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:1404.4732 · Physical Review A

Geometric phase gate for entangling two Bose-Einstein condensates

Mahmood Irtiza Hussain, Ebubechukwu O. Ilo-Okeke, Tim Byrnes

Published May 9, 2014• 26 citations
arXivHTMLPDF

Abstract

We propose a method of entangling two spinor Bose-Einstein condensates using a geometric phase gate. The scheme relies upon only the ac Stark shift and a common controllable optical mode coupled to the spins. Our scheme allows for the creation of an ${S}^{z}{S}^{z}$-type interaction where ${S}^{z}$ is the total spin. The geometric phase gate can be executed in times of the order of $2\ensuremath{\pi}\ensuremath{\hbar}/G$, where $G$ is the magnitude of the Stark shift. In contrast to related schemes which relied on a fourth-order interaction to produce entanglement, this is a second-order interaction in the number of atomic transitions. Closed expressions for the entangling phase are derived and the effects of decoherence due to cavity decay, spontaneous emission, and incomplete de-entangling of the light to the Bose-Einstein condensates are analyzed.

DOI
10.1103/physreva.89.053607

Related papers

Entanglement generation between two spinor Bose-Einstein condensates with cavity QED

Daniel Rosseau, Qianqian Ha, Tim Byrnes

We analyze a scheme for generating entanglement between two spinor Bose-Einstein condensates (BECs). The BECs are off-resonantly coupled to a common photon mode and are controlled by external lasers to induce a ${S}^{z}{S}^{z}$ interaction, where ${S}^{z}$ is the total spin of the BEC. We directly simulate the scheme numerically for small systems and show the performance of the scheme. The scaling of the entanglement to large-scale systems under realistic conditions of spontaneous emission and cavity photon loss is analyzed. It is shown that both entanglement in the beyond-continuous-variable regime can be generated, where the entanglement is of the order of the maximal entanglement between the systems.

arXiv:1410.3600•Physical Review A•Nov 13, 2014•26 citations

Geometric phases of mesoscopic spin in Bose-Einstein condensates

Ivette Fuentes, Jiannis K. Pachos, Sougato Bose +2 more

We propose a possible scheme for generating spin-J geometric phases using a coupled two-mode Bose-Einstein condensate (BEC). First we show how to observe the standard Berry phase using Raman coupling between two hyperfine states of the BEC. We find that the presence of intrinsic interatomic collisions creates degeneracy in energy that allows implementation of the non-Abelian geometric phases as well. The evolutions produced can be used to produce interference between different atomic species with high numbers of atoms or to fine control the difference in atoms between the two species. Finally, we show that errors in the standard Berry phase due to elastic collisions may be corrected by controlling inelastic collisions between atoms.

arXiv:quant-ph/0108078•Physical Review A•Aug 5, 2002•46 citations

Unconventional geometric quantum phase gates with a cavity QED system

Shi‐Biao Zheng

We propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift with atoms in a cavity. In the scheme the atoms interact simultaneously with a highly detuned cavity mode and a classical field. The atoms undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, aquiring a geometric phase conditional upon the atomic state. Under certain conditions, the atoms are disentangled with the cavity mode and thus the gate is insensitive to both the atomic spontaneous emission and the cavity decay.

arXiv:1202.5387•Physical Review A•Nov 19, 2004•94 citations

Generating two-spin squeezed states of separated Bose-Einstein condensates

Juan E Aristizabal-Zuluaga, Iuliia Skobleva, Lars Richter +4 more

ABSTRACT: We theoretically study a scheme for generating squeezing between two Bose-Einstein condensates (BECs). The scheme involves placing two BECs in the path of a Mach-Zehnder interferometer, where the coherent light interacts with the atoms due to the ac Stark shift. The most relevant regime for producing squeezing is in the short time regime, defined as when the interaction time scales as the inverse square root of the atom number. In this regime it is possible to construct a very simple approximate theory for the overall effect of the scheme: amplitudes in the superposition between the two BECs with unequal spin eigenvalues are damped. We analyze the types of correlations, entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell correlations that are produced and show that the state is similar to a spin-EPR state. Using a two-pulse sequence the correlations can be dramatically improved, where the state further approaches a spin-EPR state.

•Jan 1, 2020•0 citations

An unconventional geometric phase gate between two arbitrary qubits in a two-dimensional network

Zhi‐Rong Zhong, Xiaobin Huang

We show that an unconventional geometric phase gate between an arbitrary pair of distant qubits in a two-dimensional network can be obtained. In the scheme, the off-resonant Raman transitions between two ground states of the trapped atoms, which, induced by the cavity modes and external fields, can lead to selective qubit–qubit coupling. As a typical application, this interaction mechanism can be used to realize unconventional geometric phase gates. The advantage of the proposed scheme is that the atomic spontaneous emission is effectively suppressed, which makes the scheme very robust against decoherence.

Journal of the Optical Society of America B•Jan 12, 2015•4 citations

Decoherence-free dynamical and geometrical entangling phase gates

Jiannis K. Pachos, Almut Beige

It is shown that entangling two-qubit phase gates for quantum computation with atoms inside a resonant optical cavity can be generated via common laser addressing, essentially, within one step. The obtained dynamical or geometrical phases are produced by an evolution that is robust against dissipation in form of spontaneous emission from the atoms and the cavity and demonstrates resilience against fluctuations of control parameters. This is achieved by using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903 (2002)] and employing entangling Raman- or STIRAP-like transitions that restrict the time evolution of the system onto stable ground states.

arXiv:quant-ph/0309180•Physical Review A•Mar 26, 2004•38 citations
We propose a method of entangling two spinor Bose-Einstein condensates using a geometric phase gate. The scheme relies upon only the ac Stark shift and a common controllable optical mode coupled to the spins. Our scheme allows for the creation of an SzSz{S}^{z}{S}^{z}SzSz-type interaction where Sz{S}^{z}Sz is the total spin. The geometric phase gate can be executed in times of the order of 2\ensuremathπ\ensuremathℏ/G2\ensuremath{\pi}\ensuremath{\hbar}/G2\ensuremathπ\ensuremathℏ/G, where GGG is the magnitude of the Stark shift. In contrast to related schemes which relied on a fourth-order interaction to produce entanglement, this is a second-order interaction in the number of atomic transitions. Closed expressions for the entangling phase are derived and the effects of decoherence due to cavity decay, spontaneous emission, and incomplete de-entangling of the light to the Bose-Einstein condensates are analyzed.
We analyze a scheme for generating entanglement between two spinor Bose-Einstein condensates (BECs). The BECs are off-resonantly coupled to a common photon mode and are controlled by external lasers to induce a SzSz{S}^{z}{S}^{z}SzSz interaction, where Sz{S}^{z}Sz is the total spin of the BEC. We directly simulate the scheme numerically for small systems and show the performance of the scheme. The scaling of the entanglement to large-scale systems under realistic conditions of spontaneous emission and cavity photon loss is analyzed. It is shown that both entanglement in the beyond-continuous-variable regime can be generated, where the entanglement is of the order of the maximal entanglement between the systems.
We propose a possible scheme for generating spin-J geometric phases using a coupled two-mode Bose-Einstein condensate (BEC). First we show how to observe the standard Berry phase using Raman coupling between two hyperfine states of the BEC. We find that the presence of intrinsic interatomic collisions creates degeneracy in energy that allows implementation of the non-Abelian geometric phases as well. The evolutions produced can be used to produce interference between different atomic species with high numbers of atoms or to fine control the difference in atoms between the two species. Finally, we show that errors in the standard Berry phase due to elastic collisions may be corrected by controlling inelastic collisions between atoms.
We propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift with atoms in a cavity. In the scheme the atoms interact simultaneously with a highly detuned cavity mode and a classical field. The atoms undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, aquiring a geometric phase conditional upon the atomic state. Under certain conditions, the atoms are disentangled with the cavity mode and thus the gate is insensitive to both the atomic spontaneous emission and the cavity decay.
ABSTRACT: We theoretically study a scheme for generating squeezing between two Bose-Einstein condensates (BECs). The scheme involves placing two BECs in the path of a Mach-Zehnder interferometer, where the coherent light interacts with the atoms due to the ac Stark shift. The most relevant regime for producing squeezing is in the short time regime, defined as when the interaction time scales as the inverse square root of the atom number. In this regime it is possible to construct a very simple approximate theory for the overall effect of the scheme: amplitudes in the superposition between the two BECs with unequal spin eigenvalues are damped. We analyze the types of correlations, entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell correlations that are produced and show that the state is similar to a spin-EPR state. Using a two-pulse sequence the correlations can be dramatically improved, where the state further approaches a spin-EPR state.
We show that an unconventional geometric phase gate between an arbitrary pair of distant qubits in a two-dimensional network can be obtained. In the scheme, the off-resonant Raman transitions between two ground states of the trapped atoms, which, induced by the cavity modes and external fields, can lead to selective qubit–qubit coupling. As a typical application, this interaction mechanism can be used to realize unconventional geometric phase gates. The advantage of the proposed scheme is that the atomic spontaneous emission is effectively suppressed, which makes the scheme very robust against decoherence.
It is shown that entangling two-qubit phase gates for quantum computation with atoms inside a resonant optical cavity can be generated via common laser addressing, essentially, within one step. The obtained dynamical or geometrical phases are produced by an evolution that is robust against dissipation in form of spontaneous emission from the atoms and the cavity and demonstrates resilience against fluctuations of control parameters. This is achieved by using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903 (2002)] and employing entangling Raman- or STIRAP-like transitions that restrict the time evolution of the system onto stable ground states.