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

Journal of the Optical Society of America B

Numerical study of large cross-phase modulation with stationary light pulses

Yi‐Hsuan Chen, Yi‐Hsin Chen

Published Apr 19, 2021• 2 citations
Publisher

Abstract

We report a systematic investigation of cross-phase modulation using techniques of light storage (LS) and stationary light pulse (SLP) based on the effect of electromagnetically induced transparency. Two light fields are stopped in the medium to prolong the interaction time, which enhances the efficiency of optical nonlinearity. We numerically study the properties of the signal SLP field such as lifetime, light pulse storage efficiency, and stored peak intensity as functions of optical density (OD) and coupling field intensity. The strong nonlinearity between LS and SLP photons leads to a phase shift of up to π at the single-photon level. Meanwhile, both the LS and SLP photons maintain energy transmission higher than 20%, as the OD of the SLP subsystem is larger than 700. The energy transmission and phase shift can be further improved by increasing the OD of the medium. The performance of the quantum phase gate between two single photons is expected by applying such strong photon interaction.

DOI
10.1364/josab.416387

Related papers

Low-Light-Level Cross-Phase-Modulation Based on Stored Light Pulses

Yong‐Fan Chen, Chang-Yi Wang, Shih-Hao Wang +1 more

We experimentally demonstrate a low-light-level cross-phase-modulation (XPM) scheme based on the light-storage technique in laser-cooled 87Rb atoms. The proposed scheme can achieve a similar phase shift and has the same figure of merit as one using static electromagnetically induced transparency under the constant coupling field. Nevertheless, the phase shift and the energy loss of a probe pulse induced by a signal pulse are neither influenced by the coupling intensity nor by the atomic optical density in the light-storage XPM scheme. This scheme enhances the flexibility of the experiment and makes possible conditional phase shifts on the order of pi with single photons.

Physical Review Letters•Feb 2, 2006•156 citations

Memory-enhanced noiseless cross-phase modulation

Mahdi Hosseini, S. Rebić, Ben M. Sparkes +3 more

Large nonlinearity at the single-photon level can pave the way for the implementation of universal quantum gates. However, realizing large and noiseless nonlinearity at such low light levels has been a great challenge for scientists in the past decade. Here, we propose a scheme that enables substantial nonlinear interaction between two light fields that are both stored in an atomic memory. Semiclassical and quantum simulations demonstrate the feasibility of achieving large cross-phase modulation (XPM) down to the single-photon level. The proposed scheme can be used to implement parity gates from which CNOT gates can be constructed. Furthermore, we present a proof of principle experimental demonstration of XPM between two optical pulses: one stored and one freely propagating through the memory medium. Researchers have developed a new technique that shows promise for constructing optical quantum logic gates. Theoretical simulations performed by Mahdi Hosseini and co-workers from the Australian National University and Macquarie University in Australia show that inducing cross-phase modulation between two single-photon light fields stored in a rubidium atomic memory should provide large phase shifts and thus allow the realization of parity gates and CNOT gates, both of which are needed for quantum computing. The researchers estimate that using cold atoms confined in a dipole trap and short-duration single-photon wavepackets should make it possible to realize phase shifts of the order of 10 mrad — orders of magnitude larger than schemes that employ electromagnetically induced transparency.

arXiv:1112.2010•Light Science & Applications•Dec 7, 2012•58 citations

Short-pulse cross-phase modulation in an electromagnetically-induced-transparency medium

Amir Feizpour, Greg Dmochowski, Aephraim M. Steinberg

Electromagnetically induced transparency (EIT) has been proposed as a way to greatly enhance cross-phase modulation, with the possibility of leading to few-photon-level optical nonlinearities [Schmidt and Imamoglu, Opt. Lett. 21, 1936 (1996)]. This enhancement grows as the transparency window width, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$, is narrowed. Decreasing ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$, however, has been shown to increase the response time of the nonlinear medium. This suggests that, for a given pulse duration, the nonlinearity would diminish once the window width became narrower than this pulse bandwidth. We show that this is not the case: the peak phase shift saturates but does not decrease. We show that in the regimes of most practical interest---narrow EIT windows perturbed by short signal pulses---the enhancement offered by EIT is not only in the magnitude of the nonlinear phase shift but also in its increased duration. That is, for the case of signal pulses much shorter (temporally) than the inverse EIT bandwidth, the narrow window serves to prolong the effect of the passing signal pulse, leading to an integrated phase shift that grows linearly with $1/{\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$; this continued growth of the integrated phase shift improves the detectability of the phase shift, in principle, without bound. For many purposes, it is this detectability which is of more interest than the absolute magnitude of the peak phase shift. We present analytical expressions based on a linear time-invariant model that accounts for the temporal behavior of the cross-phase modulation for several parameter ranges of interest. We conclude that in order to optimize the detectability of the EIT-based cross-phase shift, one should use the narrowest possible EIT window and a signal pulse that is as broadband as the excited-state linewidth and detuned by half a linewidth.

arXiv:1406.0245•Physical Review A•Jan 19, 2016•18 citations

Low-light-level cross-phase modulation by quantum interference

Hsiang-Yu Lo, Po-Ching Su, Yong‐Fan Chen

We report on the direct measurement of low-light-level cross-phase modulation (XPM) based on electromagnetically induced transparency (EIT) in the pulsed regime. A phase shift of 0.02 rad of a probe pulse modulated by a signal pulse with a peak intensity of 3 $\mathrm{\ensuremath{\mu}}\mathrm{W}/{\mathrm{cm}}^{2}$ was observed, which is the lowest intensity ever achieved for the N-type EIT-based XPM system. The experimental data make a quantitative prediction of the single-photon-level XPM phase shift arising from two interacting pulses with unequal group velocities that is consistent with the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)]. Furthermore, a proof-of-principle experiment demonstrating an enhancement of the nonlinear optical Kerr effect by shining the signal pulse twice is presented.

Physical Review A•May 18, 2010•39 citations

Simultaneous Trapping of Two Optical Pulses in an Atomic Ensemble as Stationary Light Pulses

U-Shin Kim, Yoon-Ho Kim

The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counter-propagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. Here, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to experimentally demonstrate simultaneous SLP trapping of two optical pulses for the duration from$0.8\ \mu \mathsf{s}$to$2.0\ \mu \mathsf{s}$. The characteristic dissipation time, obtained by the release efficiency measurement, is$1.22\ \mu \mathsf{s}$, which corresponds to an effective Q-factor of$2.9\times 10^{9}$[1]. As our SLP system reports a large effective N-atom cooperativity of$8\times 10^{6}$, our work is expected to bring forth interesting SLP-based applications, such as, efficient photon-photon interaction, spatially multi-mode coherent quantum memory, creation of exotic photonic gas states, etc.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 26, 2023•0 citations

Simultaneous Trapping of Two Optical Pulses in an Atomic Ensemble as Stationary Light Pulses

U-Shin Kim, Yoon-Ho Kim

The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counterpropagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. In this Letter, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to experimentally demonstrate simultaneous SLP trapping of two optical pulses for the duration from 0.8 to 2.0 μs. The characteristic dissipation time, obtained by the release efficiency measurement from the SLP trapping state, is 1.22 μs, which corresponds to an effective Q factor of 2.9×10^{9}. Our Letter is expected to bring forth interesting SLP-based applications, such as, efficient photon-photon interaction, spatially multimode coherent quantum memory, creation of exotic photonic gas states, etc.

arXiv:2208.06109•Physical Review Letters•Aug 23, 2022•12 citations
We report a systematic investigation of cross-phase modulation using techniques of light storage (LS) and stationary light pulse (SLP) based on the effect of electromagnetically induced transparency. Two light fields are stopped in the medium to prolong the interaction time, which enhances the efficiency of optical nonlinearity. We numerically study the properties of the signal SLP field such as lifetime, light pulse storage efficiency, and stored peak intensity as functions of optical density (OD) and coupling field intensity. The strong nonlinearity between LS and SLP photons leads to a phase shift of up to π at the single-photon level. Meanwhile, both the LS and SLP photons maintain energy transmission higher than 20%, as the OD of the SLP subsystem is larger than 700. The energy transmission and phase shift can be further improved by increasing the OD of the medium. The performance of the quantum phase gate between two single photons is expected by applying such strong photon interaction.
We experimentally demonstrate a low-light-level cross-phase-modulation (XPM) scheme based on the light-storage technique in laser-cooled 87Rb atoms. The proposed scheme can achieve a similar phase shift and has the same figure of merit as one using static electromagnetically induced transparency under the constant coupling field. Nevertheless, the phase shift and the energy loss of a probe pulse induced by a signal pulse are neither influenced by the coupling intensity nor by the atomic optical density in the light-storage XPM scheme. This scheme enhances the flexibility of the experiment and makes possible conditional phase shifts on the order of pi with single photons.
Large nonlinearity at the single-photon level can pave the way for the implementation of universal quantum gates. However, realizing large and noiseless nonlinearity at such low light levels has been a great challenge for scientists in the past decade. Here, we propose a scheme that enables substantial nonlinear interaction between two light fields that are both stored in an atomic memory. Semiclassical and quantum simulations demonstrate the feasibility of achieving large cross-phase modulation (XPM) down to the single-photon level. The proposed scheme can be used to implement parity gates from which CNOT gates can be constructed. Furthermore, we present a proof of principle experimental demonstration of XPM between two optical pulses: one stored and one freely propagating through the memory medium. Researchers have developed a new technique that shows promise for constructing optical quantum logic gates. Theoretical simulations performed by Mahdi Hosseini and co-workers from the Australian National University and Macquarie University in Australia show that inducing cross-phase modulation between two single-photon light fields stored in a rubidium atomic memory should provide large phase shifts and thus allow the realization of parity gates and CNOT gates, both of which are needed for quantum computing. The researchers estimate that using cold atoms confined in a dipole trap and short-duration single-photon wavepackets should make it possible to realize phase shifts of the order of 10 mrad — orders of magnitude larger than schemes that employ electromagnetically induced transparency.
Electromagnetically induced transparency (EIT) has been proposed as a way to greatly enhance cross-phase modulation, with the possibility of leading to few-photon-level optical nonlinearities [Schmidt and Imamoglu, Opt. Lett. 21, 1936 (1996)]. This enhancement grows as the transparency window width, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$, is narrowed. Decreasing ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$, however, has been shown to increase the response time of the nonlinear medium. This suggests that, for a given pulse duration, the nonlinearity would diminish once the window width became narrower than this pulse bandwidth. We show that this is not the case: the peak phase shift saturates but does not decrease. We show that in the regimes of most practical interest---narrow EIT windows perturbed by short signal pulses---the enhancement offered by EIT is not only in the magnitude of the nonlinear phase shift but also in its increased duration. That is, for the case of signal pulses much shorter (temporally) than the inverse EIT bandwidth, the narrow window serves to prolong the effect of the passing signal pulse, leading to an integrated phase shift that grows linearly with $1/{\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$; this continued growth of the integrated phase shift improves the detectability of the phase shift, in principle, without bound. For many purposes, it is this detectability which is of more interest than the absolute magnitude of the peak phase shift. We present analytical expressions based on a linear time-invariant model that accounts for the temporal behavior of the cross-phase modulation for several parameter ranges of interest. We conclude that in order to optimize the detectability of the EIT-based cross-phase shift, one should use the narrowest possible EIT window and a signal pulse that is as broadband as the excited-state linewidth and detuned by half a linewidth.
We report on the direct measurement of low-light-level cross-phase modulation (XPM) based on electromagnetically induced transparency (EIT) in the pulsed regime. A phase shift of 0.02 rad of a probe pulse modulated by a signal pulse with a peak intensity of 3 $\mathrm{\ensuremath{\mu}}\mathrm{W}/{\mathrm{cm}}^{2}$ was observed, which is the lowest intensity ever achieved for the N-type EIT-based XPM system. The experimental data make a quantitative prediction of the single-photon-level XPM phase shift arising from two interacting pulses with unequal group velocities that is consistent with the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)]. Furthermore, a proof-of-principle experiment demonstrating an enhancement of the nonlinear optical Kerr effect by shining the signal pulse twice is presented.
The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counter-propagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. Here, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to experimentally demonstrate simultaneous SLP trapping of two optical pulses for the duration from0.8 μs0.8\ \mu \mathsf{s}0.8 μsto2.0 μs2.0\ \mu \mathsf{s}2.0 μs. The characteristic dissipation time, obtained by the release efficiency measurement, is1.22 μs1.22\ \mu \mathsf{s}1.22 μs, which corresponds to an effective Q-factor of2.9×1092.9\times 10^{9}2.9×109[1]. As our SLP system reports a large effective N-atom cooperativity of8×1068\times 10^{6}8×106, our work is expected to bring forth interesting SLP-based applications, such as, efficient photon-photon interaction, spatially multi-mode coherent quantum memory, creation of exotic photonic gas states, etc.
The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counterpropagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. In this Letter, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to experimentally demonstrate simultaneous SLP trapping of two optical pulses for the duration from 0.8 to 2.0 μs. The characteristic dissipation time, obtained by the release efficiency measurement from the SLP trapping state, is 1.22 μs, which corresponds to an effective Q factor of 2.9×10^{9}. Our Letter is expected to bring forth interesting SLP-based applications, such as, efficient photon-photon interaction, spatially multimode coherent quantum memory, creation of exotic photonic gas states, etc.