karopastal / quantum_states_detector

Traveling detector of a momentum state

1. Introduction
2. Usage
3. Examples

Introduction

There are three main components to the system:

Ring is the core component where the physical configuration takes place and the computations of the prepared wave function over time. The Ring is configured by the following parameters:

    N = (Integer), number of sites.
    TAUS = (Integer), the duration of the experiment in units of tau=1.
    TAU_INTERVAL = (Integer), the resolution of 1[tau] interval (partition).
    HOPPING_AMPLITUDE = (Float), the hopping constant between sites.

SitesDetector component represent an instant of detector on a ring and configured with the following parameters:

    SITE_ZERO = (Integer), the site number where the particle is prepared at when (t=0).
    ENABLE_DETECTOR = (Boolean), enable or disable the detector.
    DETECTOR = (Integer), the site number where the detector is placed.
    DETECTOR_FREQUENCY = (Integer), determines the frequency of detection in units of `[tau]`

MomentumDetector component represent an instant of detector on a ring such that the wave function prepared at a s specific momentum state |k_m> when t=0. Moreover, the detector can be stationary or travel with the speed of the initial momentum state. Momentum Detector is configured with the following parameters:

    MOMENTUM_STATE = (Integer), the `m` index of `|k_m>` that the wave function prepared at.
    ENABLE_DETECTOR = (Boolean), enable or disable the detector.
    DETECTOR = (Integer), the site number where the detector is placed at `t=0`.
    DETECTOR_FREQUENCY = (Integer), determines the frequency of detection in units of `[tau]`.
    ENABLE_DETECTOR_VELOCITY = (Boolean), determines if the detector is stationary or traveling.

Usage

prerequisites

make sure you are using python3 for compatibility with the syntax. *nix environment is preferred, but if you are running on windows gitbash (installed with git) is the recommended terminal to run the commands.

install

    $ git clone https://github.com/karopastal/quantum_states_detector.git
    $ cd quantum_states_detector
    $ pip3 install numpy matplotlib

run expirements

At ./analysis/ you can find a templates for experiments for the two cases. After parametrization of the desired configuration run the relevant expirement with:

   $ make detector_sites_case 

Or

   $ make detector_momentum_case 

Examples

configuration:

N = 10
TAUS = 50
SITE_ZERO = 0
DETECTOR = 0
DETECTOR_FREQUENCY = 5
TAU_INTERVAL = 20
HOPPING_AMP = 0.05
ENABLE_DETECTOR = False

   $ make detector_sites_case 

detector.plot_probability_per_site:

configuration:

N = 100
TAUS = 50
SITE_ZERO = 0
DETECTOR = 50
DETECTOR_FREQUENCY = 5
TAU_INTERVAL = 20
HOPPING_AMP = 1
ENABLE_DETECTOR = True

   $ make detector_sites_case 

detector.plot_probability_density:

configuration:

N = 10
HOPPING_AMPLITUDE = 0.25
TAUS = 100
TAU_INTERVAL = 5
ENABLE_DETECTOR = True
DETECTOR = 5
DETECTOR_FREQUENCY = 5
MOMENTUM_STATE = 5
ENABLE_DETECTOR_VELOCITY = True

   $ make detector_momentum_case 

detector.plot_probability_per_site:

configuration:

N = 200
HOPPING_AMPLITUDE = 1
TAUS = 150
TAU_INTERVAL = 25
ENABLE_DETECTOR = True
DETECTOR = 100
DETECTOR_FREQUENCY = 2
MOMENTUM_STATE = 50
ENABLE_DETECTOR_VELOCITY = True

   $ make detector_momentum_case 

detector.plot_probability_density: