Operational representation of quantum states based on interference

We describe a real-valued and periodic representation of quantum states. This representation can be defined operationally using generalized position and momentum measurements on coupled systems. It turns out that the emerging quantum interference terms encode the complete state information and also allow us to formulate quantum dynamics. We discuss the close connection to the theory of analytic functions.     

The hidden phase of Fock states; quantum non-local effects

We revisit the question of how a definite phase between Bose-Einstein condensates can spontaneously appear under the effect of measurements. We first consider a system that is the juxtaposition of two subsystems in Fock states with high populations, and assume that successive individual position measurements are performed. Initially, the relative phase is totally undefined, and no interference effect takes place in the first position measurement. But, while successive measurements are accumulated, the relative phase becomes better and better defined, and a clear interference pattern emerges. It turns out that all observed results can be interpreted in terms of a pre-existing, but totally unknown, relative phase, which remains exactly constant during the experiment. We then generalize the results to more condensates. We also consider other initial quantum states than pure Fock states, and distinguish between intrinsic phase of a quantum state and phase induced by measurements. Finally, we examine the case of multiple condensates of spin states. We discuss a curious quantum effect, where the measurement of the spin angular momentum of a small number of particles can induce a big angular momentum in a much larger assembly of particles, even at an arbitrary distance. This spin observable can be macroscopic, analogous to the pointer of a measurement apparatus, which illustrates the non-locality of standard quantum mechanics with particular clarity. The effect can be described as the teleportation at arbitrary distances of the continuous classical result of a local experiment. The EPR argument, transposed to this case, takes a particularly convincing form since it does not involve incompatible measurements and deals only with macroscopic variables.     

A nonadiabatic semi-classical method for dynamics of atoms in optical lattices

We develop a semi-classical method to simulate the motion of atoms in a dissipative optical lattice. Our method treats the internal states of the atom quantum mechanically, including all nonadiabatic couplings, while position and momentum are treated as classical variables. We test our method in the one-dimensional case. Excellent agreement with fully quantum mechanical simulations is found. Our results are much more accurate than those of earlier semi-classical methods based on the adiabatic approximation.     

Uncertainty Relations in the Madelung Picture

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.     

Universal quantum uncertainty relations: Minimum-uncertainty wave packet depends on measure of spread

Based on the statistical concept of the median, we propose a quantum uncertainty relation between semi-interquartile ranges of the position and momentum distributions of arbitrary quantum states. The relation is universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We show that the median-based one is not saturated for Gaussian distributions in position. Instead, the Cauchy-Lorentz distributions in position turn out to be the one with the minimal uncertainty, among the states inspected, implying that the minimum-uncertainty state is not unique but depends on the measure of spread used. Even the ordering of the states with respect to the distance from the minimum uncertainty state is altered by a change in the measure. We invoke the completeness of Hermite polynomials in the space of all quantum states to probe the median-based relation. The results have potential applications in a variety of studies including those on the quantum-to-classical boundary and on quantum cryptography.     

Measuring position and momentum together

We describe an operational scheme for determining both the position and momentum distributions in a large class of quantum states, together with an experimental implementation.     

Infinite quantum well: A coherent state approach

A new family of 2-component vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented. They allow a consistent quantization of the classical phase space and observables for a particle in this potential. We then study the resulting position and (well-defined) momentum operators. We also consider their mean values in coherent states and their quantum dispersions.     

Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave

We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.     

A simple scheme for quantum networks based on orbital angular momentum states of photons

We propose a new quantum network scheme using orbital angular momentum states of photons to route the network and spin angular momentum states to encode the information. A four-user experimental scheme based on this efficient quantum network is analyzed in detail, which is particularly appealing for the free space quantum key distribution. Users can freely exchange quantum keys with each other.     

氢原子相干态

由Kustannheimo-Stiefel变换,可将量子力学中的氢原子问题化为带有约束条件的四维各向同性谐振子。在此基础上定义相干态,并证明力学量坐标和动量对相干态的平均,给出经典开普勒运动轨道。同时也讨论该相干态中的测不准关系式。 关键词：     

High-efficiency detection of a single quantum of angular momentum by suppression of optical pumping

We propose and demonstrate experimentally the discrimination between two spin states of an atom purely on the basis of their angular momentum. The discrimination relies on angular momentum selection rules and does not require magnetic effects such as a magnetic dipole moment of the atom or an applied magnetic field. The central ingredient is to prevent by coherent population trapping an optical pumping process which would otherwise relax the spin state before a detectable signal could be obtained. We detected the presence or absence of a single quantum (h) of angular momentum in a trapped calcium ion in a single observation with success probability 0.86. As a practical technique, the method can be applied to read out some types of quantum computer.     

利用Sagnac干涉仪实现光子轨道角动量分束器

光子轨道角动量量子态具有高维和光学涡旋特性, 在经典和量子领域展示出了巨大的应用潜力, 目前对其的研究已成为物理学的一个热点. 本实验研究了利用Sagnac干涉仪干涉的方法将具有不同轨道角动量的光束无破坏地分离到不同的路径, 即实现光子轨道角动量分束器. 实验中利用此分束器验证了对几种不同轨道角动量态(包含叠加态)的分离, 得到了与理论预期相符的实验结果. 这种对轨道角动量态的区分的方法相比已有的其他区分方法具有较好的稳定性, 而且可用于区分叠加态, 也可以达到单光子水平, 最重要的是实现了不同的轨道角动量本征态无破坏的与路径比特耦合. 这种新方法对高密度通信、量子纠缠、量子保密通信、量子计算与量子信息等方面有着重要的意义.     

Entirety of Quantum Uncertainty and Its Experimental Verification

As a foundation of quantum physics, uncertainty relations describe ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertainty relations are formulated by mathematical bounds for a specific state. Here we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables, ranging over all possible input states. We find that for the pair of position and momentum operators, Heisenberg's uncertainty principle points exactly to the attainable area of the variances of position and momentum. Moreover, for finite-dimensional systems, we prove that the corresponding area is necessarily semialgebraic; in other words, this set can be represented via finite polynomial equations and inequalities, or any finite union of such sets. In particular, we give the analytical characterization of the areas of variances of(a) a pair of one-qubit observables and(b) a pair of projective observables for arbitrary dimension,and give the first experimental observation of such areas in a photonic system.     

Uncertainty features of microscopic particles described by nonlinear Schrüdinger equation

The uncertainty relationship between position and momentum of the microscopic particles is calculated by nonlinear quantum theory in which the states of the particles are described by a nonlinear Schrüdinger equation. The results show that the uncertainty relation differs from that in the quantum mechanics and has a minimum value in this case. This means that the position and momentum of the particles could be determined simultaneously to a certain degree, which could be caused by the wave–corpuscle duality of the microscopic particles described by the nonlinear Schrüdinger equation.     

Rectified momentum transport for a kicked Bose-Einstein condensate

We report the experimental observation of rectified momentum transport for a Bose-Einstein condensate kicked at the Talbot time (quantum resonance) by an optical standing wave. Atoms are initially prepared in a superposition of the 0 and -2hkl momentum states using an optical pi/2 pulse. By changing the relative phase of the superposed states, a momentum current in either direction along the standing wave may be produced. We offer an interpretation based on matter-wave interference, showing that the observed effect is uniquely quantum.     

All-optical generation of states for "Encoding a qubit in an oscillator"

Most quantum computation schemes propose encoding qubits in two-level systems. Others exploit the use of an infinite-dimensional system. In "Encoding a qubit in an oscillator" [Phys. Rev. A 64, 012310 (2001)], Gottesman, Kitaev, and Preskill (GKP) combined these approaches when they proposed a fault-tolerant quantum computation scheme in which a qubit is encoded in the continuous position and momentum degrees of freedom of an oscillator. One advantage of this scheme is that it can be performed by use of relatively simple linear optical devices, squeezing, and homodyne detection. However, we lack a practical method to prepare the initial GKP states. Here we propose the generation of an approximate GKP state by using superpositions of optical coherent states (sometimes called "Schr?dinger cat states"), squeezing, linear optical devices, and homodyne detection.     

Property of partially disturbed polarization of Airy beam

We propose methods for the unambiguous discrimination of quantum states encoded in the spatial profile of light modes, in particular in the orbital angular momentum of light. Perfect discrimination between quantum states is possible only between orthogonal states of a known basis system. Generalised measurement strategies have been developed for the distinction between non-orthogonal states in a two-dimensional state space, e.g. the polarisation of light. Here we consider information encoded in superpositions of orbital angular momentum states of light, defined within an infinite-dimensional state space. Generalised measurements will be an important addition to quantum communication in high-dimensional spaces.     

Exact ground states of rotating Bose gases close to a Feshbach resonance

We study the ground states of rotating Bose gases when interactions are affected by a nearby Feshbach resonance. We show that exact ground states at high angular momentum can be found analytically for a general model for the resonant interactions. We identify parameter regimes where the exact ground states are exotic fractional quantum Hall states, the excitations of which obey nonabelian exchange statistics.