The quantum harmonic oscillator and catalan's constant

Quantum non-Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, we will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. We will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence of non-Markovian and non-darwinistic behaviours.

Download Full-text

Entanglement scaling in classical and quantum harmonic oscillator lattices

10.1063/1.2400881 ◽

2006 ◽

Author(s):

K. Audenaert ◽

M. Cramer ◽

J. Eisert ◽

M. B. Plenio

Keyword(s):

Harmonic Oscillator ◽

Quantum Harmonic Oscillator

Download Full-text

Time-dependent quantum harmonic oscillator: a continuous route from adiabatic to sudden changes

Journal of Physics B Atomic Molecular and Optical Physics ◽

10.1088/1361-6455/ac36ba ◽

2021 ◽

Author(s):

Daniel M. Tibaduiza ◽

Luis Barbosa Pires ◽

Carlos Farina

Keyword(s):

Harmonic Oscillator ◽

Simple Expression ◽

Time Dependent ◽

Frequency Change ◽

Quantum Harmonic Oscillator ◽

Transition Analysis ◽

Adiabatic Theorem ◽

Significant Difference ◽

The One ◽

Proper Interpretation

Abstract In this work, we give a quantitative answer to the question: how sudden or how adiabatic is a frequency change in a quantum harmonic oscillator (HO)? We do that by studying the time evolution of a HO which is initially in its fundamental state and whose time-dependent frequency is controlled by a parameter (denoted by ε) that can continuously tune from a totally slow process to a completely abrupt one. We extend a solution based on algebraic methods introduced recently in the literature that is very suited for numerical implementations, from the basis that diagonalizes the initial hamiltonian to the one that diagonalizes the instantaneous hamiltonian. Our results are in agreement with the adiabatic theorem and the comparison of the descriptions using the different bases together with the proper interpretation of this theorem allows us to clarify a common inaccuracy present in the literature. More importantly, we obtain a simple expression that relates squeezing to the transition rate and the initial and final frequencies, from which we calculate the adiabatic limit of the transition. Analysis of these results reveals a significant difference in squeezing production between enhancing or diminishing the frequency of a HO in a non-sudden way.

Download Full-text

MULTI-MODE LINEAR COMPOSITE MOMENTUM REPRESENTATION AND ITS APPLICATION

Modern Physics Letters B ◽

10.1142/s021798490901917x ◽

2009 ◽

Vol 23 (07) ◽

pp. 975-988

Author(s):

SHI-MIN XU ◽

XING-LEI XU ◽

JI-JIAN JIANG ◽

HONG-QI LI ◽

JI-SUO WANG

Keyword(s):

Harmonic Oscillator ◽

Unitary Transformation ◽

Particle System ◽

Momentum Representation ◽

Dynamic Problems ◽

Quantum Harmonic Oscillator ◽

Oscillator System ◽

Kinetic Coupling ◽

Linear Composite ◽

Multi Mode

A unitary transformation matrix, n linear-composite coordinate operators and n linear-composite momentum operators are constructed for an n-particle system, and the complete and orthonormal common eigenvectors of the multi-mode linear composite momentum operators are examined by virtue of the technique of integration within an ordered product of operators. The multi-mode linear composite momentum representation is proposed, and its application to a general two-mode forced quantum harmonic oscillator system with kinetic coupling is presented for solving some dynamic problems.

Download Full-text