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:1411.3445

Excitation of two atoms by a propagating single photon pulse

Navneeth Ramakrishnan, Yimin Wang, Valerio Scarani

Published Nov 13, 2014• 0 citations
arXivHTMLPDF

Abstract

We describe the interaction of two two-level atoms in free space with propagating modes of the quantized electromagnetic field, using the time-dependent Heisenberg-Langevin method. For single- photon pulses, we consider the effect of the pulse's spatial and temporal profiles on the atomic excitation. In particular, we find the ideal shape for a pulse to put exactly one excitation in any desired state of the bi-atomic system. Furthermore, we analyze the differences in the atomic dynamics between the cases of Fock state pulses and coherent state pulses.

DOI
10.48550/arxiv.1411.3445

Related papers

Efficient excitation of a two-level atom by a single photon in a propagating mode

Yimin Wang, Jiří Minář, Lana Sheridan +1 more

State mapping between atoms and photons, and photon-photon interactions play an important role in scalable quantum information processing. We consider the interaction of a two-level atom with a quantized propagating pulse in free space and study the probability ${P}_{e}(t)$ of finding the atom in the excited state at any time $t$. This probability is expected to depend on (i) the quantum state of the pulse field and (ii) the overlap between the pulse and the dipole pattern of the atomic spontaneous emission. We show that the second effect is captured by a single parameter $\ensuremath{\Lambda}\ensuremath{\in}[0,8\ensuremath{\pi}/3]$, obtained by weighting the dipole pattern with the numerical aperture. Then, ${P}_{e}(t)$ can be obtained by solving time-dependent Heisenberg-Langevin equations. We provide detailed solutions for both single-photon Fock state and coherent states and for various temporal shapes of the pulses.

arXiv:1010.4661•Physical Review A•Jun 28, 2011•122 citations

State-dependent atomic excitation by multiphoton pulses propagating along two spatial modes

Yimin Wang, Jiří Minář, Valerio Scarani

We investigate the dynamics of a single two-level atom, which interacts with pulses propagating in two spatial modes (right and left) and frequency continuum. Using Heisenberg equations of motion, we present the explicit analytical derivations and general formalisms for atomic excitation with two-spatial-mode multiphoton pulses in both the Fock and coherent states. Based on those formalisms, we show that perfect atomic excitation by a single-photon Fock state pulse can only be realized when it is rising exponentially shaped in the even mode, a balanced superposition of the two spatial modes. A single photon from a single spatial mode can only give half of the maximal atomic excitation probability. We also show that the maximum atomic excitation probability with multiphoton pulses in the even mode is a monotonic function of the average photon number for the coherent state, but not for the Fock states. Furthermore, we demonstrate that the atomic dynamics can be controlled by the initial relative phase between the two counterpropagating coherent state pulses incident on the atom, which is not the case with the two Fock state pulses.

arXiv:1204.5265•Physical Review A•Aug 7, 2012•11 citations

Two-level-atom excitation probability for single- and N -photon wave packets

Hemlin Swaran Rag, Julio R. Gea-Banacloche

We study how the transient excitation probability of a two-level atom by a quantized field depends on the temporal profile of the incident pulse, in the presence of external losses, for both coherent and Fock states, and in two complementary limits: when the pulse contains only one photon (on average), and when the number of photons $N$ is large. For the latter case we derive analytical expressions for the scaling of the excitation probability with $N$ that can be easily evaluated for any pulse shape.

arXiv:1707.02351•Physical Review A•Sep 11, 2017•15 citations

QUANTUM INFORMATION EXCHANGE BETWEEN PHOTONS AND ATOMS

Wang Yi-min

Quantum information processing tasks have been implemented in various physical platforms. In this thesis, we consider two specific implementations: Part I presents a detailed study of the interaction of a single atom with a light pulse. Part II examines the case of a quantum controlled-phase gate in circuit quantum electrodynamics in the ultrastrong coupling regime. They are both actively pursued by many research groups. In Part I, we first present the framework for a single two-level atom interacting with the quantized electromagnetic field. The effect of temporal and spectral properties of the pulses on atomic excitation is studied for both Fock state and coherent state pulse. The detailed analysis of atomic excited state population is provided for single photon pulse with various temporal shapes. The work is then extended to a more general case with two spatial-modes and multi-photon pulses. The difference between Fock state and coherent state pulse on atomic excitation is further investigated. We find that at few photon levels, the maximum atomic excitation probability is a monotonic function of photon number for the coherent state pulse, but not for the Fock state pulse. Furthermore, we show that the atomic dynamics can be controlled by the initial relative phase between the two counter-propagating coherent state pulses incident on the atom, which is not the case with two Fock state pulses. The theoretical prediction is then compared with an experiment, where a single trapped 87Rb atom interacts with coherent state pulses engineered in temporal shape of rising exponential and rectangular form. Next, we propose a quantum memory setup based on a single two-level atom in a half cavity with a moving mirror. The efficiency of the quantum storage process is studied analytically and

•Jan 1, 2013•0 citations

Single-photon pulse propagation in and into a medium of two-level atoms: Microscopic Fresnel equations

P. R. Berman, C. H. Raymond Ooi

The propagation of an off-resonant, single-photon pulse in and into a medium of two-level atoms is considered. When the pulse is launched from within the medium, there are two propagation speeds, neither of which is the normal group velocity. For densities as small as 10${}^{11}$ atoms/cm${}^{3}$ and detunings of order 10${}^{11}$ s${}^{\ensuremath{-}1}$, both propagation speeds approach one half the speed of light in vacuum. Moreover, rather remarkably, there are Rabi oscillations between the field and atomic excitation, even for this single-photon pulse. In contrast, for a pulse sent into the medium, the atom-field system remains adiabatically in a dressed state that propagates with the normal group velocity. In the limit that the index of refraction is approximately equal to unity, we obtain the Fresnel equations for the reflection and transmission coefficients based on this microscopic model. The transmission coefficient differs from the conventional result owing to the fact that we quantize the field in free space.

Physical Review A•Dec 30, 2011•3 citations

Dynamics of the two-atom Jaynes-Cummings model with nondegenerate two-photon transitions

Eugene K. Bashkirov

An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.

Laser Physics•Aug 1, 2006•31 citations
We describe the interaction of two two-level atoms in free space with propagating modes of the quantized electromagnetic field, using the time-dependent Heisenberg-Langevin method. For single- photon pulses, we consider the effect of the pulse's spatial and temporal profiles on the atomic excitation. In particular, we find the ideal shape for a pulse to put exactly one excitation in any desired state of the bi-atomic system. Furthermore, we analyze the differences in the atomic dynamics between the cases of Fock state pulses and coherent state pulses.
State mapping between atoms and photons, and photon-photon interactions play an important role in scalable quantum information processing. We consider the interaction of a two-level atom with a quantized propagating pulse in free space and study the probability Pe(t){P}_{e}(t)Pe​(t) of finding the atom in the excited state at any time ttt. This probability is expected to depend on (i) the quantum state of the pulse field and (ii) the overlap between the pulse and the dipole pattern of the atomic spontaneous emission. We show that the second effect is captured by a single parameter $\ensuremath{\Lambda}\ensuremath{\in}[0,8\ensuremath{\pi}/3]$, obtained by weighting the dipole pattern with the numerical aperture. Then, Pe(t){P}_{e}(t)Pe​(t) can be obtained by solving time-dependent Heisenberg-Langevin equations. We provide detailed solutions for both single-photon Fock state and coherent states and for various temporal shapes of the pulses.
We investigate the dynamics of a single two-level atom, which interacts with pulses propagating in two spatial modes (right and left) and frequency continuum. Using Heisenberg equations of motion, we present the explicit analytical derivations and general formalisms for atomic excitation with two-spatial-mode multiphoton pulses in both the Fock and coherent states. Based on those formalisms, we show that perfect atomic excitation by a single-photon Fock state pulse can only be realized when it is rising exponentially shaped in the even mode, a balanced superposition of the two spatial modes. A single photon from a single spatial mode can only give half of the maximal atomic excitation probability. We also show that the maximum atomic excitation probability with multiphoton pulses in the even mode is a monotonic function of the average photon number for the coherent state, but not for the Fock states. Furthermore, we demonstrate that the atomic dynamics can be controlled by the initial relative phase between the two counterpropagating coherent state pulses incident on the atom, which is not the case with the two Fock state pulses.
We study how the transient excitation probability of a two-level atom by a quantized field depends on the temporal profile of the incident pulse, in the presence of external losses, for both coherent and Fock states, and in two complementary limits: when the pulse contains only one photon (on average), and when the number of photons NNN is large. For the latter case we derive analytical expressions for the scaling of the excitation probability with NNN that can be easily evaluated for any pulse shape.
Quantum information processing tasks have been implemented in various physical platforms. In this thesis, we consider two specific implementations: Part I presents a detailed study of the interaction of a single atom with a light pulse. Part II examines the case of a quantum controlled-phase gate in circuit quantum electrodynamics in the ultrastrong coupling regime. They are both actively pursued by many research groups. In Part I, we first present the framework for a single two-level atom interacting with the quantized electromagnetic field. The effect of temporal and spectral properties of the pulses on atomic excitation is studied for both Fock state and coherent state pulse. The detailed analysis of atomic excited state population is provided for single photon pulse with various temporal shapes. The work is then extended to a more general case with two spatial-modes and multi-photon pulses. The difference between Fock state and coherent state pulse on atomic excitation is further investigated. We find that at few photon levels, the maximum atomic excitation probability is a monotonic function of photon number for the coherent state pulse, but not for the Fock state pulse. Furthermore, we show that the atomic dynamics can be controlled by the initial relative phase between the two counter-propagating coherent state pulses incident on the atom, which is not the case with two Fock state pulses. The theoretical prediction is then compared with an experiment, where a single trapped 87Rb atom interacts with coherent state pulses engineered in temporal shape of rising exponential and rectangular form. Next, we propose a quantum memory setup based on a single two-level atom in a half cavity with a moving mirror. The efficiency of the quantum storage process is studied analytically and
The propagation of an off-resonant, single-photon pulse in and into a medium of two-level atoms is considered. When the pulse is launched from within the medium, there are two propagation speeds, neither of which is the normal group velocity. For densities as small as 1011{}^{11}11 atoms/cm3{}^{3}3 and detunings of order 1011{}^{11}11 s${}^{\ensuremath{-}1}$, both propagation speeds approach one half the speed of light in vacuum. Moreover, rather remarkably, there are Rabi oscillations between the field and atomic excitation, even for this single-photon pulse. In contrast, for a pulse sent into the medium, the atom-field system remains adiabatically in a dressed state that propagates with the normal group velocity. In the limit that the index of refraction is approximately equal to unity, we obtain the Fresnel equations for the reflection and transmission coefficients based on this microscopic model. The transmission coefficient differs from the conventional result owing to the fact that we quantize the field in free space.
An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.