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Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence (2017)
Journal Article
Reeves, M. T., Billam, T. P., Yu, X., & Bradley, A. S. (2017). Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence. Physical Review Letters, 119(18), Article 184502. https://doi.org/10.1103/physrevlett.119.184502

We report evidence for an enstrophy cascade in large-scale point-vortex simulations of decaying twodimensional quantum turbulence. Devising a method to generate quantum vortex configurations with kinetic energy narrowly localized near a single length... Read More about Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence.

Stochastic growth dynamics and composite defects in quenched immiscible binary condensates (2016)
Journal Article
Liu, I.-K., Pattinson, R., Billam, T., Gardiner, S., Cornish, S., Huang, T.-M., Lin, W.-W., Gou, S.-C., Parker, N., & Proukakis, N. (2016). Stochastic growth dynamics and composite defects in quenched immiscible binary condensates. Physical Review A, 93(2), Article 023628. https://doi.org/10.1103/physreva.93.023628

We study the sensitivity of coupled condensate formation dynamics on the history of initial stochastic domain formation in the context of instantaneously quenched elongated harmonically trapped immiscible two-component atomic Bose gases. The spontane... Read More about Stochastic growth dynamics and composite defects in quenched immiscible binary condensates.

Analysis beyond the Thomas-Fermi approximation of the density profiles of a miscible two-component Bose-Einstein condensate (2015)
Journal Article
Polo, J., Ahufinger, V., Mason, P., Sridhar, S., Billam, T., & Gardiner, S. (2015). Analysis beyond the Thomas-Fermi approximation of the density profiles of a miscible two-component Bose-Einstein condensate. Physical Review A, 91(5), Article 053626. https://doi.org/10.1103/physreva.91.053626

We investigate a harmonically trapped two-component Bose-Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra- and interspecies interactions. We derive analytically a universal equation for... Read More about Analysis beyond the Thomas-Fermi approximation of the density profiles of a miscible two-component Bose-Einstein condensate.

Identifying a Superfluid Reynolds Number via Dynamical Similarity (2015)
Journal Article
Reeves, M., Billam, T., Anderson, B., & Bradley, A. (2015). Identifying a Superfluid Reynolds Number via Dynamical Similarity. Physical Review Letters, 114(15), Article 155302. https://doi.org/10.1103/physrevlett.114.155302

The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Perf... Read More about Identifying a Superfluid Reynolds Number via Dynamical Similarity.

Spectral energy transport in two-dimensional quantum vortex dynamics (2015)
Journal Article
Billam, T., Reeves, M., & Bradley, A. (2015). Spectral energy transport in two-dimensional quantum vortex dynamics. Physical Review A, 91(2), Article 023615. https://doi.org/10.1103/physreva.91.023615

We explore the possible regimes of decaying two-dimensional quantum turbulence, and elucidate the nature of spectral energy transport by introducing a dissipative point-vortex model with phenomenological vortex-sound interactions. The model is valid... Read More about Spectral energy transport in two-dimensional quantum vortex dynamics.

Signatures of coherent vortex structures in a disordered two-dimensional quantum fluid (2014)
Journal Article
Reeves, M., Billam, T., Anderson, B., & Bradley, A. (2014). Signatures of coherent vortex structures in a disordered two-dimensional quantum fluid. Physical Review A, 89(5), https://doi.org/10.1103/physreva.89.053631

The emergence of coherent rotating structures is a phenomenon characteristic of both classical and quantum two-dimensional (2D) turbulence. In this work we show theoretically that the coherent vortex structures that emerge in decaying 2D quantum turb... Read More about Signatures of coherent vortex structures in a disordered two-dimensional quantum fluid.

Entangling two distinguishable quantum bright solitons via collisions (2014)
Presentation / Conference Contribution
Billam, T. P., Blackley, C. L., Gertjerenken, B., Cornish, S. L., & Weiss, C. (2014, April). Entangling two distinguishable quantum bright solitons via collisions. Presented at 22nd International Laser Physics Workshop (LPHYS'13), Prague, Czech Republic

The generation of mesoscopic Bell states via collisions of distinguishable bright solitons has been suggested in Phys. Rev. Lett. 111, 100406 (2013). Here, we extend our former proposal to two hyperfine states of 85Rb instead of two different atomic... Read More about Entangling two distinguishable quantum bright solitons via collisions.

Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence (2014)
Journal Article
Billam, T., Reeves, M., Anderson, B., & Bradley, A. (2014). Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence. Physical Review Letters, 112(14), Article 145301. https://doi.org/10.1103/physrevlett.112.145301

Despite the prominence of Onsager’s point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system... Read More about Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence.

Generating Mesoscopic Bell States via Collisions of Distinguishable Quantum Bright Solitons (2013)
Journal Article
Gertjerenken, B., Billam, T., Blackley, C., Le Sueur, C., Khaykovich, L., Cornish, S., & Weiss, C. (2013). Generating Mesoscopic Bell States via Collisions of Distinguishable Quantum Bright Solitons. Physical Review Letters, 111(10), Article 100406. https://doi.org/10.1103/physrevlett.111.100406

We investigate numerically the collisions of two distinguishable quantum matter-wave bright solitons in a one-dimensional harmonic trap. We show that such collisions can be used to generate mesoscopic Bell states that can reliably be distinguished fr... Read More about Generating Mesoscopic Bell States via Collisions of Distinguishable Quantum Bright Solitons.

Controlled formation and reflection of a bright solitary matter-wave (2013)
Journal Article
Marchant, A., Billam, T., Wiles, T., Yu, M., Gardiner, S., & Cornish, S. (2013). Controlled formation and reflection of a bright solitary matter-wave. Nature Communications, 4, Article 1865. https://doi.org/10.1038/ncomms2893

Bright solitons are non-dispersive wave solutions, arising in a diverse range of nonlinear, one-dimensional systems, including atomic Bose–Einstein condensates with attractive interactions. In reality, cold-atom experiments can only approach the idea... Read More about Controlled formation and reflection of a bright solitary matter-wave.

Second-order number-conserving description of nonequilibrium dynamics in finite-temperature Bose-Einstein condensates (2013)
Journal Article
Billam, T., Mason, P., & Gardiner, S. (2013). Second-order number-conserving description of nonequilibrium dynamics in finite-temperature Bose-Einstein condensates. Physical Review A, 87(3), Article 033628. https://doi.org/10.1103/physreva.87.033628

While the Gross-Pitaevskii equation is well established as the canonical dynamical description of atomic Bose-Einstein condensates (BECs) at zero temperature, describing the dynamics of BECs at finite temperatures remains a difficult theoretical prob... Read More about Second-order number-conserving description of nonequilibrium dynamics in finite-temperature Bose-Einstein condensates.

Inverse energy cascade in forced two-dimensional quantum turbulence (2013)
Journal Article
Reeves, M., Billam, T., Anderson, B., & Bradley, A. (2013). Inverse energy cascade in forced two-dimensional quantum turbulence. Physical Review Letters, 110(10), Article 104501. https://doi.org/10.1103/physrevlett.110.104501

We demonstrate an inverse energy cascade in a minimal model of forced 2D quantum vortex turbulence. We simulate the Gross-Pitaevskii equation for a moving superfluid subject to forcing by a stationary grid of obstacle potentials, and damping by a sta... Read More about Inverse energy cascade in forced two-dimensional quantum turbulence.

Equilibrium solutions for immiscible two-species Bose-Einstein condensates in perturbed harmonic traps (2013)
Journal Article
Pattinson, R., Billam, T., Gardiner, S., McCarron, D., Cho, H., Cornish, S., …Proukakis, N. (2013). Equilibrium solutions for immiscible two-species Bose-Einstein condensates in perturbed harmonic traps. Physical Review A, 87(1), Article 013625. https://doi.org/10.1103/physreva.87.013625

We investigate the mean-field equilibrium solutions for a two-species immiscible Bose-Einstein condensate confined by a harmonic confinement with additional linear perturbations. We observe a range of equilibrium density structures, including ball an... Read More about Equilibrium solutions for immiscible two-species Bose-Einstein condensates in perturbed harmonic traps.

Scattering bright solitons: Quantum versus mean-field behavior (2012)
Journal Article
Gertjerenken, B., Billam, T. P., Khaykovich, L., & Weiss, C. (2012). Scattering bright solitons: Quantum versus mean-field behavior. Physical Review A, 86(3), Article 033608. https://doi.org/10.1103/physreva.86.033608

We investigate scattering bright solitons off a potential using both analytical and numerical methods. Our paper focuses on low kinetic energies for which differences between the mean-field description via the Gross-Pitaevskii equation (GPE) and the... Read More about Scattering bright solitons: Quantum versus mean-field behavior.

Bright matter-wave soliton collisions at narrow barriers (2012)
Journal Article
Helm, J., Billam, T., & Gardiner, S. (2012). Bright matter-wave soliton collisions at narrow barriers. Physical Review A, 85(5), Article 053621. https://doi.org/10.1103/physreva.85.053621

We study fast-moving bright solitons in the focusing nonlinear Schrödinger equation perturbed by a narrow Gaussian potential barrier. In particular, we present a general and comprehensive analysis of the case where two fast-moving bright solitons col... Read More about Bright matter-wave soliton collisions at narrow barriers.

Coherence and instability in a driven Bose–Einstein condensate: a fully dynamical number-conserving approach (2012)
Journal Article
Billam, T., & Gardiner, S. (2012). Coherence and instability in a driven Bose–Einstein condensate: a fully dynamical number-conserving approach. New Journal of Physics, 14, Article 013038. https://doi.org/10.1088/1367-2630/14/1/013038

We consider a Bose–Einstein condensate driven by periodic delta-kicks. In contrast to first-order descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate depletion... Read More about Coherence and instability in a driven Bose–Einstein condensate: a fully dynamical number-conserving approach.

Variational determination of approximate bright matter-wave soliton solutions in anisotropic traps (2012)
Journal Article
Billam, T., Wrathmall, S., & Gardiner, S. (2012). Variational determination of approximate bright matter-wave soliton solutions in anisotropic traps. Physical Review A, 85(1), Article 013627. https://doi.org/10.1103/physreva.85.013627

We consider the ground state of an attractively interacting atomic Bose-Einstein condensate in a prolate, cylindrically symmetric harmonic trap. If a true quasi-one-dimensional limit is realized, then for sufficiently weak axial trapping this ground... Read More about Variational determination of approximate bright matter-wave soliton solutions in anisotropic traps.

Realizing bright-matter-wave-soliton collisions with controlled relative phase (2011)
Journal Article
Billam, T., Cornish, S., & Gardiner, S. (2011). Realizing bright-matter-wave-soliton collisions with controlled relative phase. Physical Review A, 83(4), Article 041602. https://doi.org/10.1103/physreva.83.041602

We propose a method to split the ground state of an attractively interacting atomic Bose-Einstein condensate into two bright solitary waves with controlled relative phase and velocity. We analyze the stability of these waves against their subsequent... Read More about Realizing bright-matter-wave-soliton collisions with controlled relative phase.

Quantum resonances in the delta-kicked harmonic oscillator (2009)
Journal Article
Billam, T., & Gardiner, S. (2009). Quantum resonances in the delta-kicked harmonic oscillator. Physical Review A, 80(2), https://doi.org/10.1103/physreva.80.023414

Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator and present a theoretical discussion of the quantum resonances that co... Read More about Quantum resonances in the delta-kicked harmonic oscillator.