Quantum Carpets: a Probe to Identify Wave-Packet Fractional Revivals

We explain quantum carpets in the position and momentum spaces woven by the self-interference of the de Broglie wave of an atom or an electron trapped in an infinitely deep potential well. The recurrence of self-similar structures in designs of these carpets mimics the phenomena of quantum revivals and fractional revivals. We identify fractional revivals of various order by means of these space–time and momentum–time interference patterns.     

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.     

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.     

Quantum carpets: efficiently probing fractional revivals in position-dependent mass systems

Position-dependent-mass systems are of great importance in many physical situations,such as the transport of charge carriers in semiconductors with non-uniform composition and in the theory of many-body interactions in condensed matter.Here we investigate,numerically and analytically,the phenomenon of fractional revivals in such systems,which is a generic characteristic manifested by the wave-packet evolution in bounded Hamiltonian systems.Identifying the fractional revivals using specific probe...     

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.     

Quantum logic approach to wave packet control

We study control of wave packets with a finite accuracy, approaching it as quantum information processing. For a given control resolution, we define the analogs of several quantum bits within the shape of a single wave packet. These bits are based on wave packet symmetries. Analogs of one- and two-bit gates can be implemented using only free wave packet evolution and coordinate-dependent ac Stark shifts applied at the moments of fractional revivals. As in quantum computation, the gates form a logarithmically small set of basis operations which can be used to approximate any unitary transformation desired for quantum control of the wave packet dynamics. Numerical examples show the application of this approach to control vibrational wave packet revivals.     

Quantum Dynamical Recurrences in Position-Dependent Mass Systems

Journal of Russian Laser Research - Wave-packet dynamics in bounded systems manifests quantum recurrences at different time scales, namely, classical periodicity, quantum revivals, and fractional...     

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.     

Dynamics of a quantum oscillator strongly and off-resonantly coupled with a two-level system

Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time scale, the quantum oscillator shows collapses, revivals and fractional revivals, which are encountered in oscillator observables like the mean number of oscillator quanta and in the two-level inversion population. Also the scattered oscillator field shows doublets with symmetrically displaced peaks.     

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.     

Information Entropy to Probe Revivals in Dynamical Systems

It is shown that sum of information entropies in position and momentum space, quantifies the temporal information in wave packet dynamics of a dynamical system. Quantum fractional revivals are investigated on these bases in periodically driven Fermi-Ulam accelerator. It is observed that the entropic measure provides deeper insight of the wave packet dynamics for the long time evolution as compared with conventional autocorrelation function. It is shown that these revival times are not symmetric in driven situations and may lead to a random behavior.     

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.     

Three-dimensional molecular wave packets: Calculation of revival times from periodic orbits

We present a theoretical analysis of revivals and fractional revivals of three-dimensional wave packets, which describe the coupled vibrational motion of phosphaethyne (HCP) in its ground electronic state. The wave packets studied are chosen to evolve along the periodic orbits, which quantize the states in the three fundamental progressions. The revival times T_rev are found to depend strongly on the particular mode excited and on the mean excitation energy. Based on a semiclassical analysis, T_rev is shown to be determined by the dependence of the period of the orbits on the classical action along them.     

Robust decoupling techniques to extend quantum coherence in diamond

We experimentally demonstrate over 2 orders of magnitude increase in the room-temperature coherence time of nitrogen-vacancy centers in diamond by implementing decoupling techniques. We show that equal pulse spacing decoupling performs just as well as nonperiodic Uhrig decoupling and also allows us to take advantage of revivals in the echo to explore the longest coherence times. At short times, we can extend the coherence of particular quantum states out from T2*=2.7 μs out to an effective T2>340 μs. For preserving arbitrary states we show the experimental importance of using pulse sequences that compensate the imperfections of individual pulses for all input states through judicious choice of the phase of the pulses. We use these compensated sequences to enhance the echo revivals and show a coherence time of over 1.6 ms in ultrapure natural abundance 13C diamond.     

Tunneling time in space fractional quantum mechanics

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for $b\to \infty$ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.     

Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

Simple, controllable models play an important role in learning how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum dynamics provides us with a phenomenological approach to characterise dynamics with a variety of non-Markovian behaviours, here described in terms of the trace distance between two reduced states. By adopting a trajectory picture for the open quantum system evolution, we analyse how non-Markovianity is influenced by the constituents defining the quantum renewal process, namely the time-continuous part of the dynamics, the type of jumps and the waiting time distributions. We focus not only on the mere value of the non-Markovianity measure, but also on how different features of the trace distance evolution are altered, including times and number of 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.     

Dynamics of two atoms in a quantized radiation field

We study a model with two atoms interacting with a single-mode quantized radiation field. We show the detailed quantum collapse and “revivals” in our system.