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Time-dependent light-matter coupling and quantum dynamics

Elgbro, Daniel LU (2023) FYSK03 20231
Mathematical Physics
Department of Physics
Abstract
In this thesis, two quantum dynamical system’s of one and two qubits coupled to a field
mode confined in an optical cavity have been studied. Within the Jaynes- and Tavis-
Cummings model, the dynamics of the corresponding light-matter interaction was defined
in terms of the system’s coupling constants. From the setup of the system, the qubits
flying through the cavity, the final state of the system could be adjusted by changing the dynamics via the time-dependent coupling constants. In the two qubit system, it was
found that the entanglement between the qubits could be modified by the dynamics to
obtain a maximal entanglement in the final state. These findings provides a starting point of how entanglement can be achieved via quantum... (More)
In this thesis, two quantum dynamical system’s of one and two qubits coupled to a field
mode confined in an optical cavity have been studied. Within the Jaynes- and Tavis-
Cummings model, the dynamics of the corresponding light-matter interaction was defined
in terms of the system’s coupling constants. From the setup of the system, the qubits
flying through the cavity, the final state of the system could be adjusted by changing the dynamics via the time-dependent coupling constants. In the two qubit system, it was
found that the entanglement between the qubits could be modified by the dynamics to
obtain a maximal entanglement in the final state. These findings provides a starting point of how entanglement can be achieved via quantum dynamical light-matter interaction. (Less)
Popular Abstract
Electrons and photons are well-known entities in physics. The former are particles in
atoms: they are fundamental particles with mass. The latter are particles of light. When
these two are close to each other they can start to interact. Then, the interaction can
be seen as a coupling. This coupling depends on the magnitude of their mutual coupling
constant. In general, a coupling constant is just that: a constant. In the thesis, however, it will be investigated what happens when the coupling constant is time-dependent and how the coupling will look like then. But let us take a step back and investigate what properties of the particles are considered.

To explain this coupling, light-matter coupling, quantum mechanics must be taken... (More)
Electrons and photons are well-known entities in physics. The former are particles in
atoms: they are fundamental particles with mass. The latter are particles of light. When
these two are close to each other they can start to interact. Then, the interaction can
be seen as a coupling. This coupling depends on the magnitude of their mutual coupling
constant. In general, a coupling constant is just that: a constant. In the thesis, however, it will be investigated what happens when the coupling constant is time-dependent and how the coupling will look like then. But let us take a step back and investigate what properties of the particles are considered.

To explain this coupling, light-matter coupling, quantum mechanics must be taken into account. Consider the energy of an electron. In contrast to classical mechanics, energies in quantum mechanics are discrete: only specific values of energies are allowed called energy levels. To understand discrete energies, imagine throwing an electron in the air like a ball. You would see the electron magically disappear from your hand, appear in the air above you and then teleport back to your hand. The electrons energy can, for example, take a value of 1 or 2 but never 1.5!

Like electrons, light has discrete energies as well. One "unit" of light with a specific energy is called a photon: a particle without mass. The concept of photons are vital for light matter interaction. As famous physicist Max Planck said: only light considered as photons can interact with electrons. For light-matter interaction to occur, a photons energy must match, or be greater than, the energy difference between two energy levels of an electron.

Now, light-matter coupling can be explained. Consider a photon trapped in a box where it bounces around. Introduce an electron which has two energy levels and assume that the difference in energy between these levels correspond to the energy of the photon. When the electron, in its lower energy level, enters the box, it will absorb the photon and gain its energy. This means that the electron jumps up to its higher energy level. Then, the electron will proceed to emit the photon and go down to its original energy. This process will repeat itself indefinitely inside the box: the particles are coupled and the electron oscillates between its states.

So what would happen if the coupling changed over time? This question is to be answered in the thesis. It is known that the coupling is dependent on other physical properties, like the position of the electron, but not time. However, the position of the electron can change over time, which means that dynamical properties of the electron could affect the coupling. Therefore, the thesis will investigate a time-dependent coupling in terms of the dynamics of the system. (Less)
Please use this url to cite or link to this publication:
author
Elgbro, Daniel LU
supervisor
organization
course
FYSK03 20231
year
type
M2 - Bachelor Degree
subject
keywords
light-matter interaction, Rabi oscillations, quantum dynamics, optical cavity, qubit, coupled qubit, coupling strength, time-dependent coupling, dynamical qubits, entanglement, concurrence, qubit state manipulation, Jaynes-Cummings, Tavis-Cummings
language
English
id
9127573
date added to LUP
2023-06-20 09:34:36
date last changed
2023-06-20 09:34:36
@misc{9127573,
  abstract     = {{In this thesis, two quantum dynamical system’s of one and two qubits coupled to a field
mode confined in an optical cavity have been studied. Within the Jaynes- and Tavis-
Cummings model, the dynamics of the corresponding light-matter interaction was defined
in terms of the system’s coupling constants. From the setup of the system, the qubits
flying through the cavity, the final state of the system could be adjusted by changing the dynamics via the time-dependent coupling constants. In the two qubit system, it was
found that the entanglement between the qubits could be modified by the dynamics to
obtain a maximal entanglement in the final state. These findings provides a starting point of how entanglement can be achieved via quantum dynamical light-matter interaction.}},
  author       = {{Elgbro, Daniel}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Time-dependent light-matter coupling and quantum dynamics}},
  year         = {{2023}},
}