Numerically exact quantum dynamics of bosons with time-dependent interactions of harmonic type

Abstract

The exactly solvable quantum many-particle model with harmonic one-and two-particle interaction terms is extended to include time dependency. We show that when the external trap potential and interparticle interaction have a time dependency, the numerically exact solutions of the corresponding time-dependent many-boson Schrödinger equation are still available. We use these exact solutions to benchmark the recently developed multiconfigurational time-dependent Hartree method for bosons (MCTDHB) [Phys. Rev. Lett. 99, 030402 (2007); Phys. Rev. A 77, 033613 (2008)]. In particular, we benchmark the MCTDHB method for (i) the ground state; (ii) the breathing many-body dynamics activated by a quench scenario where the interparticle interaction strength is suddenly turned on to a finite value; (iii) the nonequilibrium dynamic for driven scenarios where both the trap-and interparticle-interaction potentials are time-dependent. Excellent convergence of the ground state and dynamics is demonstrated. The great relevance of the self-consistency and time adaptivity, which are the intrinsic features of the MCTDHB method, is demonstrated by contrasting the MCTDHB predictions and those obtained within the standard full configuration interaction method spanning a Fock space of the same size, but utilizing as one-particle basis set the fixed-shape eigenstates of the one-particle potential. Connections of the model's results to ultracold Bose-Einstein condensed systems are addressed.

Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation

“…The MCTDHB method has been shown to produce accurate many-body solutions in various applications [19,[40][41][42][43][44], and is well documented in the literature [45,46]. Until recently, MCTDHB has been applied to one-dimensional systems.…”

Controlling the velocities and the number of emitted particles in the tunneling to open space dynamics

“…The N +M −1 N linear equations of motion for the coefficients are coupled to the M non-linear integrodifferential equations of motion of the orbitals. Since the derivation is variational and the basis used is a formally complete set in the limit M → ∞, convergence with respect to the number of orbitals implies the convergence to the exact solution of TDSE for the problem under consideration [41]. The use of time-adaptive orbitals is of key importance for the achievement of numerical exactness: a much smaller number of time-adaptive orbitals is needed to achieve the same level of accuracy as compared to the number of basis functions in a static, time-independent basis [41].…”

“…The key to MCTDHB's efficiency in solving Eq. (1) exactly numerically [41] lies in the usage of a time-dependent, variationally optimized many-body basis set. The introduction of the method and computational details are deferred to Appendix A for brevity.…”

“…[41]. The method relies on expanding the wavefunction with multiple, time-dependent configurations | n; t weighted with time-dependent coefficients C n (t): |Ψ = n C n (t)| n; t .…”

“…[30] used a novel quantum many-boson method, the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) [37,40]. MCTDHB provides the means to solve the time-dependent many-boson Schrödinger equation numerically exact for a wide range of problems, see, e.g., [30,[41][42][43][44].…”