Revisiting non-degenerate parametric down-conversion

The quantum dynamics of a two-mode non-resonant parametric down-conversion process is studied by recasting the time evolution equations for the basic operators in an equivalent spin equation form with simpler exact solutions for a pump field with harmonic time dependence. Expectation values of suitable operators for studying important features such as squeezing and quantum revivals are presented in simple forms.      

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.     

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.     

Ordered space-time structures: Quantum carpets from Gaussian sum theory

The term "quantum carpet" can be observed in many closed quantum systems, where the evolution of a wave function exhibits a carpet-like pattern. Quantum carpet mechanisms are also akin to the classical interference patterns of light. Although the origins of quantum carpets have previously been studied by various researchers, many interesting details are still worth exploring. In this study, we present a unified framework for simultaneously analyzing three different features of quantum carpets: full revival,fractional revival, and diagonal canal. For the fractional revival feature, a complete formula is presented to explain its formation through Gaussian sum theory, in which all essential features, including phases and amplitudes, are captured analytically. We also reveal important relationships between the interference terms of diagonal canals and their geometric interpretations such that a better understanding of the development of diagonal canals can be supported.     

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.     

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.     

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.     

Extra revivals in cooperative atomic inversion in a cavity

We investigate collective and quantum properties of the atomic inversion of A two-level atoms interacting with a strong quantum field of a single-mode loss-free cavity. The dynamics consists of A fast scales of Rabi oscillations, each featuring collapses and revivals. The first revival of the second quasiharmonic scale can be observed with large cooperativity, demonstrating altogether the existence of the extra sidebands of the resonance fluorescence spectrum. There are also A slow cooperative scales which form the slow envelope of the inversion, which for large cooperativity can split the revivals. For the case of half excited initial atomic state the energy exchange between the field and atomic system is strongly suppressed, and there is an average energy loss by the atoms.     

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.     

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...     

Dynamic quantum revivals in phase space

We explain quantum revivals and fractional revivals in phase space of the Fermi?CUlam accelerator. We derive analytic expressions of the Wigner distribution function for the driven system describing quantum interferences in position and momentum space. We assume that the fractional revival times are nonrecurrent under certain conditions and display randomness in the occurrence of the phenomenon at these times.     

Generalized Fock spaces,new forms of quantum statistics and their algebras

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ‘infinite’, Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are: new algebras for infinite statistics,q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ‘doubly-infinite’ statistics, many representations of orthostatistics, Hubbard statistics and its variations.     

Excitation Dynamics in Chain-Mapped Environments

The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents.     

非马尔科夫耗散系统长时演化下的极限环振荡现象

本文研究结构化环境中非马尔科夫耗散系统在长时演化下可能出现的极限环振荡现象. 对于欧姆型谱密度环境中的二能级系统, 由于体系只允许一个束缚态模, 给定初态系统在Bloch空间的长时演化将收敛于一个极限环. 研究揭示了极限环半径与环心位置同环境谱密度函数间的关系. 对于多带光子晶体环境中的二能级系统, 由于其可以存在多个束缚态, 研究展现了系统在长时演化下可能出现的收敛于环面或周期或准周期的振荡行为. 有关环面的特征量与环境谱密度间的量化关系同样得以刻画. 论文随后讨论了两比特系统关联量在局域非马尔科夫耗散环境中长时演化可能出现的特征行为.     

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.     

Ergodicity in computer simulation of quantum dissipative processes

The ergodicity principle in quantum theory is employed for elaboration of a new quantum trajectory technique which is used for numerical simulation of quantum dissipative systems. With this purpose the density matrix of a quantum system is represented as a sum over an ensemble of quantum states in time intervals. The method is employed for computations of a quantum anharmonic oscillator.     

两纠缠原子与光场相互作用系统原子的纠缠特性

研究了两纠缠原子与单模相干态光场相互作用系统中原子纠缠度的时间演化特性,运用全量子理论和数值计算的方法,应用Concurrence纠缠度量标准,讨论了原子初始时刻的纠缠状态和光场强度对两原子纠缠度的影响.结果表明：双原子系统初始纠缠度越大,两原子间的纠缠在演化过程中的峰值也越大;随着光场强度的增加,两原子纠缠度的振荡曲线逐渐表现出崩塌-回复现象,周期性也越来越明显.