影响．采用LLP变分的方法研究了电子一声子相互作用．结果表明声子对极化子基态能量起了很重要的作用,而且由于极化子分裂能对极化子基态能量的贡献很大,故在量子点中研究极化子性质时不可忽略极化子分裂能的影响．自旋分裂能随动量增加呈抛物线型增加．随Rashba自旋轨道耦合常数的增加极化子基态能量表现为增加和减少两种截然相反的情况,而两个分裂态中自旋向下的能态更稳定．Rashba效应不可忽略．