Neutron Matter Wave Quantum Optics

Neutron matter-wave optics provides the basis for new quantum experiments and a step towards applications of quantum phenomena. Most experiments have been performed with a perfect crystal neutron interferometer where widely separated coherent beams can be manipulated individually. Various geometric phases have been measured and their robustness against fluctuation effects has been proven, which may become a useful property for advanced quantum communication. Quantum contextuality for single particle systems shows that quantum correlations are to some extent more demanding than classical ones. In this case entanglement between external and internal degrees of freedom offers new insights into basic laws of quantum physics. Non-contextuality hidden variable theories can be rejected by arguments based on the Kochen-Specker theorem.     

Quantum Physics with Neutrons: From Spinor Symmetry to Kochen-Specker Phenomena

In 1974 perfect crystal interferometry has been developed and immediately afterwards the 4π-symmetry of spinor wave-functions has been verified. The new method opened a new access to the observation of intrinsic quantum phenomena. Spin-superposition, quantum state reconstruction and quantum beat effects are examples of such investigations. In this connection efforts have been made to separate and measure various dynamical and geometrical phases. Non-cyclic and non-adiabatic topological phases have been identified and their stability against various fluctuations and dissipative forces has been investigated by means of ultra-cold neutrons. An entanglement between different degrees of freedom of a single neutron system demonstrated the contextuality feature of quantum mechanics. In its continuation this yields to Kochen-Specker theorem like investigations providing a new basis for information processing and for the understanding of quantum physics in general. All investigations show the equivalence of various phase spaces and show how physical phenomena are correlated by quantum laws. Some curiosa occurred during the experiments and some epistemological aspects will be discussed as well.     

Entanglement Between Degrees of Freedom in?a?Single-Particle System Revealed in Neutron Interferometry

Initially Einstein, Podolsky, and Rosen (EPR) and later Bell shed light on the non-local properties exhibited by subsystems in quantum mechanics. Separately, Kochen and Specker analyzed sets of measurements of compatible observables and found that a consistent coexistence of these results is impossible, i.e., quantum indefiniteness of measurement results. As a consequence, quantum contextuality, a more general concept compared to non-locality, leads to striking phenomena predicted by quantum theory. Here, we report neutron interferometric experiments which investigate entangled states in a single-particle system: entanglement is, in this case, achieved not between particles, but between degrees of freedom i.e., between spin, path, and energy degrees of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter in the interferometer allow an experimental verification of the violation of a Bell-like inequality. In addition, state tomography, tomographic analysis of the density matrix of a quantum system, and Kochen-Specker-like phenomena are presented to characterize neutrons’ entangled states and their peculiarity. Furthermore, a coherent energy manipulation scheme is accomplished with a radio-frequency (RF) spin-flipper. This scheme allows the (total) energy degree of freedom to be entangled: the remarkable behavior of a triply entangled GHZ-like state is demonstrated.     

Long-distance quantum teleportation assisted with free-space entanglement distribution

Faithful long-distance quantum teleportation necessitates prior entanglement distribution between two communicated locations. The particle carrying on the unknown quantum information is then combined with one particle of the entangled states for Bell-state measurements, which leads to a transfer of the original quantum information onto the other particle of the entangled states. However in most of the implemented teleportation experiments nowadays, the Bell-state measurements are performed even before successful distribution of entanglement. This leads to an instant collapse of the quantum state for the transmitted particle, which is actually a single-particle transmission thereafter. Thus the true distance for quantum teleportation is, in fact, only in a level of meters. In the present experiment we design a novel scheme which has overcome this limit by utilizing fiber as quantum memory. A complete quantum teleportation is achieved upon successful entanglement distribution over 967 meters in public free space. Active feed-forward control techniques are developed for real-time transfer of quantum information. The overall experimental fidelities for teleported states are better than 89.6%, which signify high-quality teleportation.     

The Quantum World is not Built up from Correlations

It is known that the global state of a composite quantum system can be completely determined by specifying correlations between measurements performed on subsystems only. Despite the fact that the quantum correlations thus suffice to reconstruct the quantum state, we show, using a Bell inequality argument, that they cannot be regarded as objective local properties of the composite system in question. It is well known since the work of Bell, that one cannot have locally preexistent values for all physical quantities, whether they are deterministic or stochastic. The Bell inequality argument we present here shows this is also impossible for correlations among subsystems of an individual isolated composite system. Neither of them can be used to build up a world consisting of some local realistic structure. As a corrolary to the result we argue that entanglement cannot be considered ontologically robust. The Bell inequality argument has an important advantage over others because it does not need perfect correlations but only statistical correlations. It can therefore easily be tested in currently feasible experiments using four particle entanglement.     

Complementarity Relations for Multi-Qubit Systems

No Heading We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbitrary state of two qubits, pure or mixed, quantifies a tradeoff between the amounts of entanglement, separable uncertainty, and single particle properties that are encoded in the quantum state. The separable uncertainty is a natural measure of our ignorance about the properties possessed by individual subsystems, and may be used to completely characterize the relationship between entanglement and mixedness in two-qubit systems. The two-qubit complementarity relation yields a useful geometric picture in which the root mean square values of local subsystem properties act like coordinates in the space of density matrices, and suggests possible insights into the problem of interpreting quantum mechanics.     

Gravitational modulation of particle clustering: A new class of gravitationally induced quantum interference

A gravitational potential difference between the two components of a split fermion or boson beam in a particle interferometer modulates the cross-correlation in particle fluctuations and the variance in difference counts of the two output beams received at two detectors. The gravitational potential difference also modulates the conditional probability that a fermion will be received at a single detector given that one has been registered at an earlier time. The proposed effects are particle analogues of the optical Hanbury Brown-Twiss experiments; they represent a new kind of intrinsically nonrelativistic gravitationally induced quantum interference different in concept and in observational procedure from that of the Colella-Werner-Overhauser experiment. The effects should be observable with field-emission electron beams and slow neutron beams.The original essay upon which this article is based received an honorable mention from the Gravity Research Foundation for the year 1987.     

An analytical description of the atomic information entropy in a multi-level system

We construct a complete representation of the atomic information entropy of an arbitrary multi-level system. Our approach is applicable to all scenarios in which the quantum state shared by a single particle and fields is known. As illustrations we apply our findings to a single four-level atom strongly coupled to a cavity field and driven by a coherent laser field. In this framework, we discuss connections with entanglement frustration and entropic forms. We conclude by showing how the atomic information entropy can be extended to examine entanglement in multi-level atomic systems.     

一个基于三粒子部分纠缠态的量子广播多重盲签名协议

最近有研究者提出了一个基于三粒子最大纠缠态GHZ态的量子广播多重盲签名协议,它能满足一个重要消息需要多人签发,但出于隐私保护要求每一个签名者都不能获取消息的具体内容这一应用需求,并有望应用于电子银行系统.本文给出了一个基于三粒子部分纠缠态的量子广播多重盲签名协议,与原协议相比,该协议用三粒子部分纠缠态代替三粒子极大纠缠GHZ态,并且能不降低协议的安全性.新协议不再依赖于极大纠缠态,仅仅需要在通信参与者之间分享部分纠缠态就可以完成该签名方案,这在一定程度上节约了纠缠资源,降低了协议的实现条件,提高了协议的可应用性.这也充分体现了多体部分纠缠态也可以作为一种量子资源来实现既定的量子通信任务.     

光学体系宏观-微观纠缠及其在量子密钥分配中的应用

宏观-微观纠缠最早起源于“薛定谔的猫”思想实验, 是指在宏观体系与微观体系之间建立量子纠缠. 实现宏观-微观纠缠可以利用多种物理体系来完成, 本文重点介绍了在光学体系中制备和检验宏观-微观纠缠的发展过程. 从最初的受激辐射单光子量子克隆到光学参量放大, 再到相空间的位移操作, 实验上制备宏观-微观纠缠的方法取得了长足的进步. 利用非线性光学参量放大过程制备的宏观-微观纠缠的光子数可以达到10⁴量级, 人眼已经可以观察到, 因此使用人眼作为探测器来检验宏观-微观纠缠的实验开始出现. 但随后人们意识到, 粗精度的光子数探测器, 例如人眼, 无法严格判定宏观-微观纠缠的存在. 为了解决这个难题, 提出了一种巧妙的方法, 即在制备宏-微观纠缠后, 利用局域操作过程将宏观态再变为微观态, 通过判定微观纠缠存在的方法来判定宏微观纠缠的存在. 之后相空间的位移操作方法将宏观态的粒子数提高到10⁸, 并且实现了纠缠的严格检验. 利用光机械实现宏观-微观纠缠的方案也被提出. 由于量子密钥分配中纠缠是必要条件, 而宏观-微观纠缠态光子数较多这一优势可能会对量子密钥分配的传输距离有所提高. 本文介绍了利用相位纠缠的相干态来进行量子秘钥分配的方案, 探讨了利用宏观-微观纠缠实现量子密钥分配的可能性.     

Determining the parity of a permutation using an experimental NMR qutrit

We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, it is widely believed that computational speedup requires the presence of entanglement and thus cannot be achieved by a single qubit. On the other hand, a qutrit is qualitatively more quantum than a qubit because of the existence of quantum contextuality and a single qutrit can be used for computing. We use the deuterium nucleus oriented in a liquid crystal as the experimental qutrit. This is the first experimental exploitation of a single qutrit to carry out a computational task.     

Rotating wave approximation and entropy

This Letter studies composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. Going beyond the rotating wave approximation, it is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the entropy operator and generates an irreversible time evolution. The vacuum state of the system is shown to evolve into a generalized coherent state exhibiting entanglement of the modes in which the counter-rotating terms are expressed. Possible consequences at observational level in quantum optics experiments are currently under study.     

Testing Temporal Contextuality with Quantum Entangled Histories

Quantum contextuality is a fundamental feature of quantum theory, which has been demonstrated in spatial scenario theoretically and experimentally. In this paper, we proposed a scheme to test temporal contextuality with a two-time entangled history state in the optical system. The contextuality is generated from the sequential projective measurements and revealed by the violation of the temporal Klyachko-Can-Binicioglu-Shumovsky inequality, which is obeyed by the noncontextual hidden variable theories. Compared with the existing schemes for testing quantum contextuality, ours can give the same physical result without collapsing the state. From the point of view of experiment, it is easier to implement as the measurement is projective measurement, and it can be extended to multiple time nodes.

     

Electron quantum optics in ballistic chiral conductors

The edge channels of the quantum Hall effect provide one dimensional chiral and ballistic wires along which electrons can be guided in an optics‐like setup. Electronic propagation can then be analyzed using concepts and tools derived from optics. After a brief review of electron optics experiments performed using stationary current sources which continuously emit electrons in the conductor, this paper focuses on triggered sources, which can generate on‐demand a single particle state. It first outlines the electron optics formalism and its analogies and differences with photon optics and then turns to the presentation of single electron emitters and their characterization through the measurements of the average electrical current and its correlations. This is followed by a discussion of electron quantum optics experiments in the Hanbury‐Brown and Twiss geometry where two‐particle interferences occur. Finally, Coulomb interactions effects and their influence on single electron states are considered.     

Towards a Resolution of Dilemma: Nonlocality or Nonobjectivity?

This paper discusses a possible resolution of the nonobjectivity-nonlocality dilemma in quantum mechanics in the light of experimental tests of the Bell inequality for two entangled photons and a Bell-like inequality for a single neutron. My conclusion is that these experiments show that quantum mechanics is nonobjective: that is, the values of physical observables cannot be assigned to a system before measurement. Bell’s assumption of nonlocality has to be rejected as having no direct experimental confirmation, at least thus far. I also consider the relationships between nonobjectivity and contextuality. Specifically, I analyze the impact of the Kochen-Specker theorem on the problem of contextuality of quantum observables. I argue that, just as von Neumann’s “no-go” theorem, the Kochen-Specker theorem is based on assumptions that do not correspond to the real physical situation. Finally, I present a theory of measurement based on a classical, purely wave model (pre-quantum classical statistical field theory), a model that reproduces quantum probabilities. In this model continuous fields are transformed into discrete clicks of detectors. While this model is classical, it is nonobjective. In this case, nonobjectivity is the result of the dependence of experimental outcomes on the context of measurement, in accordance with Bohr’s view.     

Coarse graining makes it hard to see micro-macro entanglement

Observing quantum effects such as superpositions and entanglement in macroscopic systems requires not only a system that is well protected against environmental decoherence, but also sufficient measurement precision. Motivated by recent experiments, we study the effects of coarse graining in photon number measurements on the observability of micro-macro entanglement that is created by greatly amplifying one photon from an entangled pair. We compare the results obtained for a unitary quantum cloner, which generates micro-macro entanglement, and for a measure-and-prepare cloner, which produces a separable micro-macro state. We show that the distance between the probability distributions of results for the two cloners approaches zero for a fixed moderate amount of coarse graining. Proving the presence of micro-macro entanglement therefore becomes progressively harder as the system size increases.     

连续变量纠缠增强对实验参量的依赖关系

具有正交振幅和正交相位分量量子关联的连续变量量子纠缠态光场是进行量子信息和量子计算研究的最基本的资源。随着量子信息和量子计算研究的深入开展,为了实现高质量的信息传递和高效率的量子计算,必须尽可能提高所利用的纠缠态光场的纠缠度。基于光学参变过程量子纠缠增强是提高连续变量纠缠态光场纠缠度的一种有效方法,详细讨论了连续变量纠缠增强与非简并光学参变放大器各实验参量的关系,讨论了这些参量对纠缠增强的影响。计算结果将为优化利用非简并光学参变放大器构建的纠缠增强系统,进一步提高量子纠缠增强效率提供参考。     

利用多光子相互作用实现量子信息传递

利用全量子理论,研究了多原子-腔场系统中多光子相互作用的过程,给出了不同情况下系统的一般演化式,发现利用此过程可实现量子纠缠信息的传递:只要控制腔场与原子相互作用的时间即原子以特定速度通过腔场时,处于基态的原子与存储纠缠信息的腔场相互作用的结果使原子获得量子纠缠信息;相反,纠缠原子中的量子纠缠信息也可传递给处于真空态的腔场;基态原子作为"飞行的量子比特"还可将量子纠缠信息从一个腔场传递到另一个腔场。该结论适应于讨论任意多个原子-腔场系统中任意多个光子相互作用的普遍情形。     

An alternative quantum theory for single particles and a proposed experimental test

An alternative quantum theory for single particles bounded in the external field proposed in 1986 (Huang X. Y., Phys. Lett. A., 1986, 115: 310) is further developed from which the energy of the state for the single particle takes one of the eigenvalues of the quantum Hamiltonian, and the usual quantum mechanics for the particle in a stationary state holds only in the statistical sense. In light of the theory, the particle of definite energy, ground-state-energy for instance, can exhibit a novel periodic behavior. This result for the ground-state-energy state neutron in the Earth’s gravitational field is experimentally testable using ultracold neutron beam passing through the same apparatus that was devised in 2002 to identify the energy quantization of neutron in the field (Nesvizhevsky V. V., et al., Nature, 2002, 415: 297).      

Energy entanglement in neutron interferometry

Entanglement between degrees of freedom, namely between the spin, path and (total) energy degrees of freedom, for single neutrons is exploited. We implemented a triply entangled Greenberger-Horne-Zeilinger(GHZ)-like state and coherently manipulated relative phases of two-level quantum subsystems. An inequality derived by Mermin was applied to analyze the generated GHZ-like state: we determined the four expectation values and finally obtained M=2.558±0.004?2. This demonstrates the violation of a Mermin-like inequality for triply entangled GHZ-like state in a single-particle system, which, in turn, exhibits a clear inconsistency between noncontextual assumptions and quantum mechanics and confirms quantum contextuality.