Optimal quantum measurement of finite-dimensional systems and coherent anti-Stokes Raman spectroscopy

Quantum measurement is a fundamental problem in quantum control theory and experiments.It can obtain unknown information of quantum systems,and can also change state of the systems inevitably.Both the outcome and back action could be used to control quantum systems.This paper presents recent research progress about optimal control of state transformation in finite-dimensional quantum systems by back action of non-selective quantum measurement,and optimal control of signal and background of CARS (coherent anti-Stokes Raman spectroscopy) by phase shaping technique.In measurement sequence control of finite-dimensional quantum systems,the necessary condition for critical points of the underlying state transformation objective is found to be a highly symmetric form as a chain of equalities,and analytical and numerical solutions in several cases are explored.In the CARS control,it is found that the maximal resonant signal and minimal background at a specific frequency can be achieved by shaping the probe pulse only while keeping pump and Stokes pulses in transform limited forms (TLFs).An arctan-type phase function is obtained for the probe pulse to simultaneously enhance the resonant signal and suppress the background.For broadband background elimination,we find that the optimal phase shaping scheme of probe pulse is quasi-time-delay while keeping the pump and Stokes pulses in TLFs.These conclusions could help design control strategies of quantum devices.     

Using photoemission spectroscopy to probe a strongly interacting Fermi gas

Ultracold atomic gases provide model systems in which to study many-body quantum physics. Recent experiments using Fermi gases have demonstrated a phase transition to a superfluid state with strong interparticle interactions. This system provides a realization of the 'BCS-BEC crossover' connecting the physics of Bardeen-Cooper-Schrieffer (BCS) superconductivity with that of Bose-Einstein condensates (BECs). Although many aspects of this system have been investigated, it has not yet been possible to measure the single-particle excitation spectrum (a fundamental property directly predicted by many-body theories). Here we use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion in a strongly interacting Fermi gas of (40)K atoms. In the experiments, a radio-frequency photon ejects an atom from the strongly interacting system by means of a spin-flip transition to a weakly interacting state. We measure the occupied density of single-particle states at the cusp of the BCS-BEC crossover and on the BEC side of the crossover, and compare these results to that for a nearly ideal Fermi gas. We show that, near the critical temperature, the single-particle spectral function is dramatically altered in a way that is consistent with a large pairing gap. Our results probe the many-body physics in a way that could be compared to data for the high-transition-temperature superconductors. As in photoemission spectroscopy for electronic materials, our measurement technique for ultracold atomic gases directly probes low-energy excitations and thus can reveal excitation gaps and/or pseudogaps. Furthermore, this technique can provide an analogue of angle-resolved photoemission spectroscopy for probing anisotropic systems, such as atoms in optical lattice potentials.     

Geometric quantum computation using nuclear magnetic resonance

A significant development in computing has been the discovery that the computational power of quantum computers exceeds that of Turing machines. Central to the experimental realization of quantum information processing is the construction of fault-tolerant quantum logic gates. Their operation requires conditional quantum dynamics, in which one sub-system undergoes a coherent evolution that depends on the quantum state of another sub-system; in particular, the evolving sub-system may acquire a conditional phase shift. Although conventionally dynamic in origin, phase shifts can also be geometric. Conditional geometric (or 'Berry') phases depend only on the geometry of the path executed, and are therefore resilient to certain types of errors; this suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations. Nuclear magnetic resonance techniques have already been used to demonstrate both simple quantum information processing and geometric phase shifts. Here we combine these ideas by performing a nuclear magnetic resonance experiment in which a conditional Berry phase is implemented, demonstrating a controlled phase shift gate.     

Demonstration of conditional gate operation using superconducting charge qubits

Following the demonstration of coherent control of the quantum state of a superconducting charge qubit, a variety of qubits based on Josephson junctions have been implemented. Although such solid-state devices are not currently as advanced as microscopic qubits based on nuclear magnetic resonance and ion trap technologies, the potential scalability of the former systems--together with progress in their coherence times and read-out schemes--makes them strong candidates for the building block of a quantum computer. Recently, coherent oscillations and microwave spectroscopy of capacitively coupled superconducting qubits have been reported; the next challenging step towards quantum computation is the realization of logic gates. Here we demonstrate conditional gate operation using a pair of coupled superconducting charge qubits. Using a pulse technique, we prepare different input states and show that their amplitude can be transformed by controlled-NOT (C-NOT) gate operation, although the phase evolution during the gate operation remains to be clarified.     

Energy spectra of quantum rings.

Quantum mechanical experiments in ring geometries have long fascinated physicists. Open rings connected to leads, for example, allow the observation of the Aharonov-Bohm effect, one of the best examples of quantum mechanical phase coherence. The phase coherence of electrons travelling through a quantum dot embedded in one arm of an open ring has also been demonstrated. The energy spectra of closed rings have only recently been studied by optical spectroscopy. The prediction that they allow persistent current has been explored in various experiments. Here we report magnetotransport experiments on closed rings in the Coulomb blockade regime. Our experiments show that a microscopic understanding of energy levels, so far limited to few-electron quantum dots, can be extended to a many-electron system. A semiclassical interpretation of our results indicates that electron motion in the rings is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots. This opens a way to experiments where even more complex structures can be investigated at a quantum mechanical level.     

Quantum suppression of superconductivity in ultrathin nanowires

It is of fundamental importance to establish whether there is a limit to how thin a superconducting wire can be, while retaining its superconducting character--and if there is a limit, to determine what sets it. This issue may also be of practical importance in defining the limit to miniaturization of superconducting electronic circuits. At high temperatures, the resistance of linear superconductors is caused by excitations called thermally activated phase slips. Quantum tunnelling of phase slips is another possible source of resistance that is still being debated. It has been theoretically predicted that such quantum phase slips can destroy superconductivity in very narrow wires. Here we report resistance measurements on ultrathin (< or = 10 nm) nanowires produced by coating carbon nanotubes with a superconducting Mo-Ge alloy. We find that nanowires can be superconducting or insulating depending on the ratio of their normal-state resistance (R(N)) to the quantum resistance for Cooper pairs (Rq). If R(N) < Rq, quantum tunnelling of phase slips is prohibited by strong damping, and so the wires stay superconducting. In contrast, we observe an insulating state for R(N) > Rq, which we explain in terms of proliferation of quantum phase slips and a corresponding localization of Cooper pairs.     

囚禁离子简并混合态的几何相位

讨论了离子阱中简并混合态的几何相位及相干度.计算得出混合态几何相位由演化时间,初态确定以及在离子的作用.另外,我们还计算出在特殊的作用下,几何相位不随离子的初态变化而变化.囚禁离子的高效检测性意味着本文所研究的混合态几何相位能够被验证.     

整形啁啾脉冲光场作用下的量子相干控制与量子全息

在一级微扰理论近似下,研究了整形啁啾脉冲光场与二能级原子系统作用过程中的量子相干控制问题.利用惠更斯-菲涅耳原理解释了整形脉冲光场作用下量子态波函数的演化过程类似于时域＂光栅衍射＂效应;利用菲涅耳波带片方法研究了布居几率的增强效应.基于利用整形脉冲实现的量子相干控制和量子全息思想在理论上提出并论证了测量波函数的一种新方法.     

Coherent dynamics of a flux qubit coupled to a harmonic oscillator

In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits (qubits). Single-qubit operations, direct coupling between two qubits and the realization of a quantum gate have been reported. However, complex manipulation of entangled states-such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments and cavity quantum electrodynamics-has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system.     

Progressive field-state collapse and quantum non-demolition photon counting

The irreversible evolution of a microscopic system under measurement is a central feature of quantum theory. From an initial state generally exhibiting quantum uncertainty in the measured observable, the system is projected into a state in which this observable becomes precisely known. Its value is random, with a probability determined by the initial system's state. The evolution induced by measurement (known as 'state collapse') can be progressive, accumulating the effects of elementary state changes. Here we report the observation of such a step-by-step collapse by non-destructively measuring the photon number of a field stored in a cavity. Atoms behaving as microscopic clocks cross the cavity successively. By measuring the light-induced alterations of the clock rate, information is progressively extracted, until the initially uncertain photon number converges to an integer. The suppression of the photon number spread is demonstrated by correlations between repeated measurements. The procedure illustrates all the postulates of quantum measurement (state collapse, statistical results and repeatability) and should facilitate studies of non-classical fields trapped in cavities.     

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.     

Tunable ion-photon entanglement in an optical cavity

Proposed quantum networks require both a quantum interface between light and matter and the coherent control of quantum states. A quantum interface can be realized by entangling the state of a single photon with the state of an atomic or solid-state quantum memory, as demonstrated in recent experiments with trapped ions, neutral atoms, atomic ensembles and nitrogen-vacancy spins. The entangling interaction couples an initial quantum memory state to two possible light-matter states, and the atomic level structure of the memory determines the available coupling paths. In previous work, the transition parameters of these paths determined the phase and amplitude of the final entangled state, unless the memory was initially prepared in a superposition state (a step that requires coherent control). Here we report fully tunable entanglement between a single (40)Ca(+) ion and the polarization state of a single photon within an optical resonator. Our method, based on a bichromatic, cavity-mediated Raman transition, allows us to select two coupling paths and adjust their relative phase and amplitude. The cavity setting enables intrinsically deterministic, high-fidelity generation of any two-qubit entangled state. This approach is applicable to a broad range of candidate systems and thus is a promising method for distributing information within quantum networks.     

利用动力学去耦合脉冲增大和调节量子相干性和三体纠缠

本文研究了动力学去耦合脉冲对腔量子电动力学系统中量子相干性, 量子失谐和量子纠缠的影响, 发现动力学去耦合脉冲不仅能够增大系统中两原子之间的量子相干性, 同时也能增大它们之间非经典关联（量子失谐和量子纠缠）. 同时, 凭借迹距离的方法, 探讨了动力学去耦合脉冲增大两原子之间量子相干性的原因, 通过探究可以看出动力学去耦合脉冲能够控制和加速量子信息从其他子系统回流到两个原子中去, 并减少两原子子系统和其他子系统之间的量子信息流动, 从而增加两原子间的量子相干性和非经典关联. 最后, 利用保真度的方法研究了系统中三体纠缠出现的情况, 结果显示在不同的时间, 系统中会出现三体纠缠, 特别值得指出的是, 可以通过动力学去耦合脉冲来调节和增加系统中三体纠缠出现的时间.     

原子分子体系的引力效应

寻找完整的量子引力理论是目前理论物理中的前沿热点问题之一,而黑洞热力学和量子干涉仪探测引力效应被认为是正在形成的量子引力理论的两个重要的"实验区".前者通过将量子概念引入到广义相对论来检验二者如何结合,特别是量子力学幺正性将在这两个理论的结合中经受严峻考验;而后者通过量子系统在引力场背景中的演化来试验引力对系统量子属性的影响,在这一方面广义相对论等效原理在微观粒子领域将接受越来越严格的实验检验.目前,原子分子物理实验中出现了类似黑洞辐射的现象,然而,这些现象出现的理论机制还不是非常明确,究竟能否用目前已有的理论解释,或者还是需要构建新的理论来解释也是不清楚的,但是无论如何,这些现象的出现为实验研究量子引力理论打开了一扇窗户.另一方面,人们已经使用量子系统测量一些弱引力效应,这不仅为研究引力对量子系统的影响提供了便利条件,也为研究二者结合提供了一个好的突破口.本综述将结合我们近几年的工作,围绕原子分子体系中的强引力和弱引力效应来介绍和讨论这些问题.     

Quantum jumps of light recording the birth and death of a photon in a cavity

A microscopic quantum system under continuous observation exhibits at random times sudden jumps between its states. The detection of this quantum feature requires a quantum non-demolition (QND) measurement repeated many times during the system's evolution. Whereas quantum jumps of trapped massive particles (electrons, ions or molecules) have been observed, this has proved more challenging for light quanta. Standard photodetectors absorb light and are thus unable to detect the same photon twice. It is therefore necessary to use a transparent counter that can 'see' photons without destroying them. Moreover, the light needs to be stored for durations much longer than the QND detection time. Here we report an experiment in which we fulfil these challenging conditions and observe quantum jumps in the photon number. Microwave photons are stored in a superconducting cavity for times up to half a second, and are repeatedly probed by a stream of non-absorbing atoms. An atom interferometer measures the atomic dipole phase shift induced by the non-resonant cavity field, so that the final atom state reveals directly the presence of a single photon in the cavity. Sequences of hundreds of atoms, highly correlated in the same state, are interrupted by sudden state switchings. These telegraphic signals record the birth, life and death of individual photons. Applying a similar QND procedure to mesoscopic fields with tens of photons should open new perspectives for the exploration of the quantum-to-classical boundary.     

De Broglie wavelength of a non-local four-photon state

Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments. Quantum entanglement, the coherent superposition of states in multi-particle systems, yields more complex phenomena. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit, or quantum lithography beyond the classical diffraction limit. It has been generally understood that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance.     

Multi-step evolution and measurement control of finite-dimensional quantum systems

For finite-dimensional quantum systems,we propose a quantum control scheme based on a multi-step unitary evolution and quantum projective measurements.The objective is to design a control law to steer the system to a target eigenstate of the measurement operator in the least number of steps.Within each control step,unitary evolution and quantum projective measurement are performed in turn until the system reaches the target state.The control process can be modeled as a finite-state Markov chain with an absorbing state.We prove that the controlled system will converge to the target eigenstate with probability one after a finite number of control steps and find a minimal-step-number condition that would steer the system to the target eigenstate in the least number of steps.     

复合脉冲控制阶梯型多态量子系统的转移通道

提出了利用复合脉冲在阶梯型多态量子系统中操控量子态演化和粒子数相干转移的方法.首先通过Morris-Shore变换,借助二能级传播算子描述多态量子系统的演化.然后利用增加脉冲序列数且单个脉冲的相位可控的技术,抑制额外的转移通道,实现高效率高鲁棒性的量子态操控和粒子数转移.最后通过数值模拟研究了额外通道和转移通道的拉比频率比、脉冲面积的变化、单光子失谐偏离零点等因素对转移效率的影响.结果表明:常被用于二能级量子系统的复合脉冲操控方法也可被应用于多态量子系统.通过增加脉冲序列数,可有效减小相关参数的扰动,保持高效率的粒子数转移.多脉冲序列复合脉冲的技术可以解决偏振不纯、激光频率不纯、控制参数扰动等造成的量子态操控效率降低等问题.研究结果对构造量子门、量子模拟等相关研究具有重要意义.     

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.