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Optics Letters

Time response of a coupled atoms–cavity system

S. L. Mielke, G. T. Foster, J. Gripp, Luis A. Orozco

Published Mar 1, 1997• 14 citations
Publisher

Abstract

We study the time response of a quantum optical system to a step excitation. The system is composed of a collection of N two-level atoms coupled to a single mode of the electromagnetic field of an optical cavity. The size of the step excitation is not limited to the low-intensity regime. Before the system reaches steady state there is an oscillatory exchange of energy between the atoms and the cavity. We compare the experimental results quantitatively with theoretical calculations and with previous transmission spectroscopy measurements.

DOI
10.1364/ol.22.000325

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We study the time response of a quantum optical system to a step excitation. The system is composed of a collection of N two-level atoms coupled to a single mode of the electromagnetic field of an optical cavity. The size of the step excitation is not limited to the low-intensity regime. Before the system reaches steady state there is an oscillatory exchange of energy between the atoms and the cavity. We compare the experimental results quantitatively with theoretical calculations and with previous transmission spectroscopy measurements.
The experiments discussed in this thesis focus on the interaction of a single trapped atom with the single mode of a high-finesse optical cavity, in the regime of strong coupling. Chapter 1 gives a brief introduction, after which Chapter 2 describes our recent measurements of the transmission spectrum of the atom-cavity system. The spectrum exhibits a clearly resolved vacuum-Rabi splitting, in good quantitative agreement with theoretical predictions. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements of this type that have required averaging over 10^3-10^5 atoms. Chapter 3 discusses our observations of photon blockade for the transmitted light in the presence of one trapped atom. Excitation of the atom-cavity system by a first photon blocks the transmission of a second one, thereby converting an incident Poissonian stream of photons into a sub-Poissonian, anti-bunched stream, as confirmed by measurements of the photon statistics of the transmitted field. The intensity correlations of the cavity transmission also reveal the energy distribution for oscillatory motion of the trapped atom. Chapter 4 details a set of simple but necessary measurements of relevant experimental parameters such as cavity geometry, linewidth, mirror properties, birefringence, and detection efficiency. The thesis concludes with Appendix A, describing the efficient laser setup we use for our magneto-optical traps.
We consider N identical two-level atoms coupled to an optical cavity, which is coherently driven by an external field. In the limit of small atomic excitation, the reflection and transmission coefficients for both fields and intensities are calculated analytically. In addition, the frequency content of the cavity field and hence also the emission spectrum of the cavity is determined. It is discussed in particular how individual collisional dephasing and common atomic energy-level fluctuations prevent the cavity field from being in a coherent state, which in turn affects the outgoing fields.
We have experimentally studied the steady-state characteristics of a cascaded quantum-optical system. The conceptually simple apparatus consists of a pair of high finesse cavities traversed by a beam of optically prepared two-level atoms. The output from the first cavity is coupled through a unidirectional device into the second cavity. The experimental results show quantitative agreement with a model that takes into account the geometric factors of the cavity modes and treats the two-level atoms as being purely radiatively broadened.
In this dissertation we study the interaction of a single atom with a single mode of the electromagnetic field in an optical cavity. We emphasize strong coupling conditions, where the dipole coupling strength is larger than the dissipation rates of the cavity and the atom. By exciting the coupled atom and cavity mode with an external field, the excited-state spectroscopy of the coupled system is explored. Both quantum mechanical and semiclassical calculations are performed and their results are compared. In the limit of a weak driving field, both results show a two-peak ("vacuum" Rabi) spectrum. With increased strength of the driving field, differences are observed. The quantum calculation shows a multi-peak ( two "vacuum" Rabi peaks plus additional peaks) spectrum, while the semiclassical calculation does not. These additional peaks are produced by transitions between the excited states of the Jaynes-Cummings IV Hamiltonian indicative of the quantum nature of the coupled atom-cavity-mode system.
For the most part, quantum statistical processes in quantum optics are investigated in a weak-coupling regime, but it has become possible recently to realize experimentally optical systems for which the internal coupling coefficient g is comparable to the external dissipative rates. Within, this context, the subject of our investigation is the quantum dynamical processes for a small collection of N two-state atoms strongly coupled to a single mode of a high-finesse optical cavity. For this system, we record input-output characteristics for steady-state operation with 3 ⪝ N ⪝ 65 intracavity atoms and observe optical bistability for N⪞15 atoms.1