Shortcuts to adiabaticity for growing condensates

Abstract

We investigate fast frictionless expansion for growing Bose–Einstein condensates described by the Gross–Pitaevskii gain equation. We show that fast frictionless expansion can be generalized to a condensate continuously replenished by pumping from the reservoir. We apply our formalism to the harmonically trapped condensate and an optical lattice.

Shortcuts to Adiabaticity

“…Decreasing the potential depth as V (t) = V 0 /Λ 2 (t), and making the first and second derivatives of Λ vanish at the boundary times guarantee a frictionless expansion. In Ozcakmakli and Yuce (2012) the results are extended to a continuously replenished BEC in a harmonic trap or in an optical lattice. Lau and James (2012) propose inverse engineering of the trap frequencies based on the Lewis-Riesenfeld invariants as part of the elementary operations necessary to implement a universal bosonic simulator using ions in separate traps.…”

“…1 There the Lewis-Riesenfeld invariants were used to inverse engineer the time dependence of a harmonic oscillator frequency between predetermined initial and final values so as to avoid final excitations. That paper and its companion on Bose-Einstein condensates (Muga et al, 2009) have indeed triggered a surge of activity, not only for harmonic expansions (Chen and Muga, 2010;Muga et al, 2010;Stefanatos et al, 2010;Schaff et al, 2010Schaff et al, , 2011adel Campo, 2011a;Schaff et al, 2011b;Stefanatos et al, 2011;Torrontegui et al, 2012c;Fasihi et al, 2012;Torrontegui et al, 2012a;del Campo and Boshier, 2012;Stefanatos and Li, 2012), but for atom transport (Torrontegui et al, 2011(Torrontegui et al, , 2012dChen et al, 2011b;Bowler et al, 2012), quantum computing (Sarandy et al, 2011), quantum simulations (Lau and James, 2012), optical lattice expansions (Yuce, 2012;Ozcakmakli and Yuce, 2012), wavepacket splitting (Torrontegui et al, 2012b), internal state control (Chen et al, 2011a;Ibáñez et al, 2011;Ruschhaupt et al, 2012;Ban et al, 2012;Ibáñez et al, 2012a;Güngördü et al, 2012), many-body state engineering (del Campo, 2011b;del Campo and Boshier, 2012;Juliá-Díaz et al, 2012), and other applications such as sympathetic cooling of atomic mixtures (Choi, Onofrio and Sundaram, 2011;Choi et al, 2012), or cooling of nanomechanical resonators ...…”

Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving

“…We close this section by mentioning that other non-linear processes that can be assisted by CD include the (meanfield) growth dynamics of a Bose-Einstein condensate [69]. Nonetheless, phase fluctuations in the newborn condensate are expected to result in the formation of solitons [70] or vortices [71], depending in the dimensionality, as dictated by the Kibble-Zurek mechanism [72,73].…”

Feshbach engine in the Thomas-Fermi regime

“…The chemical potential μ is determined via the normalization condition. Considering the TF limit in the scaling GPE (6) and choosing scaling functions as [35] a…”

“…Considering the TF limit in the scaling GPE Eq. ( 6) and choosing scaling functions as [35] ä + ω 2 a = ω 2 g(t) gi…”