Optimal Monitoring of Position in Nonlinear Quantum Systems

Optomechanics with a position-modulated Kerr-type nonlinear coupling

Cavity optomechanics has proven to be a field of research rich with possibilities for studying motional cooling, squeezing, quantum entanglement and metrology in solid state systems. While to date most studies have focused on the modulation of the cavity frequency by the moving element, the emergence of new materials will soon allow to explore the influences of nonlinear optical effects. We therefore study in this work the effects due to a nonlinear position-modulated self-Kerr interaction and find that this leads to an effective coupling that scales with the square of the photon number, meani…

Quantum Brownian motion under generalized position measurements: A converse Zeno scenario

We study the quantum Brownian motion of a harmonic oscillator undergoing a sequence of generalized position measurements. Our exact analytical results capture the interplay of the measurement backaction and dissipation. Here we demonstrate that no freeze-in Zeno effect occurs upon increasing the monitoring frequency. A similar behavior is also found in the presence of generalized momentum measurements.

Barut-Girardello coherent states for nonlinear oscillator with position-dependent mass

Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut-Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass r…

Rigorous Quantum Limits on Monitoring Free Masses and Harmonic Oscillators

There are heuristic arguments proposing that the accuracy of monitoring position of a free mass $m$ is limited by the standard quantum limit (SQL):$σ^2 (X(t)) \geq σ^2 (X(0)) +(t^2/m^2) σ^2 (P(0))\geq \hbar t/m$, where $σ^2 (X(t))$ and $σ^2 (P(t))$ denote variances of the Heisenberg representation position and momentum operators. Yuen discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL) viz. rigorous upper and lower bounds on $σ^2 (X(t))$ in terms of $σ^2 (X(0))$ and $σ^2 (P(0))$ for a free mass, and for a…

相空间测量、退相干与经典性

Phase-space measurements, decoherence and classicality

本文通过相干态POVM建模环境对相空间的监测，研究位置和动量联合测量导致的退相干，证明其使密度矩阵在位置和动量表示下对角化，并关联于双Lindblad算子动力学。

Position-dependent mass models and their nonlinear characterization

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech$^{2}$-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.

Nonlinear mechanics with photonic crystal nanomembranes

Optomechanical systems close to their quantum ground state and nonlinear nanoelectromechanical systems are two hot topics of current physics research. As high-reflectivity and low mass are crucial features to improve optomechanical coupling towards the ground state, we have designed, fabricated and characterized photonic crystal nanomembranes, at the crossroad of both topics. Here we demonstrate a number of nonlinear effects with these membranes. We first characterize the nonlinear behavior of a single mechanical mode and we demonstrate its nonlocal character by monitoring the subsequent actua…

具有位置依赖有效质量的广义二维非线性振子及其热力学性质

Generalised two-dimensional nonlinear oscillator with a position-dependent effective mass and the thermodynamic properties

本文研究具有位置依赖有效质量的二维非线性振子，利用Nikiforov-Uvarov方法获得精确能谱和波函数，并揭示二维系统比热对非线性参数$k$的强依赖性，提出调节$k$可优化量子热机与光电子器件性能。

Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators

We consider the problem of removal of ordering ambiguity in position dependent mass quantum systems characterized by a generalized position dependent mass Hamiltonian which generalizes a number of Hermitian as well as non-Hermitian ordered forms of the Hamiltonian. We implement point canonical transformation method to map one-dimensional time-independent position dependent mass Schr$ö$dinger equation endowed with potentials onto constant mass counterparts which are considered to be exactly solvable. We observe that a class of mass functions and the corresponding potentials give rise to solutio…

Standard Quantum Limits for broadband position measurement

I utilize the Caves-Milburn model for continuous position measurements to formulate a broadband version of the Standard Quantum Limit (SQL) for monitoring the position of a free mass, and illustrate the use of Kalman filtering to recover the SQL for estimating a weak classical force that acts on a quantum-mechanical test particle under continuous observation. These derivations are intended to clarify the interpretation of SQL's in the context of continuous quantum measurement.

超越线性化近似崩溃的腔量子光力学非线性与位置测量

Cavity quantum optomechanical nonlinearities and position measurement beyond the breakdown of the linearized approximation

本文提出一种非线性腔量子光力学理论框架，利用光学广义dyne检测获取机械位置信息，实现了超越线性化近似崩溃的位置测量，将推动量子计量与控制等领域发展。

Continuous intracavity monitoring of the dynamical Casimir effect

Dynamical Casimir effect (DCE) is the name assigned to the process of generating quanta from vacuum due to an accelerated motion of macroscopic neutral bodies (mirrors) or time-modulation of cavity material properties, as well as the simulation of such processes. Here I review the theoretical results on the detection of DCE using intracavity quantum detectors, such as multi-level atoms, atomic networks and harmonic oscillators. I also stress the mathematical equivalence of this problem to the physics of optical parametric oscillators interacting with atoms or quantum wells, studied in Quantum …

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrodinger equations with position-dependent effective masses

Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $\mathcal{PT}$-symmetric Scarf-II potentials. The broken linear PT symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and…