QwaveMPS

Matrix-product-state simulations of non-Markovian waveguide QED

QwaveMPS is an open-source Python package that calculates light-matter interactions in waveguide QED systems using Matrix Product States, allowing one to study delayed feedback effects in the non-Markovian regime.

QwaveMPS is an open-source Python library for simulating one-dimensional quantum many-body systems using Matrix Product States (MPS). Designed for researchers and students, it provides a user-friendly interface for constructing, evolving, and analyzing quantum states and operators, facilitating studies in quantum physics and quantum information. This approach enables efficient, scalable simulations by focusing computational resources on the most relevant parts of the quantum system. Thus, one can study delayed feedback effects in the non-Markovian regime at a highly reduced computational cost compared to full Hilbert space approaches, making it practical to model open waveguide QED systems.

Features

• Nonlinear non-Markovian waveguide-QED problems: Solve problems involving multiphoton and multiatom systems with time-delayed feedback.
• Matrix product states (MPS): Based on MPS theory for efficient numerical exact results that do not rely on Monte Carlo simulations.
• Open-source Python package: Python library with minimal dependencies on external packages.
• User-friendly framework: Designed to be accessible for researchers and students.
• Comprehensive Resources: Documentation and examples provided to support learning and usage.

Installation

This package can be installed using the following command:

pip install QwaveMPS

Usage

The following diagram summarizes the QwaveMPS framework, showing the main input and output parameters. For detailed usage information, see our documentation.

Documentation

Read the full documentation at https://qwavemps.readthedocs.io

Simple example: Population dynamics of a TLS in an infinite waveguide

Import the necessary packages:

import numpy as np
import QwaveMPS as qmps

Define the simulation parameters:

delta_t = 0.05 # Time step of the simulation
tmax = 8 # Maximum simulation time
tlist=np.arange(0,tmax+delta_t,delta_t)
d_t_l=2 #Size of right-channel time bin (choose 2 for 1 photon per bin)
d_t_r=2 #Size of left-channel time bin 
d_t_total=np.array([d_t_l,d_t_r])

d_sys1=2 # tls bin dimension
d_sys_total=np.array([d_sys1]) #total system bin

gamma_l,gamma_r=qmps.coupling('symmetrical',gamma=1)
input_params = qmps.parameters.InputParams(
    delta_t=0.05, 
    tmax = 8,
    d_sys_total=d_sys_total,
    d_t_total=d_t_total,
    gamma_l=gamma_l,
    gamma_r=gamma_r,  
    bond_max=4 # Maximum bond dimension, truncates entanglement information
)

Choose the initial state:

sys_initial_state=qmps.states.tls_excited() #TLS initially excited
wg_initial_state = qmps.states.vacuum(tmax,input_params) #waveguide in vacuum

Choose the Hamiltonian:

hm = qmps.hamiltonian_1tls(input_params)

Calculate time evolution of the system:

bins = qmps.t_evol_mar(hm,sys_initial_state,wg_initial_state,input_params)

Choose operators to calculate population dynamics:

tls_pop_op = qmps.tls_pop()
flux_op_l = qmps.b_pop_l(input_params)
flux_op_r = qmps.b_pop_r(input_params)
flux_ops = [flux_op_l, flux_op_r]

Calculate population dynamics with operators or lists of operators:

tls_pop = qmps.single_time_expectation(bins.system_states, tls_pop_op)
photon_fluxes = qmps.single_time_expectation(bins.output_field_states, flux_ops)

Plot of population dynamics:

Check the full example for more details

License

QwaveMPS is distributed under the GNU GPLv3. See LICENSE for more information.

Citing QwaveMPS

If you use QwaveMPS in your research, please consider citing our paper: arXiv

Contact

For questions or support, open an issue or email qwavemps@gmail.com.

If you encounter a bug or have a feature request, please open an issue on the issue tracker to report it.