We show set of transformations which allow to obtain analytic solutions in several quantum-optical problems. We start with the ion-laser (time dependent) interaction, continue with the problem of a slow atom interacting with a quantized field to end with a master equation that describes losses. In all cases it is shown that one may find useful transformations that simplify the problems.
We study the non-linear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the non-linear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schröndiger equation. To this end, we find a regular solution for the non-autonomous linear quantum master equation in Gorini-Kossakowski-Sudarshan-L…
We use a non-Lindbladian master equation of the Scully-Lamb laser model for the analysis of light propagation in a parity-time symmetric photonic system composed of coupled active and passive whispering-gallery microresonators. Performing the semiclassical approximation, we obtain a set of two nonlinear coupled differential equations describing the time evolution of intracavity fields. These coupled equations are able to explain the experimentally-observed light non-reciprocity [Peng {\em et al.}, Nature Physics {\bf 10}, 394 (2014), Chang {\em et al.}, Nature Photonics {\bf 8}, 524 (2014)]. W…
We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which pro- vides an useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We…
Polaron master equation theory of pulse driven phonon-assisted population inversion and single photon emission from quantum dot excitons
我们引入一个直观的半解析极化子主方程方法来模拟脉冲驱动的粒子数反转和从量子点激子发射的单光子。主方程理论允许一个确定重要的声子诱导散射率解析，并充分包括随时间变化的泵场的作用。作为该理论的应用，我们首先研究了由时变激光脉冲驱动的量子点的共振态和非共振态，发现声子发射引起的粒子数反转与Quilter { \em et al.}最近的实验直接一致，Phys Rev Lett { \bf 114}，137401（2015）。然后，我们在弱耦合腔中模拟量子点，并显示激子驱动和腔驱动系统之间的人口响应的差异。最后，我们评估的非共振声子辅助加载计划与一个量子点共振耦合到一个腔作为一个确定性的单光子源，并比较和对比的重要数字的优点与直接拉比振荡的人口使用共振$π$脉冲，后者被证明是更有效的。
In this work, dissipative effects from a phonon bath on the resonance fluorescence of a solid state two level system embedded in a high quality semiconductor microcavity and driven by an intense laser, are investigated. Within the density operator formalism, we derive a variational master equation valid for broader ranges of temperatures, pumping rates, and radiation-matter couplings, than previous studies. From the obtained master equation, fluorescence spectra for various thermal and exciting conditions are numerically calculated, and compared to those computed from weak coupling and polaron…
Open systems dynamics: Simulating master equations in the computer
主方程可能是任何研究耗散量子光学的人最基本的方程。在这种情况下，在计算机中编码和模拟这些方程的有效方法是非常有用的，在这篇笔记中，我试图以一种全面的方式介绍我是如何做到这一点的，重点是Matlab，但使其足够通用，以便可以直接翻译为任何其他语言或软件的选择。我的大部分方法都是从胡安·何塞·加西亚-里波尔（Juan José García-Ripoll）那里继承来的（他的数学能力我怎么称赞都不为过），我在这里和那里改变它们，以适应我（相当有限的）数字大脑的工作方式，并尽可能地将它们与我如何理解它们背后的理论联系起来。目前，笔记集中在如何编码主方程并找到它们的稳态，但我希望很快我就能用时间演化方法更新它们，包括如何处理依赖于时间的主方程。在过去的4年里，我在各种不同的背景下测试了这些方法，包括电路量子电动力学，激光问题，光学参量振荡器和光机系统。评论和（建设性的）批评是非常欢迎的，并将适当的信贷和承认。
We report on the controllable response of the lasing frequency to the cavity round-trip path change. This is achieved by modifying the dispersion of the intracavity medium in the four-wave mixing regime in Rb. We can either increase the response by at least a factor of $2.7$ or drastically reduce it. The former regime is useful for sensitive measurements tracking the cavity round trip length and the latter regime is useful for precision metrology.
We obtain a master equation for a parametrically driven optomechanical cavity. We use a more correct dissipation model that accounts for the modification of the quasienergy spectrum caused by the driving. When the natural frequency of the mechanical object oscillates periodically around its mean value, the master equation with the improved dissipation model is expressed using Floquet operators. We apply the corresponding master equation to model the laser cooling of the mechanical object. Using an adiabatic approximation, an analytical expression for the number of excitations of the mechanical…
The simplest model of a single-emitter laser generating in the regime of small number of photons in the cavity is theoretically investigated. Based on a system of equations for different moments of the field operators the analytical expressions for mean number of photons and its dispersion are obtained. Using the master equation approach the differential equation for the phase-averaged quasi-probability Q is derived. For some limiting cases the exact solutions of this equation are found.
The theory of open quantum system is one of the most essential tools for the development of quantum technologies. Furthermore, the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) Master Equation plays a key role as it is the most general generator of Markovian dynamics in quantum systems. In this paper, we present this equation together with its derivation and methods of resolution. The presentation tries to be as self-contained and straightforward as possible to be useful to readers with no previous knowledge of this field.
Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to consider different kinds of master equations for the same system. Here, we derive an exact connection between the time-local and the integro-differential descriptions, focusing on the class of commutative dynamics. The use of the damping-basis formalism allows us to devise a general procedure to go from one master equation to the other and vice-versa, by working with functions of time and their La…
General analytical solution to exact fermion master equation
先前在[Phys. Rev. B \textbf{78}，235311（2008）; New J. Phys. \textbf{12}，083013（2010）]中获得的精确费米子主方程描述了费米子粒子的主系统在外部费米子库（例如，纳米电子系统）的影响下的量子态的动力学。在这里，我们提出了这个精确的费米子主方程的一般解决方案。该解决方案是解析表示在最直观的粒子数表示。它适用于在任意初始状态下制备的主系统中的任意数目的轨道。我们证明了这样的通用解决方案的有用性与纳米结构的人工分子的瞬态动力学。我们展示了各种初始状态如何导致不同的瞬态动力学，表现出众多的潜在的过渡途径。
Universal gate-set for trapped-ion qubits using a narrow linewidth diode laser
我们报道了一种基于捕获$^{88}$ Sr $^+$离子的用于量子信息处理的高保真通用光量子比特门的实现。使用窄线宽二极管激光器进行所有相干操作。我们采用了主从配置的激光器，其中超低膨胀玻璃（ULE）法布里-珀罗腔被用作稳定的参考以及光谱滤波器。我们使用修正的Ramsey序列的离子来表征激光光谱，该序列消除了磁场噪声的影响。我们展示了高保真单量子位门与个人寻址，基于非均匀微动，在两个离子链以及莫默-索伦森两量子位纠缠门。
Alkali-metal-vapor magnetometers, using coherent precession of polarized atomic spins for magnetic field measurement, have become one of the most sensitive magnetic field detectors. Their application areas range from practical uses such as detections of NMR signals to fundamental physics research such as searches for permanent electric dipole moments. One of the main noise sources of atomic magnetometers comes from the light shift that depends on the frequency of the pump laser. In this work, we theoretically study the light shift, taking into account the relaxation due to the optical pumping …
