Bose-condensate tunneling dynamics: Momentum-shortened pendulum with damping

There have been many discussions of two-mode models for Bose condensates in a double well potential, but few cases in which parameters for these models have been calculated for realistic situations. Recent experiments lead us to use the Gross-Pitaevskii equation to obtain optimum twomode parameters. We find that by using the lowest symmetric and antisymmetric wavefunctions, it is possible to derive equations for a more exact two-mode model that provides for a variable tunneling rate depending on the instantaneous values of the number of atoms and phase differences. Especially for larger values of the nonlinear interaction term and larger barrier heights, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in 1D and 3D, as compared with previous models with constant tunneling, and better agreement with experimental results for the tunneling oscillation frequency [Albiez et al., cond-mat/0411757]. We also show how this approach can be used to obtain modified equations for a second quantized version of the Bose double well problem.

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“…What we have not investigated here are damping effects of thermal excitations, as considered in [6] and [43].…”

Section: Discussionmentioning

confidence: 99%

Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond

2006

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“…The extension of adiabatic methods to nonlinear systems is of great importance not only to describe experimental situations but also for the understanding of the underlying physical principles [18,19,22,23]. In this section we show how CTAP can be used with time-dependent potentials to coherently transport a cloud of interacting, Bose-condensed atoms.…”

Section: Nonlinear Systemsmentioning

confidence: 99%

Coherent adiabatic transport of atoms in radio-frequency traps

Morgan

O’Sullivan²,

Busch³

2011

Phys. Rev. A

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Coherent transport by adiabatic passage has recently been suggested as a high-fidelity technique to engineer the center-of-mass state of single atoms in inhomogeneous environments. While the basic theory behind this process is well understood, several conceptual challenges for its experimental observation have still to be addressed. One of these is the difficulty that currently available optical or magnetic micro-trap systems have in adjusting the tunneling rate time dependently while keeping resonance between the asymptotic trapping states at all times. Here we suggest that both requirements can be fulfilled to a very high degree in an experimentally realistic setup based on radio-frequency traps on atom chips. We show that operations with close to 100% fidelity can be achieved and that these systems also allow significant improvements for performing adiabatic passage with interacting atomic clouds

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“…(13), and Eq. (14). By performing two successive transformations, x = x ′ + π, and x ′ = ıy, we obtain following eigenvalue equation from Eq.…”

Section: B Energy Spectrummentioning

confidence: 99%

Quantum dynamics and macroscopic quantum tunnelling of two weakly coupled condensates

Kerkdyk

Sinha

2013

J. Phys. B: At. Mol. Opt. Phys.

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We study the quantum dynamics of a Bose Josephson junction(BJJ) made up of two coupled Bose-Einstein condensates. Apart from the usual ac Josephson oscillations, two different dynamical states of BJJ can be observed by tuning the inter-particle interaction strength, which are known as 'π-oscillation' with relative phase π between the condensates and 'macroscopic self-trapped' (MST) state with finite number imbalance. By choosing appropiate intial state we study above dynamical branches quantum mechanically and compare with classical dynamics. The stability region of the 'π-oscillation' is separated from that of 'MST' state at a critical coupling strength. Also a significant change in the energy spectrum takes place above the critical coupling strength, and pairs of (quasi)-degenerate excited states appear. The original model of BJJ can be mapped on to a simple Hamiltonian describing quantum particle in an 'effective potential' with an effective Planck constant. Different dynamical states and degenerate excited states in the energy spectrum can be understood in this 'effective potential' approach. Also possible novel quantum phenomena like 'macroscopic quantum tunneling'(MQT) become evident from the simple picture of 'effective potential'. We study decay of metastable 'π-oscillation' by MQT through potential barrier. The doubly degenerate excited states in the energy spectrum are associated with the classically degenerate MST states with equal and opposite number imbalance. We calculate the energy splitting between these quasi-degenerate excited states due to MQT of the condensate between classically degenerate MST states.

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Bose-condensate tunneling dynamics: Momentum-shortened pendulum with damping

Cited by 90 publications

References 17 publications

Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond

Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond

Coherent adiabatic transport of atoms in radio-frequency traps

Quantum dynamics and macroscopic quantum tunnelling of two weakly coupled condensates

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