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arXiv:quant-ph/0101103 · Physical Review A

Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity

Christina J. Hood, Harry J. Kimble, Jun Ye

Published Aug 13, 2001• 241 citations
arXivHTMLPDF

Abstract

An extensive characterization of high-finesse optical cavities used in cavity QED experiments is described. Different techniques in the measurement of the loss and phase shifts associated with the mirror coatings are discussed and their agreement shown. Issues of cavity-field mode structure supported by the dielectric coatings are related to our effort to achieve the strongest possible coupling between an atom and the cavity.

DOI
10.1103/physreva.64.033804

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While for the most part quantum statistical processes in quantum optics are investigated in a weak coupling regime, it has recently become possible 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 collection of N two-state atoms strongly coupled to a single mode of a high finesse optical cavity, Our particular experiment consists of a small collection of Cesium atoms (6S1/2, F = 4 → 6P3/2, F = 5 transition at 852nm) interacting with the TEM00 mode of a spherical mirror cavity. The critical technical advance for this work is the attainment of extremely low loss mirrors for high finesse (103 – 106) and hence long photon lifetime even in a small cavity.[1]

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An extensive characterization of high-finesse optical cavities used in cavity QED experiments is described. Different techniques in the measurement of the loss and phase shifts associated with the mirror coatings are discussed and their agreement shown. Issues of cavity-field mode structure supported by the dielectric coatings are related to our effort to achieve the strongest possible coupling between an atom and the cavity.
While for the most part quantum statistical processes in quantum optics are investigated in a weak coupling regime, it has recently become possible 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 collection of N two-state atoms strongly coupled to a single mode of a high finesse optical cavity, Our particular experiment consists of a small collection of Cesium atoms (6S1/2, F = 4 → 6P3/2, F = 5 transition at 852nm) interacting with the TEM00 mode of a spherical mirror cavity. The critical technical advance for this work is the attainment of extremely low loss mirrors for high finesse (103 – 106) and hence long photon lifetime even in a small cavity.[1]
Ultra-high finesse micro-resonator plays an important role in realizing the interaction between atoms and cavity field in the study of cavity quantum electrodynamics (QED) system, weak optical nonlinear effects and micro-optic devices. By measuring basic parameters of the microcavity, the atom-cavity coupling coefficient and the cavity decay rate can be determined precisely. It is also useful for exploring the dynamic characteristics of the system. However, it has difficulty in determining resonate frequency and effective cavity length due to the structure of the ultra-high finesse optical microcavity itself and the characteristics of multilayer coating. In this paper, we demonstrate the precision measurement of effective cavity length under different resonant frequencies which our cavity mirror is coated with 37 layers of dielectric film. The theoretical expectation when using the revised model of the multilayer coating agrees well with that of the experiment; and the measurement error for longitudinal mode interval is below 0.004 nm which is two orders of magnitude better than that obtained in previous unrevised model. The tiny depths into mirror coatings that the standing-wave light field inside the cavity penetrates are given for different mode numbers. This method may be applied to other micro resonator in the precision measurement.
We characterize a high-finesse Fabry-Perot resonator for coupling with single neutral atoms. Our cavity consists of two mirrors with different reflectivities: One has minimal optical loss, and the other high transmission loss where more than 90% of the intracavity photons would be emitted. Cavity finesse, birefringent effects, and mechanical resonances are measured using the lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters, we drive the adjacent longitudinal or transverse modes with two lasers simultaneously, and measure those frequencies using a precision wavelength meter (WLM). A major novelty of this method is that the parameters' uncertainty is solely determined by the resolution of the WLM, eliminating all of the temporal environment fluctuations. Moreover, the technique with two lasers consists of a vital approach for determining geometric parameters of a short cavity, with a free spectral range on the order of THz. Our system operates in the strong atom-cavity coupling regime that allows us to explore fundamental quantum optics and implement quantum network protocols.
A single two-level emitter coupled to a single mode of an electromagnetic resonator constitutes the most fundamental instance of light--matter interaction. Realizations of this type of system are investigated in the field of cavity quantum electrodynamics (cavity QED). Particularly important are schemes in which the coupling is strong enough to exceed the spontaneous emission rate as well as cavity damping. In this case, the coherent exchange of excitation between source and photon is the dominating process, providing the unique possibility to deterministically control the quantum evolution of the system. Great progress has recently been accomplished, technologically as well as conceptually, and the focus section in this issue of Journal of Optics B: Quantum and Semiclassical Optics features five articles highlighting important recent developments in the field. Strong coupling between single atoms and the electromagnetic cavity field have been achieved in two distinct regimes, the optical and the microwave region. The latter is represented by the micromaser, a high-Q microwave cavity pumped by a beam of highly excited Rydberg atoms. It has proved to be an almost ideal system for the generation of non-classical field states. A constraint in these experiments is the fact that the field inside the cavity can only be examined indirectly, by analysing the occupation of atoms leaving the cavity. While only two atomic states were previously identified for this purpose, V A Reshetov shows in his article (pages 119--126) that more information on the field may be extracted by taking advantage of the Zeeman substructure of the atomic levels. In the optical domain of cavity QED, by contrast, the state of the resonator field may be probed directly by measuring the light leaking from the cavity using photodetectors. In order to minimize damping, high-quality cavities must be employed. In most optical experiments these are Fabry--Perot resonators with ultra-high reflectivity mirrors, with losses as low as a few parts per million being state of the art. At the same time, the coupling of atoms and photons is enhanced by reducing the length of the cavity, so that strong coupling conditions are reached. A very attractive application of this type of cavity QED setup is the possibility of exerting control over the quantum dynamics of the system. An impressive example is the implementation of quantum feedback, reported in the paper by W P Smith and L A Orozco (pages 127--134). Using information gained from detecting a single photon escaping from the cavity, active feedback is applied to halt the dynamical evolution of the system. This is the first time active feedback has been used to modify the quantum evolution of a system at the single-photon level. The authors discuss how detunings between the subsystems affect the quantum feedback, an issue particularly relevant for ensembles of atoms with a spread in detuning. Perfect quantum feedback in this case requires the use of additional parameters to control the system. The majority of optical cavity QED experiments performed so far have used as a medium atoms traversing the cavity on random trajectories, such as, for example, thermal atomic beams. In this case, the observation of quantum effects is degraded in two ways. The Doppler effect and the finite transit time lead to line broadening, while the spatial structure of the cavity mode results in atoms in different locations experiencing different coupling with the photonic field. J E Reiner et al (pages 135--142) investigate the impact of these effects on quantum fluctuations in their cavity QED system. In order to overcome line broadening, they have developed a continuous cold atomic beam, extracted from a magneto-optical trap. An even better control of broadening effects and fluctuating coupling strength is provided by trapping the atoms inside the cavity and cooling them to temperatures at which their position spread is smaller than the optical wavelength. Much recent activity has been devoted to developing such an ultimate cavity QED system. A Vukics et al (pages 143--153) present a theoretical proposal for dynamically trapping and cooling atoms inside a cavity. By driving the atoms with a standing wave injected from the side of the cavity and by weakly exciting the cavity field itself, they predict three-dimensional trapping of the atom for periods around 1 second, an extremely long time on the typical scale of cavity QED dynamics. The essential component of their scheme is the interference between the two driving fields, determining the temperature of the particle and the stable trapping positions. In the quest for better confinement of radiation, lately, an appealing alternative to the Fabry--Perot cavity has been investigated -- the optical microsphere resonator. A sphere with a diameter of a few tens of microns, it supports so-called whispering gallery modes near its circumference, for which quality factors up to 10 10 have been measured. In order to exploit the correspondingly low field damping rates for cavity QED, a method must be found to couple atomic or solid state emitters to these modes. S Göotzinger et al (pages 154--158) report the coupling of single nanocrystals on the surface of a microsphere through the evanescent field of the mode. Selective excitation of a single nano-emitter was accomplished with a scanning confocal microscope. The system is a promising candidate for cavity QED with single-quantum emitters. The ability to fully control the quantum dynamics of atoms and light is beginning to spawn early applications. The most notable example is quantum information processing. This requires the coherent manipulation of single-quantum systems, which is ideally provided by cavity QED interaction in the strong-coupling limit. The development of practical devices will be among the principal future tasks for research in the field. This will include physical systems, which have not been covered in this issue, such as semiconductors, quantum dots as emitters, or photonic crystals as resonator structures. Cavity QED is therefore guaranteed to remain a vigorous field in the years to come.
Cavity-based quantum node is a competitive platform for distributed quantum networks. Here, we characterize a high-finesse Fabry-Pérot optical resonator for coupling single or few atomic quantum registers. Our cavity consists of two mirrors with different reflectivities: One has minimal optical loss, and the other high transmission loss where more than 90% of the intracavity photons would be emitted. Cavity finesse, birefringent effects, and mechanical resonances are measured using the lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters, we drive the adjacent longitudinal or transverse modes with two lasers simultaneously, and measure those frequencies using a precision wavelength meter (WLM). A major novelty of this method is that the parameters’ uncertainties are solely determined by the resolution of the WLM, eliminating all of the temporal environment fluctuations. Our scheme makes it possible to quantify the atom-cavity coupling constant up to four significant figures, the most precise and accurate estimation so far, which would become a key ingredient for benchmarking a cavity-based quantum node. Furthermore, the distortion of polarized photonic qubits would be minimized owing to the small birefringent splitting, below 4.9% of the cavity linewidth. Our system should operate in the intermediate atom-cavity coupling regime that would allow us to implement various quantum network protocols.