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arXiv:2103.07402 · Physical Review Letters

Subradiant-to-Subradiant Phase Transition in the Bad Cavity Laser

Athreya Shankar, J. Reilly, Simon B. Jäger, Murray Holland

Published Aug 13, 2021• 30 citations
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Abstract

We show that the onset of steady-state superradiance in a bad cavity laser is preceded by a dissipative phase transition between two distinct phases of steady-state subradiance. The transition is marked by a nonanalytic behavior of the cavity output power and the mean atomic inversion, as well as a discontinuity in the variance of the collective atomic inversion. In particular, for repump rates below a critical value, the cavity output power is strongly suppressed and does not increase with the atom number, while it scales linearly with atom number above this value. Remarkably, we find that the atoms are in a macroscopically entangled steady state near the critical region with a vanishing fraction of unentangled atoms in the large atom number limit.

DOI
10.1103/physrevlett.127.073603

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We show that the onset of steady-state superradiance in a bad cavity laser is preceded by a dissipative phase transition between two distinct phases of steady-state subradiance. The transition is marked by a nonanalytic behavior of the cavity output power and the mean atomic inversion, as well as a discontinuity in the variance of the collective atomic inversion. In particular, for repump rates below a critical value, the cavity output power is strongly suppressed and does not increase with the atom number, while it scales linearly with atom number above this value. Remarkably, we find that the atoms are in a macroscopically entangled steady state near the critical region with a vanishing fraction of unentangled atoms in the large atom number limit.
The dynamics of dissipative many-body quantum systems sometimes admit an emergent classical description in terms of a Markov chain even though the corresponding state space contains highly entangled states. In particular, a bad-cavity laser is a paradigm system whose dynamics can be formulated as a Markov chain in a two-dimensional state space spanned by collective angular momentum states. In this article, we investigate the connection between a dissipative phase transition that occurs in the subradiant regime of this system in the large atom number limit, and the properties of the underlying Markov chain. In one of the phases, the Markov chain approaches the detailed-balance condition with increasing atom number NNN and hence becomes effectively time-reversible. This is caused by a collective atomic emission process that effectively reduces the Markov chain to one dimension. In the other phase, we find the emergence of time-asymmetric probability currents in the two-dimensional state space that signals a breakdown of detailed balance. This is accompanied by a macroscopic internal entropy production rate in the Markov chain that scales extensively with the atom number NNN. An observable consequence of the probability currents is a self-pulsing of the cavity light output in this phase, which can be detected as an anti-correlation dip in the intensity correlation function.
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.
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.
Sub-Natural Linewidth Superradiant Lasing with Cold 88^{88}88Sr Atoms
Superradiant lasers operate in the bad-cavity regime, where the phase coherence is stored in the spin state of an atomic medium rather than in the intracavity electric field. Such lasers use collective effects to sustain lasing and could potentially reach considerably lower linewidths than a conventional laser. Here, we investigate the properties of superradiant lasing in an ensemble of ultracold 88^{88}88Sr atoms inside an optical cavity. We extend the superradiant emission on the 7.5 kHz wide 3P1^3P_13P1​ →\rightarrow→ 1S0^1S_01S0​ intercombination line to several milliseconds, and observe steady parameters suitable for emulating the performance of a continuous superradiant laser by fine tuning the repumping rates. We reach a lasing linewidth of 820 Hz for 1.1 ms of lasing, nearly an order of magnitude lower than the natural linewidth
We study the superradiant phase transition of an array of Rydberg atoms in a dissipative microwave cavity. Under the interplay of the cavity field and the long-range Rydberg interaction, the steady state of the system exhibits an interaction-enhanced superradiance, with vanishing critical atom-cavity coupling rates at a discrete set of interaction strengths. We find that, while the phenomenon can be analytically understood in the case of a constant all-to-all interaction, the enhanced superradiance persists under typical experimental parameters with spatially dependent interactions, but at modified critical interaction strengths. The diverging susceptibility at these critical points is captured by emergent quantum Rabi models, each of which comprises a pair of collective atomic states with different numbers of atomic excitations. These collective states become degenerate at the critical interaction strengths, resulting in a superradiant phase for an arbitrarily small atom-cavity coupling.
We present a cross-cavity system in which steady-state superradiance is achieved using solely collective dissipative dynamics. Two cavities symmetrically couple an ensemble of four-level atoms by driving transitions between two electronic states and two motional states along perpendicular cavity axes. Both cavities operate in the bad-cavity regime: one cavity mediates collective atomic decay, while the other cavity, together with a coherent drive, mediates collective pumping via an off-resonant Raman transition. With this, we find steady-state superradiant states that possess nonclassical properties, such as super-Poissonian photon statistics. The system thus requires a beyond mean-field description, and so we develop an exact master equation simulation technique utilizing strong symmetries of the system's jump operators. Because superradiant decay is accompanied by a momentum impulse along the corresponding cavity axis, the system exhibits substantial hybrid entanglement between the atoms' spin and motional degrees of freedom at steady state. We also demonstrate that heralded measurements of the two cavity outputs prepare a state with significant particle-particle entanglement with prospects for quantum-enhanced acceleration sensing.