Abstract:
Tensor networks have become a well-established tool for studying quantum many-body
systems. They are a mathematical framework for manipulating high-dimensional arrays of numbers,
which naturally appear in various areas of physics and beyond. In this project, we investigate the
behavior of pulse propagation in atomic ensembles using tensor networks. To achieve this, we adopt an
input-output formalism to map atomic ensembles to spin systems and then analyze the dynamics of the
spin systems through a matrix product state (MPS) toolbox. We validate our findings by testing them
under the Vacuum Induced Transparency (VIT) condition, in which a weak probe field can produce
transparency in an otherwise opaque medium. Our approach provides a powerful and versatile
framework for investigating the pulse propagation behavior in atomic ensembles, with potential
applications in quantum communication and computation. We aim to enhance our comprehension of
the fundamental physics of pulse propagation in these systems and explore the potential of using tensor
networks as a tool for quantum simulation and analysis.
Reproducibility Methodology:
The paper titled "Modeling Quantum Light Propagation Through Atomic Ensembles Using Matrix
Product States [1]" presents a theoretical investigation of quantum light propagation through atomic
ensembles using matrix product states (MPS). The authors propose a theoretical model that maps
atomic ensembles to spin systems and employs MPS to simulate the behavior of light pulses through the
system. The study demonstrates that the MPS approach is highly effective in reproducing the dynamics
of quantum light propagation through atomic ensembles. The authors show that the approach captures
essential aspects of the dynamics, such as the impacts of coherent and incoherent processes and the
interactions between the light and the atomic ensembles.
Results Reproduced:
A-C VIT Output Results ,D-F Quantum Jump statistics Results, G-I Convergence of observables with
increasing bond dimensions, J-M VIT Pulse Distortion for various average input photon number.
Future Work:
Photon propagation through dissipative Rydberg media at large input rates under EIT and the simulation
via density matrix using MPS are two directions which I am currently seeking to explore.
VIT OUTPUT FIELD
0.2
Input Intensity
0.15
Second Order Correlation
0.1
Output Intensity
0.05
0
0
A.
5
10
15
20
25
30
35
40
45
50
t
-0.05
VIT OUTPUT FIELD ZOOMED
0.038
Input Intensity
0.033
Second Order
Correlation
0.028
0.023
Output
Intensity
0.018
0.013
0.008
0.003
B.
-0.002 0
5
10
15
20
t
25
30
35
40
45
50
VIT OUTPUT IDEALIZED
0.2
Input Intensity
0.15
|3>
|2>
0.1
|1>
0.05
0
0
C. -0.05
5
10
15
20
25
t
30
35
40
45
Average number of
jumps
Stacked Bar Graphs of Quantum Jumps
0.04
3+
2
1
0.03
0.02
0.01
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45
t
D.
Average number of jumps
Stacked bar graph where only single photon is
detected
0.025
1 with jumps
1 only
0.02
0.015
0.01
0.005
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
t
E.
Post-selection of trajectories
Average number of jumps
0.025
|1>
|2>
0.02
|3>
0.015
0.01
0.005
0
0
-0.005
F.
10
20
30
t
40
50
Second Order Corelation
0.006
0.005
40
0.004
50
0.003
60
0.002
70
0.001
0
-0.001 0
5
10
15
20
G.
25
30
35
40
t
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
-0.005 0
Output Intensity
10
20
30
40
10
20
H.
30
40
50
t
0.012
0.01
ϵ tot
0.008
0.006
0.004
0.002
0
0
10
20
30
40
50
Maximum bond dimension D
I.
60
70
80
J.
K.
L.
M.