Related papers: Exact Numerical Solution of Stochastic Master Equa…
We propose a method to achieve quantum supremacy using ensembles of qubits, using only spin squeezing, basis rotations, and Fock state measurements. Each ensemble is assumed to be controllable only with its total spin. Using a repeated…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
Stochastic Master equations or quantum filtering equations for mixed states are well known objects in quantum physics. Building a mathematically rigorous theory of these equations in infinite-dimensional spaces is a long standing open…
The spin state of an atomic ensemble can be viewed as two bosonic modes, i.e., a quantum signal mode and a $c$-numbered ``local oscillator'' mode when large numbers of spin-1/2 atoms are spin-polarized along a certain axis and collectively…
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…
A model of an arbitrary spin coupled to a bath of spins 1/2 in a star configuration is considered. The exact reduced dynamics of the central spin is found for the case of non-correlated initial conditions of the system and the bath. The…
We consider squeezing of one component of the collective spin vector of an atomic ensemble inside an optical cavity. The atoms interact with a cavity mode, and the squeezing is obtained by probing the state of the light field that is…
For any mean value of a cartesian component of a spin vector we identify the smallest possible uncertainty in any of the orthogonal components. The corresponding states are optimal for spectroscopy and atomic clocks. We show that the…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
We investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with the perturbative oscillator-qubit coupling. It is shown that such a hybrid system is very suitable for…
The progress in high-precision spectroscopy requires one to verify the accuracy of theoretical models such as the master equation describing spontaneous emission of atoms. For this purpose, we apply the coarse-graining method to derive a…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
We analyze the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity and continuous quantum measurement of the transmitted cavity field in order to monitor the evolution of the atomic ensemble. Using…
We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained.…
We investigate the possibility to perform a Quantum Non Demolition measurement of the collective alignment of an atomic ensemble in the case of a $F\geq 1$ spin. We compare the case of purely vectorial and purely tensorial Hamiltonians and…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…
For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrisation principle (SP) and for massive particles also conform to super-selection rules (SSR) that prohibit coherences…
We propose a method for engineering spin dynamics in ensembles of integer-spin atoms confined within a high-finesse optical cavity. Our proposal uses cavity-assisted Raman transitions to engineer a Dicke model for integer-spin atoms, which,…