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.     

Wave-particle duality of C(60) molecules

Quantum superposition lies at the heart of quantum mechanics and gives rise to many of its paradoxes. Superposition of de Broglie matter waves' has been observed for massive particles such as electrons, atoms and dimers, small van der Waals clusters, and neutrons. But matter wave interferometry with larger objects has remained experimentally challenging, despite the development of powerful atom interferometric techniques for experiments in fundamental quantum mechanics, metrology and lithography. Here we report the observation of de Broglie wave interference of C(60) molecules by diffraction at a material absorption grating. This molecule is the most massive and complex object in which wave behaviour has been observed. Of particular interest is the fact that C(60) is almost a classical body, because of its many excited internal degrees of freedom and their possible couplings to the environment. Such couplings are essential for the appearance of decoherence, suggesting that interference experiments with large molecules should facilitate detailed studies of this process.     

Decoherence of quantum superpositions through coupling to engineered reservoirs

The theory of quantum mechanics applies to closed systems. In such ideal situations, a single atom can, for example, exist simultaneously in a superposition of two different spatial locations. In contrast, real systems always interact with their environment, with the consequence that macroscopic quantum superpositions (as illustrated by the 'Schrodinger's cat' thought-experiment) are not observed. Moreover, macroscopic superpositions decay so quickly that even the dynamics of decoherence cannot be observed. However, mesoscopic systems offer the possibility of observing the decoherence of such quantum superpositions. Here we present measurements of the decoherence of superposed motional states of a single trapped atom. Decoherence is induced by coupling the atom to engineered reservoirs, in which the coupling and state of the environment are controllable. We perform three experiments, finding that the decoherence rate scales with the square of a quantity describing the amplitude of the superposition state.     

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.     

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.     

Decoherence in crystals of quantum molecular magnets

Quantum decoherence is a central concept in physics. Applications such as quantum information processing depend on understanding it; there are even fundamental theories proposed that go beyond quantum mechanics, in which the breakdown of quantum theory would appear as an 'intrinsic' decoherence, mimicking the more familiar environmental decoherence processes. Such applications cannot be optimized, and such theories cannot be tested, until we have a firm handle on ordinary environmental decoherence processes. Here we show that the theory for insulating electronic spin systems can make accurate and testable predictions for environmental decoherence in molecular-based quantum magnets. Experiments on molecular magnets have successfully demonstrated quantum-coherent phenomena but the decoherence processes that ultimately limit such behaviour were not well constrained. For molecular magnets, theory predicts three principal contributions to environmental decoherence: from phonons, from nuclear spins and from intermolecular dipolar interactions. We use high magnetic fields on single crystals of Fe(8) molecular magnets (in which the Fe ions are surrounded by organic ligands) to suppress dipolar and nuclear-spin decoherence. In these high-field experiments, we find that the decoherence time varies strongly as a function of temperature and magnetic field. The theoretical predictions are fully verified experimentally, and there are no other visible decoherence sources. In these high fields, we obtain a maximum decoherence quality-factor of 1.49?×?10(6); our investigation suggests that the environmental decoherence time can be extended up to about 500 microseconds, with a decoherence quality factor of ～6?×?10(7), by optimizing the temperature, magnetic field and nuclear isotopic concentrations.     

量子力学基础实验的新效用

从量子力学两个基础实验———电子双缝干涉实验、Stern -Gerlach实验出发 ,引出量子信息理论的两个新概念———量子退相干与量子纠缠。并详细介绍了量子退相干概念和量子纠缠概念以及它们在量子信息领域中的应用。这样在学生可接受的范围内把物理前沿的新概念引入到了实验教学 ,从而拓宽了学生的知识面 ,加深了对物理概念的理解 ,发掘了基础实验的新效用。     

Quantum oscillations in a molecular magnet

The term 'molecular magnet' generally refers to a molecular entity containing several magnetic ions whose coupled spins generate a collective spin, S (ref. 1). Such complex multi-spin systems provide attractive targets for the study of quantum effects at the mesoscopic scale. In these molecules, the large energy barriers between collective spin states can be crossed by thermal activation or quantum tunnelling, depending on the temperature or an applied magnetic field. There is the hope that these mesoscopic spin states can be harnessed for the realization of quantum bits--'qubits', the basic building blocks of a quantum computer--based on molecular magnets. But strong decoherence must be overcome if the envisaged applications are to become practical. Here we report the observation and analysis of Rabi oscillations (quantum oscillations resulting from the coherent absorption and emission of photons driven by an electromagnetic wave) of a molecular magnet in a hybrid system, in which discrete and well-separated magnetic clusters are embedded in a self-organized non-magnetic environment. Each cluster contains 15 antiferromagnetically coupled S = 1/2 spins, leading to an S = 1/2 collective ground state. When this system is placed into a resonant cavity, the microwave field induces oscillatory transitions between the ground and excited collective spin states, indicative of long-lived quantum coherence. The present observation of quantum oscillations suggests that low-dimension self-organized qubit networks having coherence times of the order of 100 micros (at liquid helium temperatures) are a realistic prospect.     

一个新形式Kerr黑洞的纯热辐射谱与隧穿辐射谱的比较研究

根据Hawking热辐射理论和Parikh的半经典量子隧穿模型,作者选择了一种零标架对该Kerr黑洞Dirac 粒子热辐射的研究表明,其热辐射谱是纯热谱.对该Kerr黑洞量子隧穿辐射的研究结果却表明,在能量守恒和角动量守恒的条件下,此黑洞事件视界处粒子的隧穿率与Bekenstein-Hawking熵变有关,真实的辐射谱不再是严格的纯热谱,但满足量子力学中的么正性原理,这是对Hawking纯热谱的一种修正.     

Correlation,entropy, and information transfer in black hole radiation

Since the discovery of Hawking radiation, its consistency with quantum theory has been widely questioned. In the widely described picture, irrespective of what initial state a black hole starts with before collapsing, it eventually evolves into a thermal state of Hawking radiations after the black hole is exhausted. This scenario violates the principle of unitarity as required for quantum mechanics and leads to the acclaimed ‘‘information loss paradox'. This paradox has become an obstacle or a reversed touchstone for any possible theory to unify the gravity and quantum mechanics. Based on the results from Hawking radiation as tunneling, we recently show that Hawking radiations can carry off all information about the collapsed matter in a black hole. After discovering the existence of information-carrying correlation, we show in great detail that entropy is conserved for Hawking radiation based on standard probability theory and statistics. We claim that information previously considered lost remains hidden inside Hawking radiation. More specifically, it is encoded into correlations between Hawking radiations. Our study thus establishes harmony between Hawking radiation and the unitarity of quantum mechanics, which establishes the basis for a significant milestone toward resolving the long-standing information loss paradox. The paper provides a brief review of the exciting development on Hawking radiation. In addition to summarize our own work on this subject, we compare and address other related studies.     

量子相干性解除及其熵增效应的环境动力学模型

提出五个环境作用导致量子系统相干性解除及其熵增效应的量子动力学模型。这个模型具有一定的普适性，它表明，当系统耦合于适当的环境，Ｓｃｈｒｏｄｉｎｇｅｒ方程支配的动力学演化在宏观极限下将自动实现量子相干性解除和系统熵的增加。伴随着熵由零增加到最大，量子系统将由完全相干的纯态，经历相干性部分解除的中间混合态，最后变为相干性解除的最大混合态。     

退相干和量子力学的诠释

近二十年来,针对量子力学围绕其概念基础产生的哲学争议,产生了不同于“哥本哈根诠释”和“正统”解释的可供选择的解诠方案。在解决测量问题上,退相干单独不能解决测量问题,但是退相干把环境相互作用包括进来不仅提出了新的观念问题,而且暗示了基本问题的解决方案。     

平面对称黑洞的隧穿辐射特征的研究

采用Parikh的半经典量子隧穿模型,研究了Antide Sitter时空中的平面对称黑洞的量子隧穿效应.结果表明,在能量守恒的条件下,此黑洞事件视界处粒子的隧穿率与BekensteinHawking熵变有关,真实的辐射谱不再是纯热谱,但满足量子力学中的么正性原理.     

Electronic read-out of a single nuclear spin using a molecular spin transistor

Quantum control of individual spins in condensed-matter devices is an emerging field with a wide range of applications, from nanospintronics to quantum computing. The electron, possessing spin and orbital degrees of freedom, is conventionally used as the carrier of quantum information in proposed devices. However, electrons couple strongly to the environment, and so have very short relaxation and coherence times. It is therefore extremely difficult to achieve quantum coherence and stable entanglement of electron spins. Alternative concepts propose nuclear spins as the building blocks for quantum computing, because such spins are extremely well isolated from the environment and less prone to decoherence. However, weak coupling comes at a price: it remains challenging to address and manipulate individual nuclear spins. Here we show that the nuclear spin of an individual metal atom embedded in a single-molecule magnet can be read out electronically. The observed long lifetimes (tens of seconds) and relaxation characteristics of nuclear spin at the single-atom scale open the way to a completely new world of devices in which quantum logic may be implemented.     

含互感耦合的超导磁通量子比特消相干的研究

在Born—Markov近似下，根据Bloch—Redfield方程，给出了一种计算超导量子比特能量弛豫时T1与消相干时间T2的方法。在此基础上，研究了一个含互感耦合的超导磁通量子比特的消相干现象，并给出了该超导量子比特能量弛豫时间Ｔ1与消相干时间Ｔ2。结果表明：对于研究的磁通量子比特，在其他条件不变时且环境热库等效为一个纯电阻时，则去相位时间Tφ，由高能级｜j〉向低能级｜i〉的能量弛豫时间T1和量子系统的消相干时间疋都与耗散成正比。     

Allowed and forbidden transitions in artificial hydrogen and helium atoms

The strength of radiative transitions in atoms is governed by selection rules that depend on the occupation of atomic orbitals with electrons. Experiments have shown similar electron occupation of the quantized energy levels in semiconductor quantum dots--often described as artificial atoms. But unlike real atoms, the confinement potential of quantum dots is anisotropic, and the electrons can easily couple with phonons of the material. Here we report electrical pump-and-probe experiments that probe the allowed and 'forbidden' transitions between energy levels under phonon emission in quantum dots with one or two electrons (artificial hydrogen and helium atoms). The forbidden transitions are in fact allowed by higher-order processes where electrons flip their spin. We find that the relaxation time is about 200 micro s for forbidden transitions, 4 to 5 orders of magnitude longer than for allowed transitions. This indicates that the spin degree of freedom is well separated from the orbital degree of freedom, and that the total spin in the quantum dots is an excellent quantum number. This is an encouraging result for potential applications of quantum dots as basic entities for spin-based quantum information storage.     

Quantum superposition of distinct macroscopic states

In 1935, Schrodinger attempted to demonstrate the limitations of quantum mechanics using a thought experiment in which a cat is put in a quantum superposition of alive and dead states. The idea remained an academic curiosity until the 1980s when it was proposed that, under suitable conditions, a macroscopic object with many microscopic degrees of freedom could behave quantum mechanically, provided that it was sufficiently decoupled from its environment. Although much progress has been made in demonstrating the macroscopic quantum behaviour of various systems such as superconductors, nanoscale magnets, laser-cooled trapped ions, photons in a microwave cavity and C60 molecules, there has been no experimental demonstration of a quantum superposition of truly macroscopically distinct states. Here we present experimental evidence that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount of current flowing anticlockwise.     

自发辐射诱导原子质心运动退相干的理论研究

研究单个二能级原子与真空电磁场的相互作用,给出了总系统的薛定谔方程的解析波函数,并分析得出原子质心运动的约化密度矩阵。结果表明原子内部电子态与真空场的相互作用会诱导原子的质心运动与原子的内部电子态发生纠缠,从而会导致原子的质心运动发生量子退相干。文中还给出了退相干因子的解析表达式,并通过图形演示了原子质心运动退相干的动力学演化情况,以及与原子的空间尺度和原子-场耦合强度的相关性。     

Experimental entanglement purification of arbitrary unknown states

Distribution of entangled states between distant locations is essential for quantum communication over large distances. But owing to unavoidable decoherence in the quantum communication channel, the quality of entangled states generally decreases exponentially with the channel length. Entanglement purification--a way to extract a subset of states of high entanglement and high purity from a large set of less entangled states--is thus needed to overcome decoherence. Besides its important application in quantum communication, entanglement purification also plays a crucial role in error correction for quantum computation, because it can significantly increase the quality of logic operations between different qubits. Here we demonstrate entanglement purification for general mixed states of polarization-entangled photons using only linear optics. Typically, one photon pair of fidelity 92% could be obtained from two pairs, each of fidelity 75%. In our experiments, decoherence is overcome to the extent that the technique would achieve tolerable error rates for quantum repeaters in long-distance quantum communication. Our results also imply that the requirement of high-accuracy logic operations in fault-tolerant quantum computation can be considerably relaxed.