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Scientific Reports

Phase transition and optical bistability in a cold Rydberg Rb sample observed via absorption spectroscopy

Manuel Alejandro Lefrán Torres, Jorge Guillermo Marquez Díaz, Jorge Douglas Massayuki Kondo, Luís Gustavo Marcassa

Published Jul 2, 2026• 0 citations
Publisher

Abstract

In this work, we have investigated a phase transition and optical bistability in a cold [Formula: see text]Rb sample excited to the [Formula: see text] Rydberg state, using absorption spectroscopy while scanning the Rydberg excitation laser for [Formula: see text]. The system is characterized through its dependence on the Rydberg Rabi frequency and principal quantum number, exhibiting hysteretic behavior indicative of bistability. We further analyze its time evolution, revealing the characteristic dynamics of the transition between stable states. The results are consistent with optical bistability induced by a cold plasma in the presence of Rydberg blockade. This work demonstrates the role of collective many-body interactions in establishing nonlinear optical responses in strongly interacting Rydberg ensembles.

DOI
10.1038/s41598-026-60180-y

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In this work, we have investigated a phase transition and optical bistability in a cold [Formula: see text]Rb sample excited to the [Formula: see text] Rydberg state, using absorption spectroscopy while scanning the Rydberg excitation laser for [Formula: see text]. The system is characterized through its dependence on the Rydberg Rabi frequency and principal quantum number, exhibiting hysteretic behavior indicative of bistability. We further analyze its time evolution, revealing the characteristic dynamics of the transition between stable states. The results are consistent with optical bistability induced by a cold plasma in the presence of Rydberg blockade. This work demonstrates the role of collective many-body interactions in establishing nonlinear optical responses in strongly interacting Rydberg ensembles.
We observe and characterize intrinsic optical bistability in a dilute Rydberg vapor. The bistability is characterized by sharp jumps between states of low and high Rydberg occupancy with jump-up and -down positions displaying hysteresis depending on the direction in which the control parameter is changed. We find that the shift in frequency of the jump point scales with the fourth power of the principal quantum number. Also, the width of the hysteresis window increases with increasing principal quantum number, before reaching a peak and then closing again. The experimental results are consistent with predictions from a simple theoretical model based on semiclassical Maxwell--Bloch equations including the effects of interaction-induced broadening and level shifts. These results provide insight into the dynamics of driven dissipative systems.
In this work, a Y-type energy level ensemble of an alkali metal Rydberg rubidium cold atomic system under complex interactions is considered. To solve this nonlinear optical response, Newton’s iterative method is employed with random initial values for solving the multi-body density matrix equations and further observing the Rydberg excitation’s instability. The effects of self-interaction and direct and exchange interactions in the cross-interactions are comprehensively considered via three real cases: (I) only self-interaction; (II) self-interaction and direct interaction; and (III) self-interaction, direct interaction, and exchange interaction simultaneously. The results indicate that under the condition of I, since the system only has self-interaction, it exhibits only a typical bistable phenomenon. With the introduction of direct interaction, the Rydberg population in II shows a bifurcated bistable phenomenon. Finally, a more complex exchange interaction is further introduced. Under the condition of III, the system exhibits a complex multi-stable phenomenon in the same detuning direction. More importantly, such bistable and multi-stable phenomena can be well regulated by changing the cooperative nonlinearity modulated via the pump field. In addition, the bistable and multi-stable atomic excitation responses of the system on one transition branch can also be controlled by the coupling field Rabi frequency on another transition branch. This work applies numerical iterative algorithms to achieve a detailed analysis of the new phenomena with bistable and multi-stable excitation responses for nonlinear characteristics and provides theoretical support for the preparation of optical multistable materials.
Abstract We experimentally characterize the optical nonlinear response of a cold atomic medium placed inside an optical cavity, and excited to Rydberg states. The excitation to S and D Rydberg levels is carried out via a two-photon transition in an electromagnetically induced transparency configuration, with a weak (red) probe beam on the lower transition, and a strong (blue) coupling beam on the upper transition. The observed optical nonlinearities induced by S states for the probe beam can be explained using a semi-classical model with van der Waals’ interactions. For the D states, it appears necessary to take into account a dynamical decay of Rydberg excitations into a long-lived dark state. We show that the measured nonlinearities can be explained by using a Rydberg bubble model with a dynamical decay.
We have studied the decay of Rydberg excitations in a cold Rb gas. A 10 ns, pulsed-dye-amplified diode laser excites Rb atoms at $70\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in a magneto-optical trap to nsnsns or npnpnp Rydberg states with principal quantum numbers $26\ensuremath{\le}n\ensuremath{\le}40$. Time-delayed state-selective field ionization is used to directly monitor the population in the initial and neighboring Rydberg levels. The measured time dependence of the Rydberg population is well described by numerical simulations which consider only spontaneous emission and population transfer by blackbody radiation. No evidence for collective decay is found at atom densities up to $3\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. This result is in contrast to a previous study [Wang et al., Phys. Rev. A 75, 033802 (2007)], in which superradiant decay was theoretically predicted and experimentally inferred for atom density and laser focal volume conditions very similar to those considered here. Suppression of collective emission is likely due to variations in transition energies within the atom sample, dominated by inhomogeneities in dipole-dipole exchange interactions for initial sss states, or by a combination of dipole-dipole and electric field inhomogeneities for the initial ppp states.
The combination of electromagnetically induced transparency with the nonlinear interaction between Rydberg atoms provides an effective interaction between photons. In this Letter, we investigate the storage of optical pulses as collective Rydberg atomic excitations in a cold atomic ensemble. By measuring the dynamics of the stored Rydberg polaritons, we experimentally demonstrate that storing a probe pulse as Rydberg polaritons strongly enhances the Rydberg mediated interaction compared to the slow propagation case. We show that the process is characterized by two time scales. At short storage times, we observe a strong enhancement of the interaction due to the reduction of the Rydberg polariton group velocity down to 0. For longer storage times, we observe a further, weaker enhancement dominated by Rydberg induced dephasing of the multiparticle components of the state. In this regime, we observe a nonlinear dependence of the Rydberg polariton coherence time with the input photon number. Our results have direct consequences in Rydberg quantum optics and may enable the test of new theories of strongly interacting Rydberg systems.
Cold atomic gases resonantly excited to Rydberg states can exhibit strong optical nonlinearity at the single-photon level. We observe that in such samples radiation trapping leads to an additional mechanism for Rydberg excitation. Conversely we demonstrate that Rydberg excitation provides an in situ probe of the spectral, statistical, temporal, and spatial properties of the trapped rescattered light. We also show that absorption can lead to an excitation saturation that mimics the Rydberg blockade effect. Collective effects due to multiple scattering may coexist with cooperative effects due to long-range interactions between the Rydberg atoms, adding a new dimension to quantum optics experiments with cold Rydberg gases.