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Physical Review A

Dissipative phase transition in a mirrorless optical parametric oscillator

Sushree S. Sahoo, S. S. Nayak, Soumya R. Mishra, Ashok Kumar Mohapatra

Published Nov 30, 2020• 4 citations
Publisher

Abstract

We experimentally demonstrate a dissipative phase transition in a mirrorless optical parametric oscillator (MOPO) using a double-$\mathrm{\ensuremath{\Lambda}}$ system in thermal atomic vapor. Bistable behavior is observed in the output power of the beams generated via the MOPO with the variation of the input power of the driving fields. We show that the long-lived hyperfine ground-state coherence induced by the Gaussian pump and the generated fields leads to the observation of optical bistability in the MOPO threshold. We further study the critical slowing-down of nonequilibrium dynamics in the vicinity of the forward threshold where the switching time of the generated fields diverges with the critical exponent, $\ensuremath{\alpha}=\ensuremath{-}0.86\ifmmode\pm\else\textpm\fi{}0.02$. Our observations pave the way to understanding and characterizing the phase transitions in driven-dissipative systems using a simple nonlinear optical system like the MOPO.

DOI
10.1103/physreva.102.053724

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We experimentally demonstrate a dissipative phase transition in a mirrorless optical parametric oscillator (MOPO) using a double-\ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ system in thermal atomic vapor. Bistable behavior is observed in the output power of the beams generated via the MOPO with the variation of the input power of the driving fields. We show that the long-lived hyperfine ground-state coherence induced by the Gaussian pump and the generated fields leads to the observation of optical bistability in the MOPO threshold. We further study the critical slowing-down of nonequilibrium dynamics in the vicinity of the forward threshold where the switching time of the generated fields diverges with the critical exponent, \ensuremathα=\ensuremath−0.86\ifmmode±\else\textpm\fi0.02\ensuremath{\alpha}=\ensuremath{-}0.86\ifmmode\pm\else\textpm\fi{}0.02\ensuremathα=\ensuremath−0.86\ifmmode±\else\textpm\fi0.02. Our observations pave the way to understanding and characterizing the phase transitions in driven-dissipative systems using a simple nonlinear optical system like the MOPO.
Mirrorless optical parametric oscillator (MOPO) is a consequence of intrinsic feedback provided by the nonlinearity in a medium due to the interaction of a pair of strong counterpropagating fields. As the name suggests, the device does not require a cavity for lasing other than the nonlinear medium. Here we report the demonstration of MOPO under the effect of an all-optical waveguide. The efficient four-wave mixing process due to counterpropagating pump and control fields interacting with a multilevel atomic system facilitates the generation of mirrorless Stokes and anti-Stokes fields counterpropagating to each other. The maximum generated laser power could rise up to mW with pump conversion efficiency more than 30%. Furthermore, the cross-phase modulation due to the strong fields creates all-optical waveguides for the generated fields and hence induces correlated spatial modes in the Stokes and the anti-Stokes fields.
A mirrorless optical parametric oscillator (MOPO) is a very special class of optical parametric oscillators, where the feedback for oscillation is realized by counter-propagating second-order nonlinear interaction without a need for external mirrors. This arrangement makes the MOPO a very simple, self-aligned and robust oscillator. The MOPO was first proposed theoretically in 1966 however its realization was only possible using the quasi-phase matching (QPM) approach due to requirement for compensation of large momentum mismatch in such interactions. Realization of first-order counter-propagating parametric oscillation requires structures with periodicity in the sub-pm range, which poses substantial fabrication challenges. In addition to its self-aligned nature, MOPO offers unique spectral properties, whereby the spectral contents of the pump are transferred to the forward wave, while the backward wave remains narrowband. So far, only nondegenerate MOPO oscillation has been demonstrated. However, it has been theoretically proposed that a degenerate MOPO could be used to realize a high-brightness biphoton source for quantum optics applications.
We report the demonstration of a mirrorless optical parametric oscillator with a tunable threshold in laser-cooled atoms with four-wave mixing (FWM) using electromagnetically induced transparency. Driven by two classical laser beams, the generated Stokes and anti-Stokes fields counterpropagate and build up efficient intrinsic feedback through the nonlinear FWM process. This feedback does not involve any cavity or spatially distributed microstructures. We observe the transition of photon correlation properties from the biphoton quantum regime (below the threshold) to the oscillation regime (above the threshold). The pump threshold can be tuned by varying the operating parameters. We achieve the oscillation with a threshold as low as 15 μW.
This work analyzes the temporal coherence and correlation of twin beams generated in a quasi-phase-matched nonlinear crystal in a counterpropagating configuration, ranging from the low-gain regime, where counterpropagating photon pairs are generated spontaneously, to the regime of stimulated pair production, close to the mirrorless optical parametric oscillator threshold. Here, we show a critical divergence of the correlation time and slowing down of quantum fluctuations originating from the feedback mechanism responsible for the MOPO threshold.
The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.
We investigate nonequilibrium criticality and chaos in a two-photon-driven optomechanical system. The parametric drive preserves a discrete Z2\mathbb{Z}_2Z2​ symmetry of the optical field, while radiation-pressure coupling transfers the resulting nonlinear dynamics to a mechanical oscillator. Combining semiclassical stability analysis, exact Liouvillian spectra, and stochastic quantum trajectories, we show that this driven-dissipative optomechanical model supports both first- and second-order dissipative phase transitions. At negative detuning a second-order transition yields spontaneous breaking of the cavity-parity symmetry in the thermodynamic limit. At positive detuning the same symmetry breaking coexists with a first-order transition, signaled by metastability and by an additional symmetric Liouvillian mode. At stronger pump power the mean-field dynamics loses all stable fixed points and develops limit cycles and chaotic attractors with positive Lyapunov exponent. Quantum trajectories in this regime display chaotic-like motion, enhanced steady-state entropy, and delocalization over many entropic Liouvillian modes. These results establish two-photon-driven optomechanics as a platform where dissipative criticality, symmetry breaking, and quantum signatures of chaos emerge within the same experimentally accessible setting.