p complicated by the possibility of more than one atom being in the cavity at the same time. In a second analysis the paper takes up the recent idea 6 that the micromaser may be used to distinguish between quantum mechanical systems quantised by normal canonical quantisation as opposed to the quantisation imposed by the recently discovered 'quantum groups' 7-10. The Jaynes-Cummings model 1l of one 2-level atom and one ~uantised cavity mode is fundamental to the theory of the micromaser12- 4. We show how the model can be given a ~uantum group quantisation by using the q-deformed bosons ('q-bosons' 0) recently describedl5- 17 . We show that q-dependent features derived from the q-bosons would appear in the quantum revivals (as already suggested6 ) and in the second and higher Rabi split energies. The vacuum field Rabi splitting is not changed. New measurements are needed to determine whether there is any physics in this form of quantum group quantisation. The material is presented in the following way. We make a few remarks on the measurement of the cavity field in high-Q microwave cavities and on aspects of cavity q.e.d. in high and low-Q cavities in the §§2 and 3 following. In §4 we give the theory of the q-deformed Jaynes-Cummings model. In §§S-7 we show how the theory of the one-atom micromaser based on conventional quantum mechanics in cavities of finite
p complicated by the possibility of more than one atom being in the cavity at the same time. In a second analysis the paper takes up the recent idea 6 that the micromaser may be used to distinguish between quantum mechanical systems quantised by normal canonical quantisation as opposed to the quantisation imposed by the recently discovered 'quantum groups' 7-10. The Jaynes-Cummings model 1l of one 2-level atom and one ~uantised cavity mode is fundamental to the theory of the micromaser12- 4. We show how the model can be given a ~uantum group quantisation by using the q-deformed bosons ('q-bosons' 0) recently describedl5- 17 . We show that q-dependent features derived from the q-bosons would appear in the quantum revivals (as already suggested6 ) and in the second and higher Rabi split energies. The vacuum field Rabi splitting is not changed. New measurements are needed to determine whether there is any physics in this form of quantum group quantisation. The material is presented in the following way. We make a few remarks on the measurement of the cavity field in high-Q microwave cavities and on aspects of cavity q.e.d. in high and low-Q cavities in the §§2 and 3 following. In §4 we give the theory of the q-deformed Jaynes-Cummings model. In §§S-7 we show how the theory of the one-atom micromaser based on conventional quantum mechanics in cavities of finite
A distinctive signature of the granulated nature of the electromagnetic field is the revivals known to occur in the dynamics of a two-level atom interacting with a single-field mode (Jaynes-Cummings model). The development of high-Q single-mode cavities combined with progress in Rydberg atom spectroscopy has led to a possibility of verifying these predictions. Revival experiments using micromasers have been performed by Walther et al. Here the cavity mode is first allowed to reach a steady state, and then probe atoms are injected into the resonator. By measuring their state as they exit the cavity, one can infer the state of the field. We show that the micromaser experiences Jaynes-Cummingslike revivals when the pump parameter θ is varied. However, in contrast to the conventional Jaynes-Cummings situation, which considers initially coherent fields, the micromaser photon statistics are usually not Poissonian and depend sensitively on θ. The micromaser revivals cannot be explained by a semiclassical theory or linearized quantum fluctuations about the semiclassical solution. Rather, an exact quantum treatment, considering fully the granularity of the cavity mode, is required.
The microscopically pumped maser, or micromaser is a cavity QED experiment intended to be a physical realisation of the Jaynes-Cummings model of a single two-level atom interacting with a single mode electromagnetic field. This is the simplest model that describes the interaction between light and matter, yet it predicts behaviour unexpected from semiclassical models, such as the revival of Rabi oscillations of an atom interacting with an initially coherent field and non-monotonic linewidth as a function of pumping. The micromaser at the University of Leeds consists of a high quality superconducting microwave cavity designed to be resonant with the transition between two specific Rydberg states of rubidium. These two states behave like an ideal two level atom, and couple strongly to the cavity field due to a large dipole moment. These Rydberg atoms are passed through the cavity in a rarified beam such that in most instances when there is an atom in the cavity, there will only be one, closely approximating the Jaynes-Cummings model. I present experimental work on the build phase of the micromaser. Specifically I routed all of the wiring and microwave lines in the cryostat that contains the micromaser, and designed mounts for various components. I also designed several testing methods for probing high quality microwave cavity resonances and quality factors which are presented. Using the Jaynes-Cummings model as a prototype, I demonstrate how extensions to the model can be used to construct universal quantum logic gates that operate on photonic qubits in a multi-mode cavity. This could be realised in a micromaser with a multi-mode cavity. Conversely, I demonstrate that by using atoms as qubits, detuned cavities can be used to generate entangled resources such as the Greenberger-Horne-Zeilinger state, the W state, and graph states of atoms. I show that single qubit rotations on Rydberg atom qubits have already been experimentally demonstrated so that in combination these entangled resources are useful for quantum metrology, quantum computation and even tests of quantum gravity.
We propose a variation of the Jaynes-Cummings Model (JCM), which consists of a Two-Level Atom (TLA) within a cross cavity configuration. This new geometry is a suitable tool to understand the origin of new QED features that the original JCM does not reveal, showing revivals in cases where they are not expected to appear. Full Text: PDF References E.T. Jaynes, F.W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser", Proc. IEEE 51, 1 (1963). CrossRef M. Wilkens, P. Meystre, "Nonlinear atomic homodyne detection: A technique to detect macroscopic superpositions in a micromaser", Phys. Rev. A 43, 7 (1991). CrossRef I.V. Jyotsna, G.S. Agarwal, "The Jaynes-Cummings model with continuous external pumping", Opt. Commun. 99, 344 (1993). CrossRef M.S. Abdalla, M. Abdel-Aty, A.-S.F. Obada, "Quantum entropy of isotropic coupled oscillators interacting with a single atom", Opt. Comm. 211, 225 (2001). CrossRef M.A. Marchiolli, R.J. Missori, "Qualitative aspects of entanglement in the Jaynes?Cummings model with an external quantum field", J. Phys. A: Math. Gen. 36, 49 (2003). CrossRef J.C. García-Melgarejo, Ph.D. Thesis. INAOE (2015). J.R. Ackerhalt, K. Rzazewski, "Heisenberg-picture operator perturbation theory", Phys. Rev. A 12, 6 (1975) CrossRef J.H. Eberly, N.B. Narozhny, J.J. Sanchez-Mondragon, "Periodic Spontaneous Collapse and Revival in a Simple Quantum Model", Phys. Rev. Lett. 44, 20 (1980). CrossRef N.B. Narozhny, J.J. Sanchez-Mondragon, J.H. Eberly, "Coherence versus incoherence: Collapse and revival in a simple quantum model", Phys. Rev. A 23, 1 (1981). CrossRef L. Allen, J.H. Eberly, Optical resonance and two-level atoms (New York, Wiley 1975). A. Joshi, R.R. Puri, "Effects of the Binomial Field Distribution on Collapse and Revival Phenomena in the Jaynes-Cummings Model", J. Modern Optics 34, 11 (1987). CrossRef
There are only fistful of systems in physics that can be described by an exact theory from first principles and, at the same time, can be investigated under experimental conditions approaching the idealized theoretical ones. The one-atom-maser or micromaser provides such an example, making a detailed study of the fundamental properties of the atom-field interaction possible. The situation realized in a micromaser is very close to the ideal case of a single two-level atom interacting with a single quantized mode of a cavity field. In the micromaser the atoms have a dual purpose of both pumping the field and also probing it via measurements of the outgoing atoms. Any other means of measuring the field inside the resonator has the detrimental effect of lowering its Q-factor and thereby the photon storage time. The long photon storage time of the resonator allows for the decay of the field to be negligible during the passage of an atom and its interaction with the field. The behavior of atoms in a cavity is governed by the oscillatory exchange of energy between the atoms and the field, which is called Rabi oscillation. For cavity fields in the vacuum and few photon number states (Fock states), Rabi oscillations have been measured in the past. To prevent thermal effects from polluting the pure number states these experiments were performed at low temperatures (below 1 K). However, the observed resolution of the Rabi oscillations measurements was quite disappointing (only about 2% of the predicted theoretical value) and precluded more ambitious experiments like atom-atom correlations or time resolved investigations of the maser field dynamics. The observed contrast of Rabi oscillations can be considered as a figure of merit for the experimental resolution of quantum features of a maser field. Therefore, a high resolution in the measurements of Rabi oscillations is crucial. This thesis describes the methods and improvements applied to enhance the resolution of Rabi oscillations by a factor of 8. The following upgrades and developments proved to be crucial in this work: 1) The base temperature of the cryogenic system was lowered to 0.3 K, i.e. one third of the original value. At the same time, the time during which the system remains at the base temperature was improved by almost of an order of magnitude (to more than 12 h). 2) For the promotion of the atoms to the Rydberg regime new three-step diode laser setup was constructed. The excitation efficiency compared to the old dye laser was increased by two orders. Using top-of-fringe stabilization with new spectroscopic methods, specially designed error detection and feedback schemes as well as state-of-the-art PID regulators the continuous locking of lasers is about 8 h (compared to about 20 min with the old dye laser system). 3) The flexibility of using the three step excitation allows to excite different maser states and for the first time to investigate pure maser transition. 4) Various improvements on the atomic oven and the channeltron detection unit led to the reliable and stable production and detection of the atomic beam. Observed distribution of the atomic beam statistics reaches to within 6% the Poisson limit which is expected in the absence of experimental imperfections. 5) New developed techniques in magnetic field compensation allow to perform such measurements with two orders of magnitude better accuracy compared to the previous experiments. To demonstrate the new capabilities of the apparatus and to apply its improved resolution of quantum fields we performed a previously impossible in-depth analysis of mean photon number and the atomic inversion produced by a micromaser for various detunings between the cavity- and atomic resonance frequency.
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.
The experimental possibility of observing the most basic atom-radiation interactions appears to be much closer than even two years ago. Such experiments are expected to focus on properties of a single Rydberg atom interacting with an ultracold cavity. In the event that the atom is prepared so that it can be approximated as having only two levels, and the cavity is cold enough to be effectively lossless during the interaction time, it is expected to be well described by the Jaynes Cummings (J-C) model1 theory. Rabi oscillations as predicted by J-C theory have already been observed for the N-atom case.2