Farhan Saif
We investigate recurrence phenomena in coupled two degrees of freedom systems. It is shown that an initial well localized wave packet displays recurrences even in the presence of coupling in these systems. We discuss the interdependence of these time scales namely, classical period and quantum revival time, and explain significance of initial conditions.
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Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance spin systems, precise criterions to establish controllability, such as the so called rank criterion, are well known. However most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems -- encompassing quantu…
Recurrence behavior of wave packets in coupled higher dimensional systems and periodically driven systems is analyzed, which takes place in the realm of higher coupling/modulation strength. We analyze the wave packet dynamics close to nonlinear resonances developed in the systems and provide the analytical understanding of recurrence times.We apply these analytical results to investigate the recurrence times of matter waves in optical lattice in the presence of external periodic forcing. The obtained analytical results can experimentally be observed using currently available experimental setup…
Is There Quantum Recurrence in the Presence of an Energy Continuum?
该研究通过含初始态与连续谱态跃迁的简单模型，发现完整能量连续谱下存活概率仅指数衰减，而截断连续谱的存活概率会先降数个量级后出现有限回升，解答了能量连续谱下是否存在量子复发的问题。
A simple approach for understanding the quantum nature of angular momentum and its reduction to the classical limit is presented based on Schwinger's coupled-boson representation. This approach leads to a straightforward explanation of why the square of the angular momentum in quantum mechanics is given by j(j+1) instead of just j^2, where j is the angular momentum quantum number.
Resonances, Recurrence Times and Steady States in Monitored Noisy Qubit Systems
研究噪声监控量子比特系统中的非平衡稳态和复发时间，发现噪声影响稳态行为，通过统计物理模型解释监控驱动的无限温度稳态与热弛豫的竞争。
This paper is devoted to the study of continuous-time processes known as continuous-time open quantum walks (CTOQWs). A CTOQW represents the evolution of a quantum particle constrained to move on a discrete graph, but also has internal degrees of freedom modeled by a state (in the quantum mechanical sense), and contain as a special case continuous-time Markov chains on graphs. Recurrence and transience of a vertex are an important notion in the study of Markov chains, and it is known that all vertices must be of the same nature if the Markov chain is irreducible. In the present paper we addres…
A blueprint for experiments exploring the Poincaré quantum recurrence theorem
本文研究弱耦合环境中的$N$量子比特系统，解析与数值刻画复活概率及指数标度的回归时间，并提出利用超导多量子比特平台实验检验庞加莱量子回归。
It is well-known that a dilute one-dimensional (1D) gas of bosons with infinitely strong repulsive interactions behaves like a gas of free fermions. Just as with conduction electrons in metals, we consider a single-particle picture of the resulting dynamics, when the gas is isolated by enclosing it into a box with hard walls and preparing it in a special initial state. We show, by solving the nonstationary problem of a free particle in a 1D hard-wall box, that the single-particle state recurs in time, signaling the intuitively expected back-and-forth motion of a free particle moving in a confi…
The seminal work by T. Kazimierczuk et al. [Nature 514, 343 (2014)] has shown the existence of highly excited exciton states in a regime, where the correspondence principle is applicable and quantum mechanics turns into classical mechanics, however, any interpretation of exciton spectra based on a classical approach to excitons is still missing. Here, we close this gap by computing and comparing quantum mechanical and semiclassical recurrence spectra of cuprous oxide. We show that the quantum mechanical recurrence spectra exhibit peaks, which, by application of semiclassical theories and a sca…
In the case of the discrete time coined quantum walk the reduced dynamics of the coin shows non-Markovian recurrence features due to information back-flow from the position degree of freedom. Here we study how this non-Markovian behavior is modified in the presence of open system dynamics. In the process, we obtain useful insights into the nature of non-Markovian physics. In particular, we show that in the case of (non-Markovian) random telegraph noise (RTN), a further discernbile recurrence feature is present in the dynamics. Moreover, this feature is correlated with the localization of the w…
Tight bounds on recurrence time in closed quantum systems
本文研究了闭合量子系统中复发时间的上界，通过逆量子速度限制问题推导出复发时间与逃逸时间的关系，并展示随机哈密顿量下该界被普遍满足。
In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both regimes of weakly and strongly interacting oscillators from which interesting results arise concerning the coherence properties of the joint and the reduced system states. The strong coupling regime is required to achieve a large frequency shift of the oscillator normal modes, making it possible to explore the whole profile of the spectral density of the res…
The nature of spin squeezing has been studied earlier for a coupled state of two spinors by Usha Devi et. al. (J. Phys. A: Math. Gen. 36 5333 (2003)). In this paper, we extend this study to a coupled state of two spin-1 systems. Here, we show that the direct product of two spin-1 states exhibits squeezing unlike the direct product of two spinors. We investigate the nature of squeezing for non-separable coupled state of two spin-1 systems and identify the parameters which are responsible for the existence of squeezing. We also provide ways to generate them by external interactions.
The nature of the ground states for a system composed of two coupled cavities with each containing a pair of dipole-coupled two-level atoms are studied over a wide range of detunings and dipole coupling strengths. The cases for three limits of exact resonance, large positive and negative detunings are discussed, and four types of the ground states are revealed. Then the phase diagrams of the ground state are plotted by choosing three different "order parameters". We find that the phase space, determined by the combinative action of detuning and the dipole coupling strength, is divided into fou…
A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax towards an equilibrium. It is found that quantum coherence of the initial product states in the uncoupled eigenbasis can be viewed as a resource for equilibration and approach to thermalization as manifested by the entanglement. Results are given for four distinct perturbation strength regimes, the ultra-weak, weak, intermediate, and strong regimes. For each, three types of initially unentang…
Cavity quantum electrodynamics (QED) studies the interaction between a quantum emitter and a single radiation-field mode. When an atom is in strong coupling with a cavity mode1,2, it is possible to realize key quantum information processing (QIP) tasks, such as controlled coherent coupling and entanglement of distinguishable quantum systems. Realizing these tasks in the solid state is clearly desirable, and coupling semiconductor self-assembled quantum dots (QDs) to monolithic optical cavities is a promising route to this end. However, validating the efficacy of QDs in QIP applications require…
Floquet Recurrences in the Double Kicked Top
研究双 kicked top (DKT) 中的精确量子回复，通过解析证明 Floquet 算符在特定参数下的周期性，并揭示动力学量子相变与时间反演对称性的关系。
In this work we reconsider the problem discussed by Caldeira and Leggett (CL), and generalize their results for a quantum oscillator coupled bilinearly to a reservoir with dense discrete spectrum of harmonic oscillators. We show that for such systems dynamic evolution of any state of the CL Hamiltonian consists of recurrence cycles with partial revivals of the initial state amplitude. This revival or Loschmidt echo appears in each cycle due to reverse (from the reservoir) transitions (not existing in the limit of a macroscopic bath). Width and number of the Loschmidt echo components increase w…
Elementary particles, i.e. the basic constituents of nature, are characterized by quantum recurrences in time. The flow of time of every physical system can be therefore decomposed in elementary cycles of time. This allows us to enforce the local nature of relativistic time, yielding interesting unified descriptions of fundamental aspects of modern physics, as shown in recent publications and reviewed in [arXiv:1305.2802]. Every particle can be regarded as a reference clock with time resolution of the order of its Compton time, typically many orders of magnitude more accurate than the atomic c…
We solve the coupled recurrence relations for eigenenergies and -vectors in nondegenerate Rayleigh-Schrödinger perturbation theory under the constraint that the approximate eigenvector be normalised to $1$ in every order. The series can be expressed in terms of diagrams that were first introduced by C. Bloch [Nucl. Phys. 6, 329 (1958)] for the degenerate, unnormalised case. Normalisation increases the number of terms and introduces a nontrivial dependence on the diagrams' topology to the coefficients.
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