Geometric phase,entanglement, and quantum Fisher information near the saturation point

Considering a collection of two-level atoms in the presence of a saturating monochromatic, steady-state field, we investigate the geometric phase (GP) of an arbitrary medium’s atom. We find that it is possible to detect the saturation of the atomic response by the GP computation. This is an interesting result, because we can predict the collective behaviour of the atomic system—i.e., the saturation of the optical response of the medium- by investigating the GP of a single medium’s atom, described as a qubit. Moreover, we find that the plot of the atomic GP in terms of the detuning Δ$\Delta$ is very similar to the absorption spectrum of the medium. In addition, it is shown that when the intensity of the driving laser field tends to saturation intensity, the qubit approaches maximum correlation with its environment described by the driving field and other qubits in the atomic system. Furthermore, we find that the behaviour of the entanglement is very analogous to that of the GP and the absorption coefficient. Besides, we adopt the atom to estimate the decoherence parameter by using the quantum Fisher information (QFI), an important measure of the information content of quantum states. Interestingly, we find that when the atomic system approaches its saturation point, the QFI decays with increasing the laser intensity, and therefore the parameter estimation becomes more inaccurate.     

Fisher information due to a phase noisy laser under non-Markovian environment

More recently, K. Berrada [Annals of Physics 340 (2014) 60-69] [1] studied the geometric phase of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system, and collapse and revival phenomena were found for large class of states. In this paper, using this noise effect, we study the quantum fisher information (QFI) for a two-level atom system driven by a phase noise laser under non-Markovian dynamics. A new quantity, called QFI flow is used to characterize the damping effect and unveil a fundamental connection between non-Markovian behavior and dynamics of system–environment correlations under phase noise laser. It is shown that QFI flow has disappeared suddenly followed by a sudden birth depending on the kind of the environment damping. QFI flow provides an indicator to characterize the dissipative quantum system’s decoherence by analyzing the behavior of the dynamical non-Markovian coefficients.     

Quantum Fisher information of the GHZ state due to classical phase noise lasers under non-Markovian environment

The dynamics of N$N$-qubit GHZ state quantum Fisher information (QFI) under phase noise lasers (PNLs) driving is investigated in terms of non-Markovian master equation. We first investigate the non-Markovian dynamics of the QFI of N$N$-qubit GHZ state and show that when the ratio of the PNL rate and the system–environment coupling strength is very small, the oscillations of the QFIs decay slower which corresponds to the non-Markovian region; yet when it becomes large, the QFIs monotonously decay which corresponds to the Markovian region. When the atom number N$N$ increases, QFIs in both regions decay faster. We further find that the QFI flow disappears suddenly followed by a sudden birth depending on the ratio of the PNL rate and the system–environment coupling strength and the atom number N$N$, which unveil a fundamental connection between the non-Markovian behaviors and the parameters of system–environment couplings. We discuss two optimal positive operator-valued measures (POVMs) for two different strategies of our model and find the condition of the optimal measurement. At last, we consider the QFI of two atoms with qubit–qubit interaction under random telegraph noises (RTNs).     

Geometric phase of a central qubit coupled to a spin chain in a thermal equilibrium state

The geometric phase of a central qubit coupling to the surrounding XY chain in a transverse field at finite temperature is studied in this Letter. An explicit analytical expression of the geometric phase for coupled qubit is obtained in the weak coupling limit when the surrounding spin chain is in a thermal equilibrium state. It is shown that the GP displays dramatic change around the quantum phase transition points of the spin chain at zero and a finite range of temperature by numerical analysis. The result reveals that the GP can be used as a tool to detect QPT when the spin chain system is at finite temperature.     

非马尔可夫环境下原子的几何相位演化

从微观哈密顿量出发,研究了原子在非马尔可夫环境影响下的几何相位演化. 结果表明,在强耦合条件下原子的几何相位比弱耦合时获得的几何相位大, 而且这一差别随环境损耗的增加而增大. 在环境损耗较小时,原子的几何相位随时间变化出现连续和不连续两种演化行为,且不连续的范围随环境的损耗增加而增大. 总之,在非马尔可夫环境下,原子的几何相位演化将出现丰富而复杂的演化特征. 关键词： 几何相位 原子 腔场 非幺正     

Precision of estimation and entropy as witnesses of non-Markovianity in the presence of random classical noises

We investigate in detail the quantum Fisher information (QFI) behavior by examining a single qubit model in the presence of random classical noises in both Markovian and non-Markovian regimes. In particular, we precisely study the effects of noise switching rate ξ$\xi$ and qubit–environment coupling strength ν$\nu$ on the precision of estimation, when the qubit is subjected to random telegraph noise with a Lorentzian spectrum or colored noise with a spectrum of the form 1/f^α$1/f^{\alpha }$. In the Markovian regime, a monotone decay of the QFI with time is found, whereas for non-Markovian noise sudden death and revivals may occur. Despite these oscillations of the QFI in non-Markovian regime, we find that non-Markovian parameter γ=ξ/ν$\gamma =\xi /\nu$ is not the principal parameter controlling the collapse and revival of the QFI. In fact, in both Markovian and non-Markovian regimes, parameters ξ$\xi$ and ν$\nu$independently determine how the QFI varies. We also find that the QFI in the case of colored environments decreases when the number of fluctuators realizing the noise increases, and therefore the parameter estimation becomes more inaccurate. Furthermore, by analyzing the von Neumann entropy of the system density matrix, we illustratively unveil a fundamental relationship between the dynamics of this quantity and non-Markovian behavior in the presence of random classical noises. We also show that this result may lead to a better non-Markovianity interpretation, based on quantum memory effects. Moreover, we demonstrate the connection between the precision of parameter estimation and rising the non-Markovianity in our model where the environment is modeled as classical.     

激光的相位噪声特性以及抑制方法研究

回顾了到目前为止激光相位噪声的研究成果,阐述了由经典模型和弛豫振荡导致的在线宽展宽影响下的激光线宽。提出了自发辐射放大会对激光谱线产生进一步影响的问题。在噪声的抑制方面,分析了电子介入系统锁相方案的锁相效果。通过比较已锁相激光和未锁相激光与理想激光之间的互相关函数,结果表明,成功的锁相会使锁相激光的相干长度扩展到无限长。     

Time evolution of the intensity correlation function in a single-mode laser driven by both the coloured pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts

Using the linear approximation, we have studied the time evolution of intensity correlation function C（t） in a single-mode laser driven by both the colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts. In the case of the pump noise self-correlation time, we find that the time evolution of C（t） varies with modulation signal frequency Ω, amplitude B, and net gain ɑ0. (i) As the Ω increases, the time evolution of C（t） experiences a process changing from the monotonous descension to the descension with a flat appearing initially, and finally to the a form of damping oscillation; (ii) As the B increases, it experiences from monotonous descension to the appearance of a maximum; (iii) As the net gain ɑ0 increases, it experiences a process repeatedly changing from the monotonous descension to monotonous ascension, and to the appearance of a maximum, finally to monotonous descension again. However, in the case of, the time evolution of C（t） only exhibits a form of damping oscillation .     

Stochastic resonance driven by time-modulated correlated coloured noise sources in a single-mode laser

This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by time-modulated correlated coloured noise sources. The power spectrum and signal-to-noise ratio R of the laser intensity are calculated by the linear approximation. The effects caused by noise self-correlation time τ₁, τ₂ and cross-correlated time τ₃ for stochastic resonance are analysed in two ways: τ₁, τ₂ and τ₃ are taken to be the independent variables and the parameters respectively. The effects of the gain coefficient Γ and loss coefficient K on the stochastic resonance are also discussed. It is found that besides the presence of the standard form and the broad sense of stochastic resonance, the number of extrema in the curve of R versus K is reduced with the increase of the gain coefficient Γ.     

Geometric phase and Pancharatnam phase induced by light wave polarization

We use the quantum kinematic approach to revisit geometric phases associated with polarizing processes of a monochromatic light wave. We give the expressions of geometric phases for any, unitary or non-unitary, cyclic or non-cyclic transformations of the light wave state. Contrarily to the usually considered case of absorbing polarizers, we found that a light wave passing through a polarizer may acquire in general a nonzero geometric phase. This geometric phase exists despite the fact that initial and final polarization states are in phase according to the Pancharatnam criterion and cannot be measured using interferometric superposition. Consequently, there is a difference between the Pancharatnam phase and the complete geometric phase acquired by a light wave passing through a polarizer. We illustrate our work with the particular example of total reflection based polarizers.     

Divergence of fermionic correlations under non-Markovian noise in a non-inertial frame

Non-Markovian dynamics of correlations of fermionic systems is investigated beyond the single-mode approximations in a non-inertial frame. Two well known correlation measures, quantum discord and geometric quantum discord, are analyzed for the fermionic states influenced by the non-Markovian noise. Persistence of discord is seen for longer times depending upon the level of mixedness of the fermionic system. The dynamics of the fermionic systems heavily depends upon the degree of white noise. It is shown that fermionic systems remain dependent upon the choice of Unruh modes (_qR$q_R$) beyond the single-mode approximations under non-Markovian noise. Quantum discord is found to be more robust as compared to the geometric quantum discord. Furthermore, the non-Markovian effects are more stronger than the acceleration of Bob, the accelerated partner.     

低噪声环形腔掺铒光纤激光器的研究

分析了环形腔掺铒光纤激光器的输出特性,给出了稳态下的激光器输出功率、阈值泵浦功率和斜率效率的解析表达式,为激光器结构的优化提供了依据。搭建了全保偏环形腔掺铒光纤激光器,利用未泵浦铒纤中由驻波干涉和饱和吸收诱发的自写入光纤光栅的窄带滤波特性及反射波长的自适应特性,有效地解决了激光器的跳模问题。通过测量得到激光器系统的泵浦阈值为15.3mW,斜率效率为2.8%,输出偏振度为32dB。利用非平衡光纤干涉仪系统和相位产生载波(PGC)调制解调技术测得激光器的相位噪声为3×10-5rad/Hz~1/2(1kHz)。     

Non-Markovianity for a qubit system driven by a classical phase noisy laser

The nonlinear interaction between electron-acoustic shock waves in a dissipative, non-Maxwellian plasma composed of cold fluid electrons, stationary background ions, and inertialess superthermal electrons has been studied. The effects of plasma parameters on the trajectory changes (i.e., phase shifts) of shock waves after their head-on collision is our main concern. The results indicate that the interactions between shocks are different from those of solitons. Also, it is found that the occurrence and variation of trajectory shifts may be due to the combined role played by the dispersion and dissipation of the colliding nonlinear structure.     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

Geometric phase of a qubit interacting with a squeezed-thermal bath

We study the geometric phase of an open two-level quantum system under the influence of a squeezed, thermal environment for both non-dissipative as well as dissipative system-environment interactions. In the non-dissipative case, squeezing is found to have a similar influence as temperature, of suppressing geometric phase, while in the dissipative case, squeezing tends to counteract the suppressive influence of temperature in certain regimes. Thus, an interesting feature that emerges from our work is the contrast in the interplay between squeezing and thermal effects in non-dissipative and dissipative interactions. This can be useful for the practical implementation of geometric quantum information processing. By interpreting the open quantum effects as noisy channels, we make the connection between geometric phase and quantum noise processes familiar from quantum information theory.     

The statistical fluctuation of a single-mode laser system driven by coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts

Using the linear approximation method, this paper studies the statistical property of a single-mode laser driven by both coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, and calculates the steady-state mean normalized intensity fluctuation and intensity correlation time. It analyses the influences of the modulation signal, the net gain coefficient, the noise and its correlation form on the statistical fluctuation of the laser system respectively. It is found that the coloured pump noise modulated by the signal has a great suppressing action on the statistical fluctuation of the laser system; the pump noise self-correlation time and the specific frequency of modulation signal have the result that the statistical fluctuation tends to zero. Furthermore, the `colour' correlation of pump noise has much influences on the statistical fluctuation of the laser system. Increasing the intensity of pump noise will augment the statistical fluctuation of the laser system, but the intensity of quantum noise and the coefficient of cross-correlation between its real and imaginary parts have less influence on the statistical fluctuation of the laser system. Therefore, from the conclusions of this paper the statistical property can be known and a theoretical basis for steady operation and output of the laser system can be provided.     

Geometric phase as a simple closed-form integral

For a general evolution of a quantal system, the geometric phase measured with reference to a given initial state is derived as an integral of a function of the pure state density operator by invoking the Pancharatnam connection continuously.     

Emergence of phase correlation in Ramsey setting from superoperator point of view

A comparative analysis of four different approaches to the notion of phase in quantum optics is carried out in the framework of the Ramsey interferometer scheme, where phase correlation between two spatially separated quantum electromagnetic modes emerges as a consequence of resonant two-level atoms traversing the modes. The measure of correlation is expressed through the dispersion of the inter-mode phase difference cosine. A simple law obtained within a semiclassical approach is used to verify the quantum phase approaches. Somewhat unexpectedly, the definite advantage of the superoperator method by M.Ban is revealed.     

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.