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

Quantum Electronics and Laser Science Conference

Strong confinement and oscillations in two-component Bose-Einstein condensates

Q‐Han Park, Joseph H. Eberly

Published Nov 13, 2002• 2 citations
Publisher

Abstract

Summary form only given. Recent elegant experimental observations of Rabi-type oscillations in a two-component Bose-Einstein condensate (BEC) of 87Rb brings up an issue of collapse and revival in BEC which has resisted any conventional theoretical analysis. Though a heuristic argument using "twists" of an SU(2) order parameter was given in, the fundamental dynamics of the observed oscillations has not been understood. In this talk, we present a resolution to this problem in terms a new model of BEC dynamics. We go beyond revival analysis to present a new quantum mechanical picture of the multicomponent BEC physics based on a strong confinement model, which explains experimentally observed features quite well. We show that the coupled Gross-Pitaevski (GP) equations for the two-component Bose-Einstein condensate can be decoupled by a time-dependent dressing transformation.

DOI
10.1109/qels.2001.962206

Related papers

An Investigation of Quantum Dynamics in a Three- Level Bose-Einstein Condensate System

Saad J Ansari

Bose-Einstein condensates present to us the opportunity to probe into the atomic interac- tions that govern a macroscopic quantum mechanical system. The degenerate hyperfine manifold in the bosonic atoms splits in the presence of an external B-field; radio-frequency induced coupling releases experimentally-attainable knowledge about the Zeeman mani- fold in 87Rb. The purpose of this study is to investigate quantum dynamics in two and three-component Bose-Einstein condensate (BEC) systems. We start with a theoretical analysis of Josephson tunneling dynamics between identical BECs trapped in a double potential well, paying particular attention to the non-linear self-trapping effect observed as a consequence of the intra-well interaction. We present a model for the non-equilibrium dynamics in a two-level system and introduce the Rabi oscillations. This is followed by a numerical and experimental investigation of Rabi oscillations in a three-level 87Rb BEC between the F = 1 hyperfine level spin states mF = {1, 0, 1}. The relation between the observed total Rabi frequency and the detuning, along with its effect on the BEC population dynamics is explored. Finally, we explore the possible suspects for the shift of the resonance at strong Rabi frequencies .

•Jan 1, 2014•0 citations

Density-matrix approach to a strongly coupled two-component Bose-Einstein condensate

Andal Narayanan, Hema Ramachandran

The time evolution equations for average values of population and relative phase of a strongly coupled two-component Bose-Einstein condensate (BEC) are derived analytically. The two components are two hyperfine states, which are coupled by an external laser that drives fast Rabi oscillations between these states. Specifically, this derivation incorporates the two-mode model proposed in J. Williams et al., e-print cond-mat 9904399 for the strongly coupled hyperfine states $|1,\ensuremath{-}1〉$ and $|2,1〉$ of ${}^{87}\mathrm{Rb}.$ The fast Rabi cycles are averaged out and the rate equations so derived represent the slow dynamics of the system. These include the collapse and revival of Rabi oscillations and their dependence on detuning and trap displacement as reported in experiments of J. Williams. A procedure for stabilizing vortices is also suggested.

arXiv:cond-mat/9911390•Physical Review A•Oct 12, 2000•2 citations

Strong Confinement and Oscillations in Two-Component Bose-Einstein Condensates

Q‐Han Park, Joseph H. Eberly

We present a new model of Bose-Einstein condensate dynamics based on strong confinement near the ground state. The model is based on a combined particle-wave view of the condensate and predicts oscillations in a two-component condensate, based on interference of nonspreading wave packets moving within a pair of tilted nearly square potentials. The oscillations are similar to those recently reported for a magnetically trapped 87Rb condensate, and the model's predictions give good quantitative agreement with the experiments.

arXiv:cond-mat/0006110•Physical Review Letters•Nov 13, 2000•15 citations

Stability and collapse of a hybrid Bose-Einstein condensate of atoms and molecules

Sadhan K. Adhikari

The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can transform two atoms into a molecule and vice versa. We find an interesting oscillation of the number of atoms and molecules for a BEC of fixed mass. This oscillation is a consequence of continuous transformation in the condensate of two atoms into a molecule and vice versa. For the study of collapse an absorptive contact interaction and an imaginary quartic three-body recombination term are included in the GP equation. It is possible to have a collapse of one or both components when one or more of the nonlinear terms in the GP equation are attractive in nature, respectively.

arXiv:cond-mat/0105534•Journal of Physics B Atomic Molecular and Optical Physics•Oct 31, 2001•12 citations

Two-component Bose-Einstein condensates :equilibria and dynamics at zero temperature and beyond

RW Pattinson

In this Thesis we study steady state solutions and dynamical evolutions of two– component atomic Bose–Einstein Condensates. We initially investigate the equilibrium properties of condensate mixtures in harmonic trapping potentials at zero temperature. Subsequently we simulate the coupled growth of these condensates by inclusion of damping terms. Finally, we investigate the evolution of coupled Bose gases via the so-called classical–field method. A recent experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)] achieved Bose–Einstein Condensation of a two–species 87Rb–133Cs phase segregated mixture in harmonic trapping potentials. Depending on relative atom numbers of the two species, three distinct regimes of density distributions were observed. For these experimental parameters, we investigate the corresponding time–independent ground state solutions through numerical simulations of the coupled Gross–Pitaevskii equations. By including experimentally relevant shifts between the traps, we observe a range of structures including ‘ball and shell’ formations and axially/radially separated states. These are found to be very sensitive to the trap shifts. For all three experimental regimes, our numerical simulations reveal good qualitative agreement. The observed experimental profiles cannot be guaranteed to be fully equilibrated. This, coupled with the rapid sympathetic cooling of the experimental system, leads to a situation where growth may play a determining factor in the density structures formed. To investigate this further, we introduce phenomenological damping to describe the associated condensate growth/decay, revealing a range of transient structures. However, such a model always predicts the predominance of one condensate species over longer evolution times. Work undertaken by collaborators with the more elaborate Stochastic Projected Gross–Pitaevskii equations, which can describe condensate formation by coupling to a heat bath, predicts the spontaneous formation of dark–bright solitons. Motivated by this, we show how the presence of solitons can affect the condensate distribution, thus highlighting the overall dynamical role in the emerging patterns. Finally, we use classical field methods to analyse the evolution of non trapped Bose gases from strongly nonequilibrium initial distributions. The contrast between miscible (overlapping) and immiscible (phase segregated) components gives rise to important distinctions for condensate fractions and the formation of domains and vortices. In addition, splitting the particles of a single component thermalised state into two components is investigated. We then study the effects of suddenly quenching the strength of the interspecies interactions. Under suitable conditions, this quench generates isotropic vortex tangles. While this tangle subsequently decays over time, we propose how a repeat sequence of quenches at regular intervals could be employed to drive the tangle, thereby potentially providing a novel route to the generation of quantum turbulence.

•Jan 1, 2014•4 citations

Watching a Superfluid Untwist Itself: Recurrence of Rabi Oscillations in a Bose-Einstein Condensate

M. R. Matthews, Brian P. Anderson, P. C. Haljan +5 more

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length.We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of 87 Rb.

WORLD SCIENTIFIC eBooks•Jan 1, 2008•1 citation
Summary form only given. Recent elegant experimental observations of Rabi-type oscillations in a two-component Bose-Einstein condensate (BEC) of 87Rb brings up an issue of collapse and revival in BEC which has resisted any conventional theoretical analysis. Though a heuristic argument using "twists" of an SU(2) order parameter was given in, the fundamental dynamics of the observed oscillations has not been understood. In this talk, we present a resolution to this problem in terms a new model of BEC dynamics. We go beyond revival analysis to present a new quantum mechanical picture of the multicomponent BEC physics based on a strong confinement model, which explains experimentally observed features quite well. We show that the coupled Gross-Pitaevski (GP) equations for the two-component Bose-Einstein condensate can be decoupled by a time-dependent dressing transformation.
Bose-Einstein condensates present to us the opportunity to probe into the atomic interac- tions that govern a macroscopic quantum mechanical system. The degenerate hyperfine manifold in the bosonic atoms splits in the presence of an external B-field; radio-frequency induced coupling releases experimentally-attainable knowledge about the Zeeman mani- fold in 87Rb. The purpose of this study is to investigate quantum dynamics in two and three-component Bose-Einstein condensate (BEC) systems. We start with a theoretical analysis of Josephson tunneling dynamics between identical BECs trapped in a double potential well, paying particular attention to the non-linear self-trapping effect observed as a consequence of the intra-well interaction. We present a model for the non-equilibrium dynamics in a two-level system and introduce the Rabi oscillations. This is followed by a numerical and experimental investigation of Rabi oscillations in a three-level 87Rb BEC between the F = 1 hyperfine level spin states mF = {1, 0, 1}. The relation between the observed total Rabi frequency and the detuning, along with its effect on the BEC population dynamics is explored. Finally, we explore the possible suspects for the shift of the resonance at strong Rabi frequencies .
The time evolution equations for average values of population and relative phase of a strongly coupled two-component Bose-Einstein condensate (BEC) are derived analytically. The two components are two hyperfine states, which are coupled by an external laser that drives fast Rabi oscillations between these states. Specifically, this derivation incorporates the two-mode model proposed in J. Williams et al., e-print cond-mat 9904399 for the strongly coupled hyperfine states $|1,\ensuremath{-}1〉$ and ∣2,1〉|2,1〉∣2,1〉 of 87Rb.{}^{87}\mathrm{Rb}.87Rb. The fast Rabi cycles are averaged out and the rate equations so derived represent the slow dynamics of the system. These include the collapse and revival of Rabi oscillations and their dependence on detuning and trap displacement as reported in experiments of J. Williams. A procedure for stabilizing vortices is also suggested.
We present a new model of Bose-Einstein condensate dynamics based on strong confinement near the ground state. The model is based on a combined particle-wave view of the condensate and predicts oscillations in a two-component condensate, based on interference of nonspreading wave packets moving within a pair of tilted nearly square potentials. The oscillations are similar to those recently reported for a magnetically trapped 87Rb condensate, and the model's predictions give good quantitative agreement with the experiments.
The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can transform two atoms into a molecule and vice versa. We find an interesting oscillation of the number of atoms and molecules for a BEC of fixed mass. This oscillation is a consequence of continuous transformation in the condensate of two atoms into a molecule and vice versa. For the study of collapse an absorptive contact interaction and an imaginary quartic three-body recombination term are included in the GP equation. It is possible to have a collapse of one or both components when one or more of the nonlinear terms in the GP equation are attractive in nature, respectively.
In this Thesis we study steady state solutions and dynamical evolutions of two– component atomic Bose–Einstein Condensates. We initially investigate the equilibrium properties of condensate mixtures in harmonic trapping potentials at zero temperature. Subsequently we simulate the coupled growth of these condensates by inclusion of damping terms. Finally, we investigate the evolution of coupled Bose gases via the so-called classical–field method. A recent experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)] achieved Bose–Einstein Condensation of a two–species 87Rb–133Cs phase segregated mixture in harmonic trapping potentials. Depending on relative atom numbers of the two species, three distinct regimes of density distributions were observed. For these experimental parameters, we investigate the corresponding time–independent ground state solutions through numerical simulations of the coupled Gross–Pitaevskii equations. By including experimentally relevant shifts between the traps, we observe a range of structures including ‘ball and shell’ formations and axially/radially separated states. These are found to be very sensitive to the trap shifts. For all three experimental regimes, our numerical simulations reveal good qualitative agreement. The observed experimental profiles cannot be guaranteed to be fully equilibrated. This, coupled with the rapid sympathetic cooling of the experimental system, leads to a situation where growth may play a determining factor in the density structures formed. To investigate this further, we introduce phenomenological damping to describe the associated condensate growth/decay, revealing a range of transient structures. However, such a model always predicts the predominance of one condensate species over longer evolution times. Work undertaken by collaborators with the more elaborate Stochastic Projected Gross–Pitaevskii equations, which can describe condensate formation by coupling to a heat bath, predicts the spontaneous formation of dark–bright solitons. Motivated by this, we show how the presence of solitons can affect the condensate distribution, thus highlighting the overall dynamical role in the emerging patterns. Finally, we use classical field methods to analyse the evolution of non trapped Bose gases from strongly nonequilibrium initial distributions. The contrast between miscible (overlapping) and immiscible (phase segregated) components gives rise to important distinctions for condensate fractions and the formation of domains and vortices. In addition, splitting the particles of a single component thermalised state into two components is investigated. We then study the effects of suddenly quenching the strength of the interspecies interactions. Under suitable conditions, this quench generates isotropic vortex tangles. While this tangle subsequently decays over time, we propose how a repeat sequence of quenches at regular intervals could be employed to drive the tangle, thereby potentially providing a novel route to the generation of quantum turbulence.