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:2109.13183 · Journal of the Optical Society of America B

Time-ordering effects in a one-atom laser based on electromagnetically induced transparency

D. B. Horoshko, Chang‐shui Yu, S. Ya. Kilin

Published Sep 10, 2021• 4 citations
arXivHTMLPDF

Abstract

The one-atom laser based on electromagnetically induced transparency, suggested recently [ Phys. Rev. Lett. 124 , 093603 ( 2020 ) PRLTAO 0031-9007 10.1103/PhysRevLett.124.093603 ], is capable of generating Schrödinger cat states in the regime of strong ground-state coupling. In this regime, we find the exact solution for the Schrödinger equation with a time-dependent effective Hamiltonian by considering the Magnus expansion of the time-ordered exponential and calculating analytically the time-ordering terms, omitted in the previous study. We show that the time-ordering term affects the relative phase of two coherent components of the generated Schrödinger cat state. We show this influence by calculating various nonclassicality indicators for the cavity field, such as total noise, average parity, and relative total noise. We find that time-ordering becomes important at the average photon number in the cavity below 1, in striking contrast to the case of single-pass parametric downconversion, where it becomes important at average photon number in one optical mode above 4.

DOI
10.1364/josab.436004

Related papers

Photon-photon interactions in cavity electromagnetically induced transparency

M. J. Werner, Ataç İmamoğlu

Dissipation-free photon-photon interaction at the single-photon level is studied in the context of cavity electromagnetically induced transparency (EIT). For a single multilevel atom exhibiting EIT in the strong cavity-coupling regime, the anharmonicity of the atom-cavity system has an upper bound determined by single atom-photon coupling strength. A photon blockade effect is inferred to occur for both single- and multiatom cases from the behavior of transition rates between dressed states of the system. Numerical calculations of the second-order coherence function indicate that photon antibunching in both single- and two-atom cases are strong and comparable.

arXiv:quant-ph/9902005•Physical Review A•Dec 8, 1999•162 citations

“Parity effect” based generation of Schrodinger cat like states in high-

Anna Napoli, ANTONINO MESSINA

It has been very recently shown that the dynamics of a two-level atom coupled to a bimodal degenerate cavity field by two-photon processes, is characterized by an interesting nonclassical dynamical behavior christened “parity effect”. This effect consists in the fact that if the cavity field is prepared leaving one mode in its vacuum state and exciting the other one in a generic linear combination of even number states only, or odd number states only, then there exists an appropriate intensity-dependent interval of time after which the bimodal cavity exhibits macroscopically different parity-dependent quantum features. We show that this nonclassical effect is at the origin of the possibility of generating Schrodinger cat like states of the bimodal field appropriately selecting its initial conditions.

Mysteries, Puzzles, and Paradoxes in Quantum Mechanics•Jan 1, 1999•1 citation

Very Nonlinear Quantum Optics

Quesada Mejia, Juan Nicolas

This thesis presents a study of photon generation and conversion processes in nonlinear optics. Our results extend beyond the first order perturbative regime, in which only pairs of photons are generated in spontaneous parametric down-conversion or four wave mixing. They also allow us to identify the limiting factors for achieving unit efficiency frequency conversion, and to correctly account for the propagation of bright nonclassical photon states generated in the nonlinear material. This is done using the Magnus expansion, which allows us to incorporate corrections due to time-ordering effects in the time evolution of the state, while also respecting the quantum statistics associated with squeezed states (in photon generation) and single photons or coherent states (in photon conversion). We show more generally that this expansion should be the preferred strategy when dealing with any type of time-dependent Hamiltonian that is a quadratic form in the creation and annihilation operators of the fields involved. Using the Magnus expansion, simple figures of merit to estimate the relevance of these time-ordering corrections are obtained. These quantities depend on the group velocities of the modes involved in the nonlinear process and provide a very simple physical picture of the interactions between the photons at different times. These time-ordering effects are shown to be important only when the photons and pump beam overlap within the nonlinear material for a significant amount of time. We also discuss the possibility of preparing Fock states with many photons using parametric down-conversion sources and realistic photon-number-resolving detectors. After discussing photon generation processes, we study photon conversion processes in which a nonlinear material and a classical strong pump field are used modify the frequency of a second incoming low-intensity field. We show that time-ordering effects limit the efficiency of this conversion process, re-examine strategies to get around this problem, and show that it should be possible to have a clear observation of modified upconversion probabilities due to these effects, and thus have an experimental demonstration of time-ordering effects in nonlinear optics.

•Nov 1, 2015•7 citations

Time ordering in the classically driven nonlinear Jaynes-Cummings model

Tobias Lipfert, F. Krumm, Mikhail I. Kolobov +1 more

Recently [F. Krumm and W. Vogel, Phys. Rev. A 97, 043806 (2018)], the detuned and nonlinear Jaynes-Cummings model describing the quantized motion of a trapped ion was introduced and its corresponding dynamics was solved via considering the driving laser in a quantized manner. For the dynamics with a classical driving laser an approximation in terms of neglected time ordering was considered to obtain analytical expressions and compared to numerically obtained exact dynamics, which revealed the insufficiency of this approximation. In the present work we reconsider this model and show that it can likewise be solved analytically, i.e., including time ordering, with a classical driving laser field. Using the analytical solution, we investigate the quantum time-ordering effects of the system with respect to nonclassicality and nonsimulatability of the motional states of the ion. Furthermore, we use the Magnus expansion to analyze the impact of certain orders of the time ordering. We derive an exact radius of convergence for these time-ordering corrections beyond the established and only sufficient criterion. Finally, the differences between the solution derived here and the previously found one using a quantized pump are discussed.

arXiv:1809.04391•Physical Review A•Dec 12, 2018•4 citations

Generation of Schrödinger Cat States in a Hybrid Cavity Optomechanical System

Xing‐Wei An, Tong‐Hui Deng, Lei Chen +2 more

We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom-cavity-oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, the proposed proposal consider the second order approximation on the Lamb-Dicke parameter, which is more universal in the experiment. Numerical simulations confirm the validity of our derivation.

Entropy•Oct 29, 2022•3 citations

Strongly driven one-atom laser and decoherence monitoring

Pavel Lougovski, Federico Casagrande, ALFREDO LULLI +1 more

We propose the implementation of a strongly driven one-atom laser, based on the off-resonant interaction of a three-level atom in $\ensuremath{\Lambda}$ configuration with a single cavity mode and three laser fields. We show that the system can be described equivalently by a two-level atom resonantly coupled to the cavity and driven by a strong effective coherent field. The effective dynamics can be solved exactly, including a thermal field bath, allowing an analytical description of field statistics and entanglement properties. We also show the possible generation of quantum superposition (Schr\"odinger cat) states for the whole atom-field system and for the field alone after atomic measurement. We propose a way to monitor the system decoherence by measuring atomic populations. Finally, we confirm the validity of our model through numerical solutions.

arXiv:quant-ph/0702054•Physical Review A•Sep 7, 2007•38 citations
The one-atom laser based on electromagnetically induced transparency, suggested recently [ Phys. Rev. Lett. 124 , 093603 ( 2020 ) PRLTAO 0031-9007 10.1103/PhysRevLett.124.093603 ], is capable of generating Schrödinger cat states in the regime of strong ground-state coupling. In this regime, we find the exact solution for the Schrödinger equation with a time-dependent effective Hamiltonian by considering the Magnus expansion of the time-ordered exponential and calculating analytically the time-ordering terms, omitted in the previous study. We show that the time-ordering term affects the relative phase of two coherent components of the generated Schrödinger cat state. We show this influence by calculating various nonclassicality indicators for the cavity field, such as total noise, average parity, and relative total noise. We find that time-ordering becomes important at the average photon number in the cavity below 1, in striking contrast to the case of single-pass parametric downconversion, where it becomes important at average photon number in one optical mode above 4.
Dissipation-free photon-photon interaction at the single-photon level is studied in the context of cavity electromagnetically induced transparency (EIT). For a single multilevel atom exhibiting EIT in the strong cavity-coupling regime, the anharmonicity of the atom-cavity system has an upper bound determined by single atom-photon coupling strength. A photon blockade effect is inferred to occur for both single- and multiatom cases from the behavior of transition rates between dressed states of the system. Numerical calculations of the second-order coherence function indicate that photon antibunching in both single- and two-atom cases are strong and comparable.
It has been very recently shown that the dynamics of a two-level atom coupled to a bimodal degenerate cavity field by two-photon processes, is characterized by an interesting nonclassical dynamical behavior christened “parity effect”. This effect consists in the fact that if the cavity field is prepared leaving one mode in its vacuum state and exciting the other one in a generic linear combination of even number states only, or odd number states only, then there exists an appropriate intensity-dependent interval of time after which the bimodal cavity exhibits macroscopically different parity-dependent quantum features. We show that this nonclassical effect is at the origin of the possibility of generating Schrodinger cat like states of the bimodal field appropriately selecting its initial conditions.
This thesis presents a study of photon generation and conversion processes in nonlinear optics. Our results extend beyond the first order perturbative regime, in which only pairs of photons are generated in spontaneous parametric down-conversion or four wave mixing. They also allow us to identify the limiting factors for achieving unit efficiency frequency conversion, and to correctly account for the propagation of bright nonclassical photon states generated in the nonlinear material. This is done using the Magnus expansion, which allows us to incorporate corrections due to time-ordering effects in the time evolution of the state, while also respecting the quantum statistics associated with squeezed states (in photon generation) and single photons or coherent states (in photon conversion). We show more generally that this expansion should be the preferred strategy when dealing with any type of time-dependent Hamiltonian that is a quadratic form in the creation and annihilation operators of the fields involved. Using the Magnus expansion, simple figures of merit to estimate the relevance of these time-ordering corrections are obtained. These quantities depend on the group velocities of the modes involved in the nonlinear process and provide a very simple physical picture of the interactions between the photons at different times. These time-ordering effects are shown to be important only when the photons and pump beam overlap within the nonlinear material for a significant amount of time. We also discuss the possibility of preparing Fock states with many photons using parametric down-conversion sources and realistic photon-number-resolving detectors. After discussing photon generation processes, we study photon conversion processes in which a nonlinear material and a classical strong pump field are used modify the frequency of a second incoming low-intensity field. We show that time-ordering effects limit the efficiency of this conversion process, re-examine strategies to get around this problem, and show that it should be possible to have a clear observation of modified upconversion probabilities due to these effects, and thus have an experimental demonstration of time-ordering effects in nonlinear optics.
Recently [F. Krumm and W. Vogel, Phys. Rev. A 97, 043806 (2018)], the detuned and nonlinear Jaynes-Cummings model describing the quantized motion of a trapped ion was introduced and its corresponding dynamics was solved via considering the driving laser in a quantized manner. For the dynamics with a classical driving laser an approximation in terms of neglected time ordering was considered to obtain analytical expressions and compared to numerically obtained exact dynamics, which revealed the insufficiency of this approximation. In the present work we reconsider this model and show that it can likewise be solved analytically, i.e., including time ordering, with a classical driving laser field. Using the analytical solution, we investigate the quantum time-ordering effects of the system with respect to nonclassicality and nonsimulatability of the motional states of the ion. Furthermore, we use the Magnus expansion to analyze the impact of certain orders of the time ordering. We derive an exact radius of convergence for these time-ordering corrections beyond the established and only sufficient criterion. Finally, the differences between the solution derived here and the previously found one using a quantized pump are discussed.
We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom-cavity-oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, the proposed proposal consider the second order approximation on the Lamb-Dicke parameter, which is more universal in the experiment. Numerical simulations confirm the validity of our derivation.
We propose the implementation of a strongly driven one-atom laser, based on the off-resonant interaction of a three-level atom in $\ensuremath{\Lambda}$ configuration with a single cavity mode and three laser fields. We show that the system can be described equivalently by a two-level atom resonantly coupled to the cavity and driven by a strong effective coherent field. The effective dynamics can be solved exactly, including a thermal field bath, allowing an analytical description of field statistics and entanglement properties. We also show the possible generation of quantum superposition (Schr\"odinger cat) states for the whole atom-field system and for the field alone after atomic measurement. We propose a way to monitor the system decoherence by measuring atomic populations. Finally, we confirm the validity of our model through numerical solutions.