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Non-classical states in light-matter interactions.

Moya-Cessa, Hector Manuel

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

In this thesis we investigate the possibilities to create non-classical states by using light-matter interactions. Our basic approach to describe these interactions is the Jaynes-Cummings model. It describes interactions between a two-level atom and a quantized field in a lossless cavity (ultra high Q quality factor). The model can be easily generalized to describe multi-level atoms, Stark shifts, Kerr interactions, micromasers, etc. We use some of these generalizations in our study. Our main interest is in the production of Schrodinger cat states, that is, the coherent superposition of two or more classical macroscopic states; and the production of sub-Poissonian photostatistics. First of all, we use the simple Jaynes-Cummings model to investigate the interaction of coherent states with two-level atoms, and compare it to the case of interaction with a statistical mixture to show that we can discern between the two. We investigate as well the interaction of two level atoms and squeezed light, where we show that these states have a strong coherent character. However, the model itself is very simple, and as we have said before, some generalizations are necessary if we are to describe more realistically the atom field interactions. In particular, we use a phenomenological Hamiltonian, which incorporates Stark shifts in the atomic levels due to the electric field in the cavity, and show that some experimental results concerning the lineshapes in micromasers may be explained by such effects. Another step is to allow the atoms to enter and leave the cavity, which leads us to investigate a micromaser system. Within this structure, we allow for one- and two-photon transitions. In the latter case, it is shown that sub-Poissonian fields (by using special atom-field interaction times) and multi Schrodinger cat states (by measuring the state of the atoms as they leave the cavity) can be generated.

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Cambridge University Press eBooks•Oct 28, 2004•0 citations
In this thesis we investigate the possibilities to create non-classical states by using light-matter interactions. Our basic approach to describe these interactions is the Jaynes-Cummings model. It describes interactions between a two-level atom and a quantized field in a lossless cavity (ultra high Q quality factor). The model can be easily generalized to describe multi-level atoms, Stark shifts, Kerr interactions, micromasers, etc. We use some of these generalizations in our study. Our main interest is in the production of Schrodinger cat states, that is, the coherent superposition of two or more classical macroscopic states; and the production of sub-Poissonian photostatistics. First of all, we use the simple Jaynes-Cummings model to investigate the interaction of coherent states with two-level atoms, and compare it to the case of interaction with a statistical mixture to show that we can discern between the two. We investigate as well the interaction of two level atoms and squeezed light, where we show that these states have a strong coherent character. However, the model itself is very simple, and as we have said before, some generalizations are necessary if we are to describe more realistically the atom field interactions. In particular, we use a phenomenological Hamiltonian, which incorporates Stark shifts in the atomic levels due to the electric field in the cavity, and show that some experimental results concerning the lineshapes in micromasers may be explained by such effects. Another step is to allow the atoms to enter and leave the cavity, which leads us to investigate a micromaser system. Within this structure, we allow for one- and two-photon transitions. In the latter case, it is shown that sub-Poissonian fields (by using special atom-field interaction times) and multi Schrodinger cat states (by measuring the state of the atoms as they leave the cavity) can be generated.
We demonstrate that the generalization of the two-level Jaynes-Cummings model (JCM) to an N-level atom leads to the creation of up to N macroscopically distinct field states. These field states are Schmidt-orthogonalized superpositions of Fock states. They correspond to macroscopic states of the field, attainable with large mean photon numbers. Unlike the situation with a two-level atom and a coherent-state field, which evolves into a macroscopic coherent superposition state (a Schrodinger cat), we find that when the additional levels participate strongly in the excitation (e.g all transitions are resonant with equal dipole moments) then the system does not evolve into a pure state. We will present some examples of special cases, giving insight into the behavior of three-level atoms and the two-level two-photon JCM.
We investigate some of the basic features of the interaction of superpositions of coherent states of light with two-level atoms in the framework of the Jaynes-Cummings model. We compare the behaviour of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. We investigate the collapses and revivals of the atomic inversion by studying the evolution of the Q function of the cavity field. We also establish the connection between the purity of the field and the collapses and revivals of the atomic inversion.
We uncover new features on the study of a two-level atom interacting with one of two cavities in a coherent superposition. The James-Cummings model is used to describe the atom-field interaction and to study the effects of quantum indefiniteness on such an interaction. We show that coherent control of the two cavities in an undefined manner allows novel possibilities to manipulate the atomic dynamics on demand which are not achievable in the conventional way. In addition, it is shown that the coherent control of the atom creates highly entangled states of the cavity fields taking a Bell-like or Schrödinger-cat-like state form. Our results are a step forward to understand and harness quantum systems in a coherent control, and open a new research avenue in the study of atom-field interaction exploiting quantum indefiniteness.
In this work, we uncover new features on the study of a two-level atom interacting with one of two cavities in a coherent superposition. The James-Cummings model is used to describe the atom-field interaction and to study the effects of quantum indefiniteness on such an interaction. We show that coherent control of the two cavities in an undefined manner allows novel possibilities to manipulate the atomic dynamics on demand which are not achievable in the conventional way. In addition, it is shown that the coherent control of the atom creates highly entangled states of the cavity fields taking a Bell-like or Schrödinger-cat-like state form. Our results are a step forward to understand and harness quantum systems in a coherent control, and open a new research avenue in the study of atom-field interaction exploiting quantum indefiniteness.
Due to the improvement within cavity quantum electrodynamics experiments during the last decades, what was former seen as 'toy models' are today realized in laboratories. A controlled isolated coherent evolution of one or a few atoms coupled to a single mode inside a cavity is achievable. Such systems are well suited for studying purely quantum mechanical effects, and also for performing quantum gates, necessary for quantum computing. The Jaynes-Cummings model has served as a theoretical description of the interaction. However, as the experimental techniques are improved, for example, atom cooling, the use of multi-level atoms or multi-modes and driving of atoms or elds by external lasers, extensions of the original Jaynes-Cummings model are needed. In this thesis we study some of these extended models, and in particular multi-level models, time-dependent models and quantized motion models. Both analytical and numerical analysis are considered. The two-level structure of the Jaynes-Cummings model leads to applications of known solvable time-dependent two-level Schrödinger equations. In other cases, di erent forms of adiabatic approximate solutions are used, and with the analytically solvable models, the amplitudes of non-adiabatic contributions may be estimated. For higher dimensional systems, STIRAP and multi-STIRAP methods are applied. It is shown how the time-dependent models may be used for preparation of various kinds of non-classical states, and also to generate universal sets of quantum gates, both on atomic and eld qubits. When the atoms are cooled to very low temperatures, their velocities must be treated quantum mechanically, and we have studied the dynamics of such cases for di erent coupling shapes. Again numerical and analytical approaches have been used and compared, wave-packet propagations of the atom, approaching and traversing the cavity, have been performed. For periodic couplings, standing wave cavity modes, the dynamics has been described by e ective parameters; group velocity or atomic index of refraction and effective mass. Tunneling resonances for ultra cold atoms have been exhibited in the STIRAP models for certain initial conditions.
In this chapter, we discuss two more experimental realizations of quantum optical phenomena, namely the interaction of an effective two-level atom with a quantized electromagnetic field in a high Q microwave cavity, the subject usually referred to as cavity QED, or sometimes CQED, and in the quantized motion of a trapped ion. Strictly speaking, these experiments are not optical, but they do realize interactions of exactly the type that are of interest in quantum optics, namely the Jaynes–Cummings interaction between a two-level system (an atom) and a bosonic degree of freedom, a single-mode cavity field in the case of a microwave cavity, and a vibrational mode of the center-of-mass motion of a trapped ion, the quanta being phonons in this case. We shall begin with a description of the useful properties of the so-called Rydberg atoms that are used in the microwave CQED experiments, proceed to discuss some general considerations of the radiative behavior of atoms in cavities, the CQED realization of the Jaynes–Cummings model, and then discuss the use of the dispersive, highly off-resonant, version of the model to generate superpositions of coherent states, i.e. the Schrödinger cat states of the type discussed in Chapters 7 and 9 for traveling wave optical fields but this time for a microwave cavity field. Finally, we discuss the realization of the Jaynes–Cummings interaction in the vibrational motion of a trapped ion.