We analyze the non-Markovian spontaneous-emission dynamics of a two-level test atom placed in a cavity formed by two atomic arrays in a waveguide quantum electrodynamics (QED) setup. We demonstrate a crossover from single-mode to multimode strong-coupling cavity QED as the cavity length $\ensuremath{\sim}d$ becomes comparable to the coherence length associated with collective spontaneous emission $\ensuremath{\sim}v/(N\ensuremath{\gamma})$. The resulting non-Markovian dynamics of the test atom and the emergent spectral density of the field are analyzed as a function of various tunable atomic array parameters: the number of atoms, length of the atomic cavity, and resonance frequency of the atoms forming the atomic mirrors. Our results show limitations to cooperatively enhanced light-matter coupling in the presence of time-delayed feedback. We further illustrate that the non-Markovian system dynamics can be efficiently approximated in terms of a few modes of the emergent spectral density of the field.We analyze the non-Markovian spontaneous-emission dynamics of a two-level test atom placed in a cavity formed by two atomic arrays in a waveguide quantum electrodynamics (QED) setup. We demonstrate a crossover from single-mode to multimode strong-coupling cavity QED as the cavity length $\ensuremath{\sim}d$ becomes comparable to the coherence length associated with collective spontaneous emission $\ensuremath{\sim}v/(N\ensuremath{\gamma})$. The resulting non-Markovian dynamics of the test atom and the emergent spectral density of the field are analyzed as a function of various tunable atomic array parameters: the number of atoms, length of the atomic cavity, and resonance frequency of the atoms forming the atomic mirrors. Our results show limitations to cooperatively enhanced light-matter coupling in the presence of time-delayed feedback. We further illustrate that the non-Markovian system dynamics can be efficiently approximated in terms of a few modes of the emergent spectral density of the field.

arXiv:2504.09281Physical Review ASep 30, 20254 citations

Experimental study of absorption and gain by two-level atoms in a time-delayed non-Markovian optical field

Michael H. Anderson, Gautam Vemuri, J. Cooper +2 more

We have measured the absorption from a weak time-delayed probe field by a two-level atomic system [Na 3 ${\mathit{s}}_{1/2}$ (F=2, ${\mathit{m}}_{\mathit{F}}$ =2)\ensuremath{\rightarrow}3 ${\mathit{p}}_{3/2}$ (F=3, ${\mathit{m}}_{\mathit{F}}$ =3)] saturated by a phase-diffusing pump field. The pump and probe, derived from the same artificially-noise-modulated phase-diffusing laser beam, are frequency degenerate and resonant with the atomic transition. The probe is a time-delayed replica of the pump. Our results, carried out in a regime where the field bandwidth and the Rabi frequency are comparable, provide confirmation of recent theoretical predictions [K. Gheri, M. A. M. Marte, and P. Zoller, J. Opt. Soc. Am. B 5, 1559 (1991)] for the atomic response to the non-Markovian composite of a pump and time-delayed probe, valid for arbitrary bandwidths and intensities. Amplification of the probe field is observed for delays comparable to the lifetime of the upper level and again for very long delays, if the bandwidth is less than the decay rate of the upper state.We have measured the absorption from a weak time-delayed probe field by a two-level atomic system [Na 3${\mathit{s}}_{1/2}$(F=2,${\mathit{m}}_{\mathit{F}}$=2)\ensuremath{\rightarrow}3${\mathit{p}}_{3/2}$(F=3,${\mathit{m}}_{\mathit{F}}$=3)] saturated by a phase-diffusing pump field. The pump and probe, derived from the same artificially-noise-modulated phase-diffusing laser beam, are frequency degenerate and resonant with the atomic transition. The probe is a time-delayed replica of the pump. Our results, carried out in a regime where the field bandwidth and the Rabi frequency are comparable, provide confirmation of recent theoretical predictions [K. Gheri, M. A. M. Marte, and P. Zoller, J. Opt. Soc. Am. B 5, 1559 (1991)] for the atomic response to the non-Markovian composite of a pump and time-delayed probe, valid for arbitrary bandwidths and intensities. Amplification of the probe field is observed for delays comparable to the lifetime of the upper level and again for very long delays, if the bandwidth is less than the decay rate of the upper state.

Physical Review AApr 1, 199330 citations

Non-Markovian relaxation of a quantum system

Horacio M. Cataldo

Physica A Statistical Mechanics and its ApplicationsMay 1, 199010 citations

Markovian and non-markovian behavior in two-level atom fluorescence

K. Wódkiewicz, Joseph H. Eberly

Annals of PhysicsOct 1, 197685 citations

We have measured the absorption from a weak time-delayed probe field by a two-level atomic system [Na 3

{\mathit{s}}_{1/2}

(F=2,

{\mathit{m}}_{\mathit{F}}

=2)\ensuremath{\rightarrow}3

{\mathit{p}}_{3/2}

(F=3,

{\mathit{m}}_{\mathit{F}}

=3)] saturated by a phase-diffusing pump field. The pump and probe, derived from the same artificially-noise-modulated phase-diffusing laser beam, are frequency degenerate and resonant with the atomic transition. The probe is a time-delayed replica of the pump. Our results, carried out in a regime where the field bandwidth and the Rabi frequency are comparable, provide confirmation of recent theoretical predictions [K. Gheri, M. A. M. Marte, and P. Zoller, J. Opt. Soc. Am. B 5, 1559 (1991)] for the atomic response to the non-Markovian composite of a pump and time-delayed probe, valid for arbitrary bandwidths and intensities. Amplification of the probe field is observed for delays comparable to the lifetime of the upper level and again for very long delays, if the bandwidth is less than the decay rate of the upper state.