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

Physical Review A

Optical response of two-level atoms with reflection geometry as a model of a quantum phase gate

Hisaki Oka, Shigeki Takeuchi, Keiji Sasaki

Published Jul 20, 2005• 11 citations
Publisher

Abstract

The nonlinear optical response obtained from a model system of a quantum phase gate is investigated. The model system consists of a thin infinite atomic layer of two-level atoms placed in front of a perfect reflecting mirror. The optical response obtained from the model system is semiclassically analyzed using the finite difference time domain method with the optical Bloch equations. It is shown that a nonlinear phase shift of $\ensuremath{\pi}$ is achieved when the atomic layer is placed at an antinode of the input field. This result is consistent with the theoretical result obtained from a one-dimensional atom model [H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B: Quantum Semiclassical Opt. 5, 218 (2003)]. The dependence of the nonlinear phase shift on the position of the atomic layer is also studied in detail.

DOI
10.1103/physreva.72.013816

Related papers

Quantum phase gate using single atom nonlinearlity

Shigeki Takeuchi, Hisaki Oka, Kunihiro Kojima +2 more

The nonlinear optical response obtained from a single two level atom in a one-sided cavity is studied using a model system, where a infinite atomic layer sits in front of a reflecting mirror. When the atomic layer is placed at the antinode of input field, the result given by finite difference time domain method coupled with the optical Bloch equations is consistent with previous analytical result [ H F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B 5, 218 (2003) ] based on one-dimensional atom model.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 18, 2005•0 citations

Nonlinear optical phase shift obtained from two-level atoms confined in a planar microcavity

Hisaki Oka, Hideki Fujiwara, Shigeki Takeuchi +1 more

We investigate the nonlinear optical phase shift obtained from a thin atomic layer confined in a distributed Bragg reflector (DBR) microcavity with reflection geometry. The optical response of the atom-cavity system is numerically analyzed using finite-difference time-domain method with the optical Bloch equations. The optimal position of atomic layer, at which a maximal phase shift of π is realized, drastically changes with the quality factor Q of the cavity. We show that for high Q the maximal phase shift of π can be obtained anywhere in the cavity field independently of atomic layer position. This result is in contrast to that obtained from a one-dimensional atom model in the limit of bad cavity, where a maximal phase shift of π is obtained only at the antinode of the cavity field. We also show that the independence of phase shift on atom position realized in high-Q regime is due to an interference effect in the surface layers of the DBR cavity.

Journal of Applied Physics•Mar 1, 2010•0 citations

Effects of Decoherence on the Nonlinear Optical Phase Shift Obtained from a One-Dimensional Atom

Hisaki Oka, Holger Friedrich Hofmann, Shigeki Takeuchi +1 more

We investigate the effects of decoherence on the nonlinear phase shift obtained from a one-dimensional atom implemented by a one-sided microcavity. The one-dimensional atom is realized by coupling a single atom confined in the cavity to the one-dimensional input-output fields of the cavity. The nonlinear optical response obtained from the one-dimensional atom can then be analyzed by using the optical Bloch equations. It is shown that the nonlinear phase shift depends on the coupling efficiency η, which is defined by the ratio of the coherent atom-field coupling rate and the total dipole relaxation rate. In particular, a maximal phase shift of π is obtained on resonance for coupling efficiencies η larger than one half, while the maximal phase shifts for coupling efficiencies η smaller than one half are obtained off resonance and are always smaller than π/2.

Japanese Journal of Applied Physics•Nov 10, 2004•9 citations

Polarization phase gate with a tripod atomic system

S. Rebić, David Vitali, Carlo Ottaviani +4 more

We analyze the nonlinear optical response of a four-level atomic system driven into a tripod configuration. The large cross-Kerr nonlinearities that occur in such a system are shown to produce nonlinear phase shifts of order $\ensuremath{\pi}$. Such a substantial shift may be observed in a cold atomic gas in a magneto-optical trap where it could be feasibly exploited towards the realization of a polarization quantum phase gate. The experimental feasibility of such a gate is here examined in detail.

arXiv:quant-ph/0310148•Physical Review A•Sep 21, 2004•185 citations

Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate

Kunihiro Kojima, Holger Friedrich Hofmann, Shigeki Takeuchi +1 more

We investigate the single-mode operation of a quantum optical nonlinear $\ensuremath{\pi}$ phase-shift gate implemented by a single two-level atom in one-dimensional free space. Since the single-mode property of the input photons at the atom is not preserved in the interaction at the atom, we analyze the efficiency of single-mode operation that can still be achieved. We show how the input pulse shape can be optimized to obtain high efficiencies for the nonlinear single-mode operation. With this analysis, we obtain an optimal single-mode transmittance per photon of 78% for the successful nonlinear $\ensuremath{\pi}$ phase-shift operation.

arXiv:quant-ph/0405121•Physical Review A•Jul 23, 2004•25 citations

Pulse-shape effects on photon-photon interactions in nonlinear optical quantum gates

Holger Friedrich Hofmann, Hitoshi Nishitani

Ideally, strong nonlinearities could be used to implement quantum gates for photonic qubits by well-controlled two-photon interactions. However, the dependence of the nonlinear interaction on frequency and time makes it difficult to preserve a coherent pulse shape that could justify a single-mode model for the time-frequency degree of freedom of the photons. In this paper, we analyze the problem of temporal multimode effects by considering the pulse shape of the average output field obtained from a coherent input pulse. It is shown that a significant part of the two-photon state transformation can be derived from this semiclassical description of the optical nonlinearity. The effect of a nonlinear system on a two-photon state can then be determined from the density-matrix dynamics of the coherently driven system using input-output theory. As an example, the resonant nonlinearity of a single two-level atom is characterized. The results indicate that the most efficient nonlinear effect may not be the widely studied single-mode phase shift, but the transfer of one of the photons to an orthogonal mode distinguished by its temporal and spectral properties.

arXiv:0905.1576•Physical Review A•Jul 23, 2009•9 citations
The nonlinear optical response obtained from a model system of a quantum phase gate is investigated. The model system consists of a thin infinite atomic layer of two-level atoms placed in front of a perfect reflecting mirror. The optical response obtained from the model system is semiclassically analyzed using the finite difference time domain method with the optical Bloch equations. It is shown that a nonlinear phase shift of \ensuremathπ\ensuremath{\pi}\ensuremathπ is achieved when the atomic layer is placed at an antinode of the input field. This result is consistent with the theoretical result obtained from a one-dimensional atom model [H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B: Quantum Semiclassical Opt. 5, 218 (2003)]. The dependence of the nonlinear phase shift on the position of the atomic layer is also studied in detail.
The nonlinear optical response obtained from a single two level atom in a one-sided cavity is studied using a model system, where a infinite atomic layer sits in front of a reflecting mirror. When the atomic layer is placed at the antinode of input field, the result given by finite difference time domain method coupled with the optical Bloch equations is consistent with previous analytical result [ H F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B 5, 218 (2003) ] based on one-dimensional atom model.
We investigate the nonlinear optical phase shift obtained from a thin atomic layer confined in a distributed Bragg reflector (DBR) microcavity with reflection geometry. The optical response of the atom-cavity system is numerically analyzed using finite-difference time-domain method with the optical Bloch equations. The optimal position of atomic layer, at which a maximal phase shift of π is realized, drastically changes with the quality factor Q of the cavity. We show that for high Q the maximal phase shift of π can be obtained anywhere in the cavity field independently of atomic layer position. This result is in contrast to that obtained from a one-dimensional atom model in the limit of bad cavity, where a maximal phase shift of π is obtained only at the antinode of the cavity field. We also show that the independence of phase shift on atom position realized in high-Q regime is due to an interference effect in the surface layers of the DBR cavity.
We investigate the effects of decoherence on the nonlinear phase shift obtained from a one-dimensional atom implemented by a one-sided microcavity. The one-dimensional atom is realized by coupling a single atom confined in the cavity to the one-dimensional input-output fields of the cavity. The nonlinear optical response obtained from the one-dimensional atom can then be analyzed by using the optical Bloch equations. It is shown that the nonlinear phase shift depends on the coupling efficiency η, which is defined by the ratio of the coherent atom-field coupling rate and the total dipole relaxation rate. In particular, a maximal phase shift of π is obtained on resonance for coupling efficiencies η larger than one half, while the maximal phase shifts for coupling efficiencies η smaller than one half are obtained off resonance and are always smaller than π/2.
We analyze the nonlinear optical response of a four-level atomic system driven into a tripod configuration. The large cross-Kerr nonlinearities that occur in such a system are shown to produce nonlinear phase shifts of order $\ensuremath{\pi}$. Such a substantial shift may be observed in a cold atomic gas in a magneto-optical trap where it could be feasibly exploited towards the realization of a polarization quantum phase gate. The experimental feasibility of such a gate is here examined in detail.
We investigate the single-mode operation of a quantum optical nonlinear $\ensuremath{\pi}$ phase-shift gate implemented by a single two-level atom in one-dimensional free space. Since the single-mode property of the input photons at the atom is not preserved in the interaction at the atom, we analyze the efficiency of single-mode operation that can still be achieved. We show how the input pulse shape can be optimized to obtain high efficiencies for the nonlinear single-mode operation. With this analysis, we obtain an optimal single-mode transmittance per photon of 78% for the successful nonlinear $\ensuremath{\pi}$ phase-shift operation.
Ideally, strong nonlinearities could be used to implement quantum gates for photonic qubits by well-controlled two-photon interactions. However, the dependence of the nonlinear interaction on frequency and time makes it difficult to preserve a coherent pulse shape that could justify a single-mode model for the time-frequency degree of freedom of the photons. In this paper, we analyze the problem of temporal multimode effects by considering the pulse shape of the average output field obtained from a coherent input pulse. It is shown that a significant part of the two-photon state transformation can be derived from this semiclassical description of the optical nonlinearity. The effect of a nonlinear system on a two-photon state can then be determined from the density-matrix dynamics of the coherently driven system using input-output theory. As an example, the resonant nonlinearity of a single two-level atom is characterized. The results indicate that the most efficient nonlinear effect may not be the widely studied single-mode phase shift, but the transfer of one of the photons to an orthogonal mode distinguished by its temporal and spectral properties.