The transversely confined propagating modes of an optical fiber mediate virtually infinite range energy exchanges among atoms placed within their field, which adds to the inherent free space dipole–dipole coupling. Typically, the single atom free space decay rate largely surpasses the emission rate into the guided fiber modes. However, scaling up the atom number as well as the system size amounts to entering a collective emission regime, where fiber-induced superradiant spontaneous emission dominates over free space decay. We numerically study this super- and subradiant decay of highly excited atomic states for one or several transverse fiber modes as present in hollow core fibers. As particular excitation scenarios we compare the decay of a totally inverted state to the case of π /2 pulses applied transversely or along the fiber axis as in standard Ramsey or Rabi interferometry. While a mean field approach fails to correctly describe the initiation of superradiance, a second-order approximation accounting for pairwise atom–atom quantum correlations generally proves sufficient to reliably describe superradiance of ensembles from two to a few hundred particles. In contrast, a full account of subradiance requires the inclusion of all higher order quantum correlations. Considering multiple guided modes introduces a natural effective cut-off for the interaction range emerging from the dephasing of different fiber contributions.
The transversely confined propagating modes of an optical fiber mediate virtually infinite range energy exchanges among atoms placed within their field, which adds to the inherent free space dipole–dipole coupling. Typically, the single atom free space decay rate largely surpasses the emission rate into the guided fiber modes. However, scaling up the atom number as well as the system size amounts to entering a collective emission regime, where fiber-induced superradiant spontaneous emission dominates over free space decay. We numerically study this super- and subradiant decay of highly excited atomic states for one or several transverse fiber modes as present in hollow core fibers. As particular excitation scenarios we compare the decay of a totally inverted state to the case of π /2 pulses applied transversely or along the fiber axis as in standard Ramsey or Rabi interferometry. While a mean field approach fails to correctly describe the initiation of superradiance, a second-order approximation accounting for pairwise atom–atom quantum correlations generally proves sufficient to reliably describe superradiance of ensembles from two to a few hundred particles. In contrast, a full account of subradiance requires the inclusion of all higher order quantum correlations. Considering multiple guided modes introduces a natural effective cut-off for the interaction range emerging from the dephasing of different fiber contributions.
In contrast to free space, in waveguides the dispersive and dissipative dipole–dipole interactions among quantum emitters exhibit a periodic behavior over remarkably long distances. We propose a novel setup, to our knowledge, exploiting this long-range periodicity in order to create highly excited subradiant states and facilitate fast controlled collective energy transport among far-apart ensembles coupled to a waveguide. For sufficiently large ensembles, collective superradiant emission into the fiber modes dominates over its free space counterpart. We show that, for a large number of emitters, a fast transverse coherent pulse can create almost perfect subradiant states with up to 50% excitation. On the other hand, for a coherent excitation of one sub-ensemble above an overall excitation fraction of 50% we find a nearly lossless and fast energy transfer to the ground state sub-ensemble. This transport can be enhanced or suppressed by controlling the positions of the ensembles relative to each other, while it can also be realized with a random position distribution. In the optimally enhanced case this fast transfer appears as superradiant emission with subsequent superabsorption, yet, without a superradiant decay after the absorption. The highly excited subradiant states, as well as the superradiant excitation transfer, appear as suitable building blocks in applications such as active atomic clocks, quantum batteries, quantum information protocols, and quantum metrology procedures such as fiber-based Ramsey schemes.
In this thesis, I am intending to understand the cooperative effect of an ensemble of quantum emitters, which constitutes the preliminary elements of our current experimental investigations towards realization of an ultra-narrow linewidth superriant laser. In the first part of the thesis, I investigate the basics of the theory of superradiance (SR), which includes the full derivation of the Hamiltonian and the Lindblad equation for an ensemble of two-level atoms in both free-space and a single-mode waveguide. In addition, I construct the simulations for observing the transition from single-atom uncorrelated spontaneous emission to superradiance in various physical settings, as well as a simulation for the understanding of the cooperative effects of an ensemble of two-level atoms inside an optical cavity. Then, in the second part of the thesis, I introduce the experimental progress we have been making to observe SR with an ensemble of laser-cooled Cs atoms inside a hollow-core photonic crystal fiber (HCPCF). In our experiment, the Cs atoms, initially cooled using a magneto-optical trap (MOT), are guided and confined inside a short piece of HCPCF with a magic-wavelength dipole trap. Currently we have successfully implemented a novel detection methods for studying superradiance.
Spontaneous emission of atoms in free space is modified by the presence of other atoms in close vicinity inducing collective super- and subradiance. For two nearby atoms with a single decay channel the entangled antisymmetric superposition state of the two single excited states will not decay spontaneously. No such excited two-atom dark state exists, if the excited state has two independent optical decay channels of different frequencies or polarizations. However, we show that for an excited atomic state with N-1 independent spontaneous decay channels one can find a highly entangled N-particle dark state, which completely decouples from the vacuum radiation field. It does not decay spontaneously, nor will it absorb resonant laser light. Mathematically, we see that this state is the only such state orthogonal to the subspace spanned by the atomic ground states. Moreover, by means of generic numerical examples we demonstrate that the subradiant behavior largely survives at finite atomic distances including dipole-dipole interactions.
When an inverted ensemble of atoms is tightly packed on the scale of its emission wavelength or when the atoms are collectively strongly coupled to a single cavity mode, their dipoles will align and decay rapidly via a superradiant burst. However, a spread-out dipole phase distribution theory predicts a required minimum threshold of atomic excitation for superradiance to occur. Here we experimentally confirm this predicted threshold for superradiant emission on a narrow optical transition when exciting the atoms transversely and show how to take advantage of the resulting sub- to superradiant transition. A π/2-pulse places the atoms in a subradiant state, protected from collective cavity decay, which we exploit during the free evolution period in a corresponding Ramsey pulse sequence. The final excited state population is read out via superradiant emission from the inverted atomic ensemble after a second π/2-pulse, and with minimal heating this allows for multiple Ramsey sequences within one experimental cycle. Our scheme is an innovative approach to atomic state readout characterized by its speed, simplicity, and highly directional emission of signal photons. It demonstrates the potential of sensors using collective effects in cavity-coupled quantum emitters.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.
Superradiance and subradiance are collective effects that emerge from coherent interactions between quantum emitters. Due to their many-body nature, theoretical studies of extended samples with length larger than the atomic transition wavelength are usually restricted to their early-time behavior or to the few-excitation limit. We use herein a mean-field approach to reduce the complex many-body system to an effective two-atom master equation that includes all correlations up to second order and that can be numerically propagated in time. We find that three-dimensional and two-dimensional inverted atomic arrays sustain superradiance below a critical lattice spacing and quantify the scaling of the superradiant peak for both dimensionalities. Finally, we study the late-time dynamics of the system and demonstrate that a subradiant phase appears before the system finally relaxes.