Tutorial: projector approach to open quantum systems
- URL: http://arxiv.org/abs/2305.19704v2
- Date: Thu, 1 Jun 2023 06:07:28 GMT
- Title: Tutorial: projector approach to open quantum systems
- Authors: C. Gonzalez-Ballestero
- Abstract summary: This tutorial aims at providing quantum theorists across multiple fields with a self-contained practical toolbox to derive effective quantum dynamics.
First, we summarize the projector approach to open quantum systems and the derivation of the fundamental Nakajima-Zwanzig equation.
Then, we show how three common effective equations, namely the Born-Markov Master Equation, the adiabatic elimination used in atom physics, and a different adiabatic elimination used in sideband cooling, can be derived from different perturbative expansions of the Nakajima-Zwanzig equation.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Most quantum theorists are familiar with different ways of describing the
effective quantum dynamics of a system coupled to external degrees of freedom,
such as the Born-Markov master equation or the adiabatic elimination.
Understanding the deep connection between these apparently unrelated methods
can be a powerful tool, allowing us to derive effective dynamics in
unconventional systems or regimes. This tutorial aims at providing quantum
theorists across multiple fields (e.g. quantum and atom optics, optomechanics,
or hybrid quantum systems) with a self-contained practical toolbox to derive
effective quantum dynamics, applicable to systems ranging from N-level emitters
to mechanical resonators. First, we summarize the projector approach to open
quantum systems and the derivation of the fundamental Nakajima-Zwanzig
equation. Then, we show how three common effective equations, namely the
Born-Markov Master Equation, the adiabatic elimination used in atom physics,
and a different adiabatic elimination used in sideband cooling, can be derived
from different perturbative expansions of the Nakajima-Zwanzig equation. We
also solve in detail two specific examples using this formalism, namely the
adiabatic elimination in a Lambda system and the effective equations of a
mechanical resonator cooled by an optical cavity.
Related papers
- Markovian dynamics for a quantum/classical system and quantum trajectories [0.0]
We develop a general approach to the dynamics of quantum/classical systems.
An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative.
arXiv Detail & Related papers (2024-03-24T08:26:54Z) - A dynamic programming interpretation of quantum mechanics [0.0]
We introduce a transformation of the quantum phase $S'=S+frachbar2logrho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of particles.
We show that the quantum potential can be removed from the transformed quantum Hamilton-Jacobi equations if they are solved as Hamilton-Jacobi-Bellman equations.
arXiv Detail & Related papers (2024-01-08T18:43:40Z) - Effective description of cooling and thermal shifts in quantum systems
coupled to bosonic modes [0.0]
An effective Lindblad master equation for quantum systems with dissipative bosonic modes has been introduced.
Here, we demonstrate that this effective master equation can also be used to describe cooling in systems with light-matter interactions.
In addition, we present how the effective master equation can be extended to the case of non-vanishing mean thermal occupations of the bosonic mode.
arXiv Detail & Related papers (2023-05-04T22:06:58Z) - Third quantization of open quantum systems: new dissipative symmetries
and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods.
We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians.
For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z) - A Quantum-Classical Model of Brain Dynamics [62.997667081978825]
Mixed Weyl symbol is used to describe brain processes at the microscopic level.
Electromagnetic fields and phonon modes involved in the processes are treated either classically or semi-classically.
Zero-point quantum effects can be incorporated into numerical simulations by controlling the temperature of each field mode.
arXiv Detail & Related papers (2023-01-17T15:16:21Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - Parity measurement in the strong dispersive regime of circuit quantum
acoustodynamics [1.7673364730995766]
We show direct measurements of the phonon number distribution and parity of nonclassical mechanical states.
These measurements are some of the basic building blocks for constructing acoustic quantum memories and processors.
Our results open the door to performing even more complex quantum algorithms using mechanical systems.
arXiv Detail & Related papers (2021-10-01T08:40:26Z) - From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation.
We describe quantum decays in a 2-level system as coherent and continuous processes.
arXiv Detail & Related papers (2021-07-29T18:27:38Z) - Revealing higher-order light and matter energy exchanges using quantum
trajectories in ultrastrong coupling [0.0]
We extend the formalism of quantum trajectories to open quantum systems with ultrastrong coupling.
We analyze the impact of the chosen unravelling (i.e., how one collects the output field of the system) for the quantum trajectories.
arXiv Detail & Related papers (2021-07-19T11:22:12Z) - Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor.
We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
arXiv Detail & Related papers (2021-01-21T22:18:49Z) - Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics.
The formalism shows remarkable analogies to the use of Green functions in quantum field theory.
The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
arXiv Detail & Related papers (2020-06-04T09:41:08Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.