Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2312.03402 · Physical review. B./Physical review. B

Multiple wave packets running in the photon number space

Luca Nimmesgern, Moritz Cygorek, Adam Mielnik-Pyszczorski, Doris E. Reiter, Alexei Vagov, V. M. Axt

Published Apr 26, 2024• 1 citation
arXivHTMLPDF

Abstract

If a two-level system coupled to a single-mode cavity is strongly driven by an external laser, instead of a continuous accumulation of photons in the cavity, oscillations in the mean photon number occur. These oscillations correspond to peaks of finite width running up and down in the photon number distribution, reminiscent of wave packets in linear chain models. A single wave packet is found if the cavity is resonant to the external laser. Here, we show that for finite detuning, multiple packet structures can exist simultaneously, oscillating at different frequencies and amplitudes. We further study the influence of dissipative effects resulting in the formation of a stationary state, which, depending on the parameters, can be characterized by a bimodal photon number distribution. While we give analytical limits for the maximally achievable photon number in the absence of any dissipation, surprisingly, dephasing processes can push the photon occupations towards higher photon numbers.

DOI
10.1103/physrevb.109.155436

Related papers

Multiple single-photon generations in three-level atoms coupled to a cavity with non-Markovian effects

H. Z. Shen, Y. Chen, T. Z. Luan +1 more

In this paper we show how to generate multiple single-photon wave packets of arbitrary temporal shape from an optical cavity coupled with $N$ three-level atoms driven by a driving field in the non-Markovian regime. We derive an exact analytical expression of the optimal driving field to generate such wave packets, which depends on two detunings of the cavity and driving field with respect to the three-level atoms. The cavity we use consists of two mirrors facing each other, where one is perfect and the other includes dissipation (a one-sided cavity), which couples with the corresponding non-Markovian input-output fields. If the first single-photon wave packet generated by the Markovian system is the same as the non-Markovian case, the Markovian system cannot generate the same multiple single-photon wave packets as the non-Markovian system when the spectral widths of the other environments take values different from the spectral width of the first environment, while setting the equal spectral widths for the different environments can generate this. The generated multiple different single-photon wave packets are not independent of each other, which satisfies certain relations with non-Markovian spectral parameters. We analyze the transition from Markovian to non-Markovian regimes and compare the differences between them, where the cavity interacts simultaneously with the multiple non-Markovian environments. Finally, we extend the above results to a general non-Markovian quantum network involving many cavities coupled with driven three-level atoms.

arXiv:2404.09641•Physical Review A•May 8, 2023•13 citations

Generation and manipulation of photon number wave packets in photonic cavities

Luca Nimmesgern, Moritz Cygorek, Doris E. Reiter +1 more

Quantum emitters inside optical cavities can create not only fixed photon number states but also photon number wave packets, which are states with a finite photon number distribution that oscillates in time. These states emerge when the emitter is driven by an external field while coupled to the cavity. We show that by rapidly changing the driving strength, new wave packets can be generated, allowing multiple packets to coexist and evolve independently. We classify the resulting wave packet behavior into distinct dynamical subclasses between which we choose through the choice of relevant parameters. Based on this understanding, we develop simple and robust protocols to generate a specified number of photon number wave packets on demand. We propose that the rich dynamics can be experimentally investigated by merely measuring the mean photon number.

arXiv:2509.03083•Physical review. B./Physical review. B•Feb 19, 2026•0 citations

Theory of a Wave Packet in a Laser Cavity

L. W. Davis

When describing the behavior of a multimode laser, it sometimes is convenient to express the cavity field in terms of an evolving wave packet that is reflected by the mirrors. We consider here the general relation between the normal-mode description of the field, where mode amplitudes and frequencies characterize the oscillations, and features of the corresponding wave packet. It is shown that in this problem it is natural to represent a packet as a linear superposition of monochromatic waves, integrating over wave number $k$. To illustrate some of the concepts, an example is treated that relates packet parameters to parameters of a theoretical model for the laser medium.

Physical Review A•Jun 1, 1972•3 citations

Photon correlations and spectra in the bimodal regime of single-atom cavity-enhanced absorption

P. M. Alsing, H. J. Carmichael, Perry R. Rice

We recently reported that the transmitted light from a driven optical cavity containing a single-atom absorber shows strong nonclassical features.1 Also, Savage and Carmichael2 have shown that this single-atom system can be operated in a regime in which the transmitted light has a bimodal photon-counting distribution; as the saturation photon number is increased this bimodality develops into a single-atom version of absorptive optical bistability. We present results for the degree of second-order coherence and the spectrum of the transmitted light in the operating regime at the onset of bimodality. In this regime we can study the onset of low frequency behavior associated with transitions between the local states defined by the peaks of the bimodal distribution. Our results are calculated numerically, using a supercomputer to solve matrix element equations derived in the Fock-state basis. Our numerical approach also allows us to extend our analytical study of nonclassical effects in single-atom cavity-enhanced absorption. Our analytical results are restricted either to the bad-cavity limit1 or to weak driving fields outside this limit. We can now study how the nonclassical effects identified in these analytical calculations are changed by using finite driving fields outside the bad-cavity limit.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Multimode entanglement in coupled cavity arrays

T. C. H. Liew, V Savona

We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can also be generated in the limit where the nonlinearity is much smaller than the losses, contrary to common expectations. Quantum correlations in this case arise from the interference between different pathways that the system can follow in the Hilbert space to reach its steady state under the effect of coherent driving fields. We characterize, in particular, two systems: a linear chain of three coupled cavities and an array of eight coupled cavities. We demonstrate the existence of a parameter range where the system emits photons with continuous-variable bipartite and quadripartite entanglement, in the case of the first and the second system, respectively. This entanglement is shown to survive realistic rates of pure dephasing and opens up a new perspective for the realization of quantum simulators or entangled photon sources without the challenging requirement of strong optical nonlinearities.

arXiv:1209.1543•New Journal of Physics•Feb 7, 2013•41 citations

Multimode entanglement in coupled cavity arrays

T. C. H. Liew, Vincenzo Savona

We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can also be generated in the limit where the nonlinearity is much smaller than the losses, contrary to common expectations. Quantum correlations in this case arise from the interference between different pathways that the system can follow in the Hilbert space to reach its steady state under the effect of coherent driving fields. We characterize, in particular, two systems: a linear chain of three coupled cavities and an array of eight coupled cavities. We demonstrate the existence of a parameter range where the system emits photons with continuous-variable bipartite and quadripartite entanglement, in the case of the first and the second system, respectively. This entanglement is shown to survive realistic rates of pure dephasing and opens up a new perspective for the realization of quantum simulators or entangled photon sources without the challenging requirement of strong optical nonlinearities.

•Aug 17, 2016•21 citations
If a two-level system coupled to a single-mode cavity is strongly driven by an external laser, instead of a continuous accumulation of photons in the cavity, oscillations in the mean photon number occur. These oscillations correspond to peaks of finite width running up and down in the photon number distribution, reminiscent of wave packets in linear chain models. A single wave packet is found if the cavity is resonant to the external laser. Here, we show that for finite detuning, multiple packet structures can exist simultaneously, oscillating at different frequencies and amplitudes. We further study the influence of dissipative effects resulting in the formation of a stationary state, which, depending on the parameters, can be characterized by a bimodal photon number distribution. While we give analytical limits for the maximally achievable photon number in the absence of any dissipation, surprisingly, dephasing processes can push the photon occupations towards higher photon numbers.
In this paper we show how to generate multiple single-photon wave packets of arbitrary temporal shape from an optical cavity coupled with NNN three-level atoms driven by a driving field in the non-Markovian regime. We derive an exact analytical expression of the optimal driving field to generate such wave packets, which depends on two detunings of the cavity and driving field with respect to the three-level atoms. The cavity we use consists of two mirrors facing each other, where one is perfect and the other includes dissipation (a one-sided cavity), which couples with the corresponding non-Markovian input-output fields. If the first single-photon wave packet generated by the Markovian system is the same as the non-Markovian case, the Markovian system cannot generate the same multiple single-photon wave packets as the non-Markovian system when the spectral widths of the other environments take values different from the spectral width of the first environment, while setting the equal spectral widths for the different environments can generate this. The generated multiple different single-photon wave packets are not independent of each other, which satisfies certain relations with non-Markovian spectral parameters. We analyze the transition from Markovian to non-Markovian regimes and compare the differences between them, where the cavity interacts simultaneously with the multiple non-Markovian environments. Finally, we extend the above results to a general non-Markovian quantum network involving many cavities coupled with driven three-level atoms.
Quantum emitters inside optical cavities can create not only fixed photon number states but also photon number wave packets, which are states with a finite photon number distribution that oscillates in time. These states emerge when the emitter is driven by an external field while coupled to the cavity. We show that by rapidly changing the driving strength, new wave packets can be generated, allowing multiple packets to coexist and evolve independently. We classify the resulting wave packet behavior into distinct dynamical subclasses between which we choose through the choice of relevant parameters. Based on this understanding, we develop simple and robust protocols to generate a specified number of photon number wave packets on demand. We propose that the rich dynamics can be experimentally investigated by merely measuring the mean photon number.
When describing the behavior of a multimode laser, it sometimes is convenient to express the cavity field in terms of an evolving wave packet that is reflected by the mirrors. We consider here the general relation between the normal-mode description of the field, where mode amplitudes and frequencies characterize the oscillations, and features of the corresponding wave packet. It is shown that in this problem it is natural to represent a packet as a linear superposition of monochromatic waves, integrating over wave number kkk. To illustrate some of the concepts, an example is treated that relates packet parameters to parameters of a theoretical model for the laser medium.
We recently reported that the transmitted light from a driven optical cavity containing a single-atom absorber shows strong nonclassical features.1 Also, Savage and Carmichael2 have shown that this single-atom system can be operated in a regime in which the transmitted light has a bimodal photon-counting distribution; as the saturation photon number is increased this bimodality develops into a single-atom version of absorptive optical bistability. We present results for the degree of second-order coherence and the spectrum of the transmitted light in the operating regime at the onset of bimodality. In this regime we can study the onset of low frequency behavior associated with transitions between the local states defined by the peaks of the bimodal distribution. Our results are calculated numerically, using a supercomputer to solve matrix element equations derived in the Fock-state basis. Our numerical approach also allows us to extend our analytical study of nonclassical effects in single-atom cavity-enhanced absorption. Our analytical results are restricted either to the bad-cavity limit1 or to weak driving fields outside this limit. We can now study how the nonclassical effects identified in these analytical calculations are changed by using finite driving fields outside the bad-cavity limit.
We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can also be generated in the limit where the nonlinearity is much smaller than the losses, contrary to common expectations. Quantum correlations in this case arise from the interference between different pathways that the system can follow in the Hilbert space to reach its steady state under the effect of coherent driving fields. We characterize, in particular, two systems: a linear chain of three coupled cavities and an array of eight coupled cavities. We demonstrate the existence of a parameter range where the system emits photons with continuous-variable bipartite and quadripartite entanglement, in the case of the first and the second system, respectively. This entanglement is shown to survive realistic rates of pure dephasing and opens up a new perspective for the realization of quantum simulators or entangled photon sources without the challenging requirement of strong optical nonlinearities.
We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can also be generated in the limit where the nonlinearity is much smaller than the losses, contrary to common expectations. Quantum correlations in this case arise from the interference between different pathways that the system can follow in the Hilbert space to reach its steady state under the effect of coherent driving fields. We characterize, in particular, two systems: a linear chain of three coupled cavities and an array of eight coupled cavities. We demonstrate the existence of a parameter range where the system emits photons with continuous-variable bipartite and quadripartite entanglement, in the case of the first and the second system, respectively. This entanglement is shown to survive realistic rates of pure dephasing and opens up a new perspective for the realization of quantum simulators or entangled photon sources without the challenging requirement of strong optical nonlinearities.