This dissertation considers both a lossless and a dissipative micromaser in which a monoenergetic beam of two-level atoms in a coherent superposition of their upper and lower states is injected inside a single mode, high-Q cavity. In the lossless case, we find that under appropriate conditions a field initially in a mixed state will evolve to previously unknown pure states, which we call the tangent and cotangent states. In various limits, these states exhibit interesting properties such as sub-Poissonian photon statistics and squeezing, and most importantly they acquire the characteristics of "macroscopic" quantum superpositions. When dissipation of the cavity mode is incorporated into the model, we find that although the field no longer evolves to a pure state, the mixed steady-state field may still retain the properties of a macroscopic superposition under experimentally realizable damping rates. We then evaluate the experimental conditions necessary for the preparation and detection of such macroscopic superpositions.
We consider a lossless micromaser in which a monoenergetic, low-density beam of two-level atoms in a coherent superposition of their upper and lower states is injected inside a single-mode high-Q cavity. This is a realization of a harmonic oscillator driven by a quantum current. We find that under appropriate conditions the field may evolve to pure states, which we call tangent and cotangent states, even for mixed-state initial conditions. In various limits, they exhibit nonclassical properties such as sub-Poissonian photon statistics, or even more interestingly acquire the characteristics of ``macroscopic'' quantum superpositions. The conditions under which these states are reached, as well as the dynamical approach of the system to steady state, are discussed in detail.
Quantum interference effects are theoretically investigated in the steady-state photon statistics of single-mode Λ- and V-type micromasers with injected three-level atoms in a superposition of their internal states. The two lower (upper) levels are nondegenerate and coherent in a general case. For the Λ-type case, we have discussed how detunings affect the photon statistics of the noninversion micromaser. Under the proper conditions strongly sub-Poissonian field states with a large number of photons can be easily produced in this novel micromaser even if there exists no coherence between the two lower levels. For the V-type case, we have analysed how the photon statistics changes with the increase of the ground-state population. Although the generation of the strongly sub-Poissonian states is always possible in the micromaser under the noninversion case, their photon intensities become very weak compared to the Λ-type case. Our results indicate that it is perfectly possible to experimentally realize a noninversion micromaser with strongly sub-Poissonian statistics in the Λ-type system.
A single beam of excited two-level atoms couples two micromasers in a series. It is shown that in the absence of dissipation the possible steady states of their fields are superpositions, of two-field trapping number states. Which one is realized depends upon the initial state of the fields and the interaction parameters, g'\ensuremath{\tau}' and g''\ensuremath{\tau}'', of the two cavities. A large number of these trapping states are pure quantum states, some of them showing entanglement of the two nonlocal micromaser fields of the form \ensuremath{\Vert}N,N+M〉\ifmmode\pm\else\textpm\fi{}\ensuremath{\Vert}N+M,N〉. Here, N and N+M are arbitrary trapping numbers that belong to disconnected blocks of the photon number space and M specifies the order of correlation between the fields. The time evolution of the system toward steady states is investigated numerically, mainly concentrating on the production of pure entangled trapping states of the form discussed earlier. We describe a special procedure to amplify a number state, \ensuremath{\Vert}N,N〉, into such states that is based on conditions regarding the interaction parameters. In principle, N and M can be made arbitrarily large resulting in a steady-state nonlocal quantum superposition of distinct macroscopical fields (nonlocal ``Schr\"odinger cat''). We also present a solution of the standard master equation of a damped harmonic oscillator at finite temperature and apply it to study the effect of dissipation on the production of entangled trapping states at regular and Poissonian pump statistics.It is found that although the entanglement does not survive at a steady state it can build up in the short-time transient regime when cavity losses and the number of thermal photons are not too large. In this small-loss (large
Nex) regime the quantum correlation between the micromaser fields decays into a steady-state classical superposition at a rate that depends on the cavity lifetime and the difference (or order of correlation), M, between the superposed photon numbers. In the large-loss (small
Nex) regime, however, no transient correlation can be produced and the photon statistics spreads out towards a vacuum for increasing losses. The system undergoes a transition from an uncorrelated to a correlated behavior when the pumping parametrized by
Nex exceeds the threshold between the large- and small-loss regimes. Thermal photons enhance the decay of the correlation and by coupling the disconnected blocks of the photon number space they populate the trapping number states of adjacent blocks. However, it is shown that the production of transient entanglement is not significantly affected by either thermal radiation or pumping fluctuations. The experimental realization of the entanglement of nonlocal micromaser fields employing these two-field trapping states of small photon numbers is shown to be feasible in the short-time transient regime using the presently available high-Q cavities and low temperatures, and could be possible on the macroscopic scale in the near future.
We study the dynamics of a two-photon micromaser driven by a sequence of polarized Rydberg atoms. If cavity losses are neglected, the density matrix of the cavity mode consists of four dynamically decoupled components. Under appropriate trapping conditions, similar to those for the one-photon micromaser, it evolves to a stationary state. When the bare two-photon frequency cancels the ac Stark shift we cannot satisfy the trapping conditions for odd and even photon number states simultaneously. For specific initial conditions, where either only odd or only even number states are initially populated, we may find, however, stationary states that are pure and that can lead to macroscopic superpositions. These pure states are analogous to the cotangent and tangent states of the one-photon micromaser. When the two atomic levels are in resonance with the bare two-photon transition, trapping conditions for odd and even photon number states can be fulfilled simultaneously. Although the ac Stark shift does not allow for pure stationary states, the stationary state resembles an incoherent superposition of only two pure states, to within a relative deviation of 10-3 off purity.
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.