矩形弹子球中的量子波包分析(英文)

利用波包分析量子力学体系的动力学行为在研究经典和量子的对应关系方面越来越成为一个非常重要的方法.利用高斯波包分析方法,我们计算了矩形弹子球体系的自关联函数,自关联函数的峰和经典周期轨道的周期符合的很好,这表明经典周期轨道的周期可以通过含时的量子波包方法产生.我们还讨论了矩形弹子球的波包回归和波包的部分回归,计算结果表明在每一个回归时间,波包出现精确的回归.对于动量为零的波包,初始位置在弹子球内部的特殊对称点处,出现一些时间比较短的附加的回归.     

Phase control of rotational wave packets and quantum information

Lasers can create rotational wave packets in gas-phase molecules which periodically revive as field-free, aligned distributions. We control the wave packet evolution with relatively weak laser pulses at fractional revivals which modify the phase between wave packet components. We demonstrate two phase control effects in oxygen: coherently switching revivals off and on, and doubling the revival frequency. When viewed as a quantum logic system, these effects correspond to a Hadamard and a T operation.     

一般幂指数中心势作用下的波包回归和部分回归

利用WKB近似和自关联函数方法,我们研究了一般幂指数中心势V(r)=rk (-20)作用下波包的回归和部分回归。对于排斥势(>0, k>0), 势是一长程势,量子化能级结构中只有一个量子数,波包的回归结构和一维幂指数势的情况类似。这一结果表明能级结构相同的体系具有相同的波包回归结构。 对于吸引势,能级结构中有两个量子数, 当 k取不同的值时,波包的回归结构不同。对于库仑吸引势,波包回归和部分回归出现; 但是对于其它的k值, 经过一段时间后,波包出现坍塌。本文的研究对于探讨里德堡原子和分子中电子运动的经典极限提供了一个新的方法。     

一般幂指数中心势作用下的波包回归和部分回归

利用WKB近似和自关联函数方法,我们研究了一般幂指数中心势V(r)=γrk (-20)作用下波包的回归和部分回归.对于排斥势(γ>0, k>0), 势是一长程势,量子化能级结构中只有一个量子数,波包的回归结构和一维幂指数势的情况类似.这一结果表明能级结构相同的体系具有相同的波包回归结构.对于吸引势,能级结构中有两个量子数, 当 k取不同的值时,波包的回归结构不同.对于库仑吸引势,波包回归和部分回归出现;但是对于其它的k值, 经过一段时间后,波包出现坍塌.本文的研究对于探讨里德堡原子和分子中电子运动的经典极限提供了一个新的方法.     

Fisher information,nonclassicality and quantum revivals

Wave packet revivals and fractional revivals are studied by means of a measure of nonclassicality based on the Fisher information. In particular, we show that the spreading and the regeneration of initially Gaussian wave packets in a quantum bouncer and in the infinite square-well correspond, respectively, to high and low nonclassicality values. This result is in accordance with the physical expectations that at a quantum revival wave packets almost recover their initial shape and the classical motion revives temporarily afterward.     

Quantum packet switching generation using correlated photons in a microring resonator system

We propose a new system of a packet of quantum bits generation using a soliton pulse within a microring resonator. A quantum gate can be formed by using a polarization control unit incorporating into the system. The random signal and idler pairs can be formed within the photon correlation bandwidth, which can be generated, and randomly form the packet quantum bits, i.e. quantum packet switching. Each random code (logic) can be performed by combining the signal and idler of each entangled photon pair via the quantum gate. Results obtained have shown that the packet of quantum logic bits can be generated using the entangled photon pairs generated by the proposed system.     

Quantum bits generation using correlated photons: Fidelity and error corrections

We propose a new system of quantum bits generation using a soliton pulse within a micro ring resonator. A quantum gate can be formed using a polarization control unit incorporating into the system. The random signal and idler pairs can be formed within the photon correlation bandwidth, which can be generated and randomly formed the packet quantum bits, i.e. quantum packet codes. Each random code (logic) can be performed by combining the signal and idler of each entangled photon pair via the quantum gate. Results obtained have shown that the packet of quantum logic bits can be generated using the entangled photon pairs generated by the proposed system. The quantum bits transmission fidelity and error corrections are also described.     

Driven state transfer and state storage in a tight-binding chain using two local barriers

A theoretical scheme to realize quantum state transfer and state storage in a uniformly coupled tight-binding chain is introduced in this paper. Two controllable gate voltages acting as local barriers are applied onto specific sites of the system, which separate the chain into three regions. By setting two gate voltages being equal, we show that an initially localized quantum wave packet undergoes perfect periodic revivals, allowing for perfect quantum state transfer between two nonadjacent spatial regions of the system. We also show that the wave packet can be trapped in its initial region by setting two gate voltages being unequal, which relates to the problem of storing quantum information. Moreover an efficient time-dependent quantum state transfer protocol is presented by smoothly varying the two gate voltages. Significantly, in our setup, the transferred state can be trapped, with a high fidelity of storage, at the end of the transfer protocol.     

Invariants of the dynamics of molecular vibrational wave packets in phase modulation

An exact analytic solution was obtained for the correlation function of the motion of a phase-modulated Gauss wave packet in an anharmonic potential. The solution is expressed through the theta-function with the parameters depending on both the potential and phase modulation of the initial wave packet. Changes in both linear and quadratic chirps result in an invariant correlation function time shift in a weakly anharmonic potential with the conservation of all the total and fractional revivals. At a strong potential anharmonicity, translational invariance with respect to a quadratic chirp is preserved in certain instances, whereas the dynamics of packets experiences qualitative changes depending on linear phase modulation. This approach can be used to qualitatively analyze intramolecular dynamics if the potential energy surface is not known exactly, which is especially useful for quantum control of large molecules, in particular, photochromes.     

Quantum Dynamical Behavior of the Morse Oscillator: the Wigner Function Approach

We explore the quantum dynamical behavior of the Morse oscillator in the phase space using the Wigner function. For an initial wave packet excited with Gaussian probability distribution, we calculate the associated Wigner function and compute its time evolution. By calculating the marginal probabilities, we study the formation of quantum carpets both in the position space and in the momentum space. In addition, in view of these probabilities, we present the time evolution of the position and momentum expectation values. The structure of quantum carpets and the time-evolved expectation values mimic the emergence of quantum revivals and fractional revivals.     

Control of Wave Packet Revivals Using Geometric Phases

Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that, by varying the parameters in the Hamiltonian cyclically with a period T and thus inducing suitable geometric phases in the states, fractional revivals can be eliminated at the relevant times T, 2T,... . Further, with the introduction of this time step T, the occurrence of near full revivals can be mapped onto that of Poincaré recurrences in an irrational rotation map of the circle. The distinctive recurrence statistics of the latter can thus serve as a clear signature of the dynamics of wave packet revivals.     

Coherent control of rotational wave-packet dynamics via fractional revivals

We show (i) how the evolution of a wave packet created from an initial thermal ensemble can be controlled by manipulating interferences during the wave packet's fractional revivals and (ii) how the wave-packet evolution can be mapped onto the dynamics of a few-state system, where the number of states is determined by the amount of information one wants to track about the wave packet in the phase space. We illustrate our approach by (i) switching off and on field-free molecular axis alignment induced by a strong laser pulse and (ii) converting alignment into field-free orientation, starting with rotationally cold or hot systems.     

Observing the phase space trajectory of an entangled matter wave packet

We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin-dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon distributions throughout the action of the displacement force. Our investigation shows corrections to simplified models of the system evolution. The precise knowledge of these dynamics may improve quantum gates for ion crystals and lead to entangled matter wave states with large displacements.     

Isotope-selective femtosecond wave packet dynamics: The rare molecule

For the first time, the femtosecond real-time vibrational dynamics of the rare ^41,41K₂ isotope, excited to the electronic state, could be selectively studied by means of time-resolved three photon ionization. A vibrational period of fs is determined. Superimposed, a beat structure with a period of 20 ps is observed. A detailed Fourier analysis reveals a strong band of three lines centered around 65.5 cm^-1. A significant perturbation of the wave packet caused by spin-orbit coupling of the A and the crossing state is found. This perturbation is the reason for the fast dephasing of the initially generated wave packet within about 10 ps. The spectrogram of the real-time data shows total revivals of the wave packet at 20 ps and 40 ps. Fractional revivals are found for times around 10 ps and 30 ps. Due to high intensity effects a remarkable slightly broadened line at 90 cm^-1 appears and can be assigned to the wave packet propagation generated in the dimer's ground state by impulsive stimulated Raman scattering. Revivals of this ground state wave packet are found at 17ps and 34ps. A comparison with other isotopes of K₂ is given. Received: 9 February 1998 / Revised: 15 May 1998 / Accepted: 2 June 1998     

Quantum wave packet revival in two-dimensional circular quantum wells with position-dependent mass

We study quantum wave packet revivals on two-dimensional infinite circular quantum wells (CQWs) and circular quantum dots with position-dependent mass (PDM) envisaging a possible experimental realization. We consider CQWs with radially varying mass, addressing particularly the cases where M(r)∝rw with w=1,2, or −2. The two PDM Hamiltonians currently allowed by theory were analyzed and we were able to construct a strong theoretical argument favoring one of them.     

Efficient decomposition of quantum gates

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4(n)) which coincides with the theoretical lower bound.     

Observation of an amplitude collapse and revival of chirped coherent phonons in bismuth

We have studied the A(1g) coherent phonons in bismuth generated by high fluence ultrashort laser pulses. We observed that the nonlinear regime, where the phonons' oscillation parameters depend on fluence, consists of subregimes with distinct dynamics. Just after entering the nonlinear regime, the phonons become chirped. Increasing the fluence further leads to the emergence of a collapse and revival, which next turns into multiple collapses and revivals. This is explained by the dynamics of a wave packet in an anharmonic potential, where the packet periodically breaks up and reconstitutes in its original form, giving convincing evidence that the phonons are in a quantum state, with no classical analog.     

Extracting continuum electron dynamics from high harmonic emission from molecules

We show that high harmonic generation is the most sensitive probe of rotational wave packet revivals, revealing very high-order rotational revivals for the first time using any probe. By fitting high-quality experimental data to an exact theory of high harmonic generation from aligned molecules, we can extract the underlying electronic dipole elements for high harmonic emission and uncover that the electron gains angular momentum from the photon field.     

Virtual parallel computing and a search algorithm using matrix product States

We propose a form of parallel computing on classical computers that is based on matrix product states. The virtual parallelization is accomplished by representing bits with matrices and by evolving these matrices from an initial product state that encodes multiple inputs. Matrix evolution follows from the sequential application of gates, as in a logical circuit. The action by classical probabilistic one-bit and deterministic two-bit gates such as NAND are implemented in terms of matrix operations and, as opposed to quantum computing, it is possible to copy bits. We present a way to explore this method of computation to solve search problems and count the number of solutions. We argue that if the classical computational cost of testing solutions (witnesses) requires less than O(n^{2}) local two-bit gates acting on n bits, the search problem can be fully solved in subexponential time. Therefore, for this restricted type of search problem, the virtual parallelization scheme is faster than Grover's quantum algorithm.     

Quantum logic gates based on coherent electron transport in quantum wires

It is shown that the universal set of quantum logic gates can be realized using solid-state quantum bits based on coherent electron transport in quantum wires. The elementary quantum bits are realized with a proper design of two quantum wires coupled through a potential barrier. Numerical simulations show that (a) a proper design of the coupling barrier allows one to realize any one-qbit rotation and (b) Coulomb interaction between two qbits of this kind allows the implementation of the CNOT gate. These systems are based on a mature technology and seem to be integrable with conventional electronics.