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arXiv:2205.14435

A Computational and Experimental Analysis of Higher Order Modes in a Strongly Focusing Optical Cavity

Mehmet Öncü, Mohsen Izadyari, Özgür Esat Müstecaplıoğlu, Kadir Durak

Published May 28, 2022• 0 citations
arXivHTMLPDF

Abstract

Optical cavities operating in the near-concentric regime are the fundamental tools to perform high precision experiments like cavity QED applications. A strong focusing regime unfortunately is prone to excite higher-order modes. Higher-order mode excitation is challenging to avoid for the realistic strong focusing cavities, and if these modes are closely spaced, overall cavity linewidth gets significantly broadened. In this study, a computational method alongside the experiment is provided for the optical mode decomposition into cavity eigenmodes with justified approximations. It is shown that it is possible to recreate the intensity and spectral profile of the cavity transmission, with the provided model. As a result, a more complete treatment of the realistic near-concentric cavities can be done.

DOI
10.48550/arxiv.2205.14435

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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. 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Journal of Optics B Quantum and Semiclassical Optics•Feb 1, 2004•0 citations
Optical cavities operating in the near-concentric regime are the fundamental tools to perform high precision experiments like cavity QED applications. A strong focusing regime unfortunately is prone to excite higher-order modes. Higher-order mode excitation is challenging to avoid for the realistic strong focusing cavities, and if these modes are closely spaced, overall cavity linewidth gets significantly broadened. In this study, a computational method alongside the experiment is provided for the optical mode decomposition into cavity eigenmodes with justified approximations. It is shown that it is possible to recreate the intensity and spectral profile of the cavity transmission, with the provided model. As a result, a more complete treatment of the realistic near-concentric cavities can be done.
In the near-concentric regime, the transverse modes of an optical cavity have small mode volumes with a beam waist on the order of the atomic cross section. This shows potential for strong interaction between single atoms and light, which is a key component in distributed quantum computing architectures [1] . Furthermore, with centimetresized near-concentric cavities, the frequency spacing of the transverse modes ranges from tens of MHz to a GHz, matching well with the hyperfine or the Zeeman level splitting of an atom [2] . This near-degeneracy in resonant frequencies close to the critical point allows to explore the physics of atomic nonlinearities with multiple photonic modes strongly coupled to different hyperfine or magnetic energy levels of a quantum emitter.
Optical cavities in the near-concentric regime have near-degenerate transverse modes; the tight focusing transverse modes in this regime enable strong coupling with atoms. These features provide an interesting platform to explore multi-mode interaction between atoms and light. Here, we use a spatial light modulator (SLM) to shape the phase of an incoming light beam to match several Laguerre-Gaussian (LG) modes of a near-concentric optical cavity. We demonstrate coupling efficiency close to the theoretical prediction for single LG modes and well-defined combinations of them, limited mainly by imperfections in the cavity alignment.
Summary form only given. Cavity Quantum Electrodynamics (CQED) has been at the forefront of modem atomic physics and quantum optics. Of particular importance of CQED is the strong coupling regime whereby the coupling rate between atoms and cavity field dominates other dissipative rates [1]. To date, the requirements to obtain such significant interaction have been presumed to have micro-cavities with a high finesse and small mode volumes. Though having demonstrated remarkable results and progress, such cavities with limited optical access, high reflectivity coating and close distance between mirrors pose a challenge for scaling up and embedding other systems with CQED such as ion traps.In this work, we take an alternative approach of employing cavity designs with strong focusing modes [2]. Central to our experiment is a cavity in the near concentric point with a finesse of 150. The cavity has a length of 11mm, a radius of curvature of 5.5mm and accommodates a focusing mode of approximately 5um beam waist. We trapped a single Rb87 atom at the centre of the cavity by an intra-cavity dipole trap. We observed the lineshape splitting in the transmission spectrum of cavity under the present of the trapped single atoms. The cooperativity of 0.1 can be deduced from Fig 1 and place our system in the intermediate coupling regime. This first observation of lineshape splitting with centimetre long and low finesse cavity promises the broader use of CQED and new exploration of CQED physics at strong focusing regime, where all optical cavity modes become degenerate.
Atom-photon interfaces are one of the building blocks of the future quantum information protocols. Accomplishing a strong interaction between the atom and the photons can be successfully done by high finesse and small mode volume cavities. However, this method requires sophisticated dielectric coatings and stabilization of the cavity against even small vibrations and small line width of those cavities impose higher input photon numbers if spontaneously emitted photons are to be used, which make it seem hard to scale up such atom-light interfaces to form quantum networks. An alternative method is to use a nearly concentric cavity, which has a strongly focused optical mode [1].
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.
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.