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Theory of Steady-State Superradiance

Minghui Xu

Published Jan 1, 2016• 3 citations
OpenAlex

Abstract

In this thesis, I describe the theoretical development of the superradiant laser, or laser in the extreme bad-cavity regime. In this regime, the cavity decay rate is much greater than the atomic dynamics. The atoms emit photons into the cavity mode superradiantly in steady state. We develop group-theoretic methods that enable us to exactly solve mesoscopic systems with hundreds of atoms. We demonstrate the synchronization of atomic dipoles in steady-state superradiance. With this synchronized system, we propose conditional Ramsey spectroscopy which allows us to observe Ramsey fringes indefinitely, even in the presence of atomic decoherence. Furthermore, we explore manifestations of synchronization in the quantum realm with two superradiant atomic ensembles. We show that two such ensembles exhibit a dynamical phase transition from two disparate oscillators to quantum phase-locked dynamics. Finally, we study the mechanical eect of the light-atom interaction in the steady-state superradiance. We find efficient many-body cooling of atoms. The work described in this thesis lays the theoretical foundation for the superradiant laser and for a potential future of active optical frequency standards.

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arXiv:1609.00478•Physical Review A•Nov 8, 2016•9 citations
In this thesis, I describe the theoretical development of the superradiant laser, or laser in the extreme bad-cavity regime. In this regime, the cavity decay rate is much greater than the atomic dynamics. The atoms emit photons into the cavity mode superradiantly in steady state. We develop group-theoretic methods that enable us to exactly solve mesoscopic systems with hundreds of atoms. We demonstrate the synchronization of atomic dipoles in steady-state superradiance. With this synchronized system, we propose conditional Ramsey spectroscopy which allows us to observe Ramsey fringes indefinitely, even in the presence of atomic decoherence. Furthermore, we explore manifestations of synchronization in the quantum realm with two superradiant atomic ensembles. We show that two such ensembles exhibit a dynamical phase transition from two disparate oscillators to quantum phase-locked dynamics. Finally, we study the mechanical eect of the light-atom interaction in the steady-state superradiance. We find efficient many-body cooling of atoms. The work described in this thesis lays the theoretical foundation for the superradiant laser and for a potential future of active optical frequency standards.
Superradiant lasers may soon achieve state-of-the-art frequency purity, with linewidths of 1 mHz or less. In a superradiant (or bad-cavity) laser, coherence is primarily stored in the atomic gain medium instead of the optical field. This phase storage is characterized by spontaneous quantum synchronization of the optical dipole moments of each atom. To observe this synchronization, we create two independent superradiant atomic ensembles lasing in a single optical cavity and observe the dynamics of phase realignment, collective power enhancement, and steady-state frequency locking. This work introduces superradiant ensembles as a testbed for fundamental study of quantum synchronization as well and informs research on narrow linewidth superradiant lasers.
Lasing and steady state superradiance are two phenomena that may appear at first glance to be distinct. In a laser, phase information is maintained by a macroscopic intracavity light field, and the robustness of this phase is what leads to the coherence of the output light. In contrast, the coherence of steady-state superradiant systems derives from the macroscopic collective dipole of a many-atom ensemble. In this paper, we develop a quantum theory that connects smoothly between these two extreme limits. We show that lasing and steady-state superradiance should be thought of as the two extreme limits of a continuous crossover. The properties of systems that lie in the superradiance, lasing, and crossover parameter regions are compared. We find that for a given output intensity a narrower linewidth can be obtained by operating closer to the superradiance side of the crossover. We also find that the collective phase is robust against cavity frequency fluctuations in the superradiant regime and against atomic level fluctuations in the lasing regime.
Steady-state collective emission from ensembles of laser cooled atoms has been proposed as a method for generating sub-millihertz linewidth optical lasers, with potential for broad impacts across science and technology. We have built a model system that tests key predictions for such active oscillators using a Raman laser with laser cooled atoms as the gain medium. The laser operates deep in the bad-cavity, or superradiant, regime of laser physics, where the cavity decay rate is much greater than the atomic coherence decay rate. Specifically, we demonstrate that a system of 106 87Rb atoms trapped in a 1D standing wave optical lattice can spontaneously synchronize and collectively emit a quasi-continuous coherent optical output, even when the intracavity field contains on average < 1 photon.
We consider various approaches to the creation of a high-stability active optical frequency standard, where the atomic ensemble itself produces a highly stable and accurate frequency signal. The short-time frequency stability of such standards may overcome the stability of lasers stabilized to macroscopic cavities which are used as local oscillators in the modern optical frequency standard systems. The main idea is to create a “superradiant” laser operating deep in the bad cavity regime, where the decay rate of the cavity field significantly exceeds the decoherence rate of the lasing transition. Two main approaches towards the realization of an active optical frequency standard have been proposed already: the optical lattice laser, and the atomic beam laser. We consider these and some alternative approaches, and discuss the parameters for atomic ensembles necessary to attain the metrology relevant level of short-time frequency stability, and various effects and main challenges critical for practical implementations.
We investigate laser cooling of an ensemble of atoms in an optical cavity. We demonstrate that when atomic dipoles are synchronized in the regime of steady-state superradiance, the motion of the atoms may be subject to a giant frictional force leading to potentially very low temperatures. The ultimate temperature limits are determined by a modified atomic linewidth, which can be orders of magnitude smaller than the cavity linewidth. The cooling rate is enhanced by the superradiant emission into the cavity mode allowing reasonable cooling rates even for dipolar transitions with ultranarrow linewidth.
We theoretically investigate the effect of long-range dipole-dipole interaction (LRDDI) on a superradiant laser (SL). This effect is induced from the atom-photon interaction in the dissipation process. In the bad-cavity limit usually performed to initiate SL, we demonstrate that cavity photon number oscillates as an interparticle distance of the atoms varies. Similarly the atom-atom coherence alternates with signs, showing critical transitions alternatively in SL operations. This suggests a complexity of the collective effect emerging in a large ensemble of atoms. Therefore this effect in a SL cannot be simply interpreted by only a part of the whole ensemble. We numerically solve for a steady-state SL including the spatially dependent LRDDI, and locate the maximal cavity photon number and the minimal spectral linewidth respectively at the optimal atomic separations in the setting of an equidistant atomic array. The scaling of a finite number of atoms shows that a steady-state SL outperforms the one without LRDDI, which allows for probing narrow atomic transitions and is potentially useful for precision measurements and next-generation optical clocks.