We study the quantum dynamics of an ultracold atomic gas trapped in an optical lattice within an optical high-$Q$ resonator. The atoms are coherently illuminated with the cavity resonance tuned to a blue vibrational sideband so that stimulated gain of the resonator mode is accompanied by vibrational cooling of the atoms. This system exhibits a threshold above which pairwise stimulated generation of a cavity photon and an atom in the lowest vibrational band dominates spontaneous scattering and we find a combination of optical lasing with a buildup of a macroscopic population in the lowest lattice band. Including output coupling of ground-state atoms and replenishing of hot atoms into the cavity volume leads to a coherent, quantum correlated atom-photon pair source very analogous to twin light beam generation in a nondegenerate optical parametric oscillator.
We study the quantum dynamics of an ultracold atomic gas trapped in an optical lattice within an optical high-Q resonator. The atoms are coherently illuminated with the cavity resonance tuned to a blue vibrational sideband so that stimulated gain of the resonator mode is accompanied by vibrational cooling of the atoms. This system exhibits a threshold above which pairwise stimulated generation of a cavity photon and an atom in the lowest vibrational band dominates spontaneous scattering and we find a combination of optical lasing with a buildup of a macroscopic population in the lowest lattice band. Including output coupling of ground-state atoms and replenishing of hot atoms into the cavity volume leads to a coherent, quantum correlated atom-photon pair source very analogous to twin light beam generation in a nondegenerate optical parametric oscillator.
We consider ultracold atoms in a far detuned optical lattice across a high-Q optical resonator. Applying an external driving laser to the atoms red detuned from the cavity mode by one vibrational quantum induces cavity-enhanced sideband cooling. For a dense and cold enough atomic ensemble we predict an oscillation threshold for optical Raman sideband lasing concurrent with coherent matter-wave amplification. Above threshold, photons and atoms in the lowest band are dominantly created pairwise via stimulated emission with a strong suppression of competing spontaneous processes. In close analogy to a nondegenerate parametric oscillator, we find sub-Poissonian photon statistics and almost perfect nonclassical atom-photon number correlations. Injecting atoms in higher vibrational bands via tunneling or incoherent scattering then leads to continuous, simultaneous generation of a coherent atom beam and laser light with nonclassical atom-field correlations.
The interaction of laser cooled atoms with resonant light is determined by the natural linewidth of the excited state. An optical cavity is another optically resonant system where the loss from the cavity determines the resonant optical response of the system. The near resonant combination of an optical Fabry-Pérot cavity with laser cooled and trapped atoms couples two distinct optical resonators via light and has great potential for precision measurements and the creation of versatile quantum optics systems. Here we show how driven magneto-optically trapped atoms in collective strong coupling regime with the cavity leads to lasing at a frequency red detuned from the atomic transition. Lasing is demonstrated experimentally by the observation of a lasing threshold accompanied by polarization and spatial mode purity, and line-narrowing in the outcoupled light. Spontaneous emission into the cavity mode by the driven atoms stimulates lasing action, which is capable of operating as a continuous wave laser in steady state, without a seed laser. The system is modeled theoretically, and qualitative agreement with experimentally observed lasing is seen. Our result opens up a range of new measurement possibilities with this system.
This thesis summarizes the research work we did in the past years, which focuses on the theoretical study of quantum effects of ordered atomic structures interacting with the quantum electric field of an optical resonator. Within this work we investigated the quantum properties of the light at the cavity output, emitted by this kind of system, and the quantum state of the atoms confined by the light fields of the cavity mode. Following one possible partition, we have organized the thesis in two parts. The first part of the thesis is devoted to the quantum properties of the light at the output of optical cavities, in which atoms are confined. After a brief introduction on the basics of atom-photon interactions, we show theoretically, that two atomic dipoles in a resonator can behave as a quantum non-linear medium, whose response can be controlled through the interactomic distance of the atoms inside the resonator. We identify the parameter regime, for which the system operates as a parametric amplifier, based on the atoms' collective dipole cascade emission. Moreover we also determine the corresponding field squeezing spectrum at the cavity output. These dynamics could be observed as a result of self-organization processes of laser-cooled atoms in resonators. The second part of the thesis studies the quantum ground state of an ultracold atomic gas trapped inside an optical resonator by the mechanical effects of atom-photon interactions. Due to the strong coupling regime, the ultracold atomic gas feels a quantum potential, where the fluctuations at the single photon level may be relevant in determining the trapping conditions. This potential depends on the atomic distribution, which at the same time determines the intracavity field amplitude. Here, after a brief introduction on ultracold atoms in optical lattices, we study the low temperature physics of an ultracold atomic gas in the quantum potential formed inside a pumped cavity, by mapping the dynamics to an effective Bose-Hubbard model. We predict the existence of non-compressible states of the atomic gas, and determine a phase diagram as a function of the cavity parameters. Novel effects are encountered, such as the existence of overlapping stability regions corresponding to competing insulator-like states when the laser pumps the cavity, to provide one example out of many. At the end of the thesis a concluding chapter presents some general outlooks to this thesis work.
We study a single incoherently pumped atom moving within an optical high-Q resonator in the strong-coupling regime. Using a semiclassical description for the atom and field dynamics, we derive a closed system of differential equations to describe this coupled atom-field dynamics. For sufficiently strong pumping, the system starts lasing when the atom gets close to a field antinode, and the associated light forces provide for self-trapping of the atom. For a cavity mode blue detuned with respect to the atomic transition frequency, this is combined with cavity-induced motional cooling, allowing for long-term steady-state operation of such a laser. The analytical results for temperature and field statistics agree well with our earlier predictions based on quantum Monte Carlo simulations. We find sub-Doppler temperatures that decrease with gain and coupling strength, and can even go beyond the limit of passive cavity cooling. Besides demonstrating the importance of light forces in single-atom lasers, this result also gives strong evidence to enhance laser cooling through stimulated emission in resonators.
Prospects for reaching persistent entanglement between two spatially-separated atomic Bose–Einstein condensates are outlined. The system setup comprises two condensates loaded in an optical lattice, which, in return, is confined within a high-Q optical resonator. The system is driven by an external laser that illuminates the atoms, such that photons can scatter into the cavity. In the superradiant phase, a cavity field is established, and we show that the emerging cavity-mediated interactions between the two condensates is capable of entangling them despite photon losses. This macroscopic atomic entanglement is sustained throughout the time-evolution apart from occasions of sudden deaths/births. Using an auxiliary photon mode and coupling it to a collective quadrature of the two condensates, we demonstrate that the auxiliary mode’s squeezing is proportional to the atomic entanglement, and as such, it can serve as a probe field of the macroscopic entanglement.
Lasing [1, 2] and superradiance [3‐5] phenomena are currently enjoying a renaissance as research topics in atomic physics. Fundamentally based on the interaction of matter with an electromagnetic (light) field, the atomic dipoles in a “lasing medium” collectively emit into selected modes of the electromagnetic field and thereby create an amplified and coherent source of light. Present-day lasers use di erent types of gain media and cover a wide range of output frequencies for application in both, fundamental research and industry. A recent string of papers has reported on superradiance [6, 7] and lasing-type instabilities using Bose gases of various type (thermal atoms [8, 9], photon gases [10] and Bose-Einstein condensed atoms [11‐14]) in optical cavities. Buoyed by experimental control over essentially single excitation quanta of atoms and photons [15‐19] in cavity quantum electrodynamics, these works o er intriguing prospects for the next wave of experiments on strongly interacting light-mattter systems including a new regime where unexpected many-body and quantum fluctuation e ects of the lasing medium may become visible. Bohnet et al. [20] recently operated a superradiant “bad-cavity” laser in the few-photon regime based on coherent oscillations of the inter-atomic, collective dipole of the ultracold atoms in the cavity [21]. In this paper, we point out that a quantum degenerate Fermi gas has remarkable features as a lasing medium in a transversally driven cavity as sketched in Fig. 1. We show that the quantum statistics of the Fermi gas puts the coupled cavity+atoms system generically close to superradiance threshold as a consequence of the Pauli exclusion principle (“Pauli pressure”). Physically, this arises from enhanced scattering of fermions between di erent points on the Fermi surface with radiusjkFj by exchanging relatively large photon momenta Q from the cavity as illustrated in Fig. 1. By changing the power of the pump laser at a given density of the Fermi gas, the lasing transition is concomitant with the spontaneous formation of a charge density wave oscillating with 1=Q in real space. Tuning the ratiojkFj=jQj allows to generate a cavity spectrum with “broadband light” in certain spectral ranges or, for energies outside the particle-hole continuum of the fermions, light with relatively narrow linewidth. The normal mode splitting of the cavity by a single atom is completely replaced by many-body Ω |kF| Q