Controlled excitation and resonant acceleration of ultracold few-boson systems by driven interactions in a harmonic trap

We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.

Figure 1

(a) Three lowest eigenenergies of the symmetric (0, 2, 4) and antisymmetric (1, 3, 5) eigenstates of the relative motion for two particles with increasing interaction strength $g$. (b) The energy difference between the eigenstates of the relative motion ${\epsilon }_2-{\epsilon }_0$ and ${\epsilon }_4-{\epsilon }_2$ with increasing $g$.

Figure 2

Population of instantaneous eigenstates with time variation, for (a) $g_0=0.0$, $\Delta g=0.05$, $\omega =0.99$, (b) $g_0=0.0$, $\Delta g=0.05$, $\omega =0.997$, (c) $g_0=2.0$, $\Delta g=0.1$, $\omega =0.925$. Profile of the resonances via the minimal occupation of the ground state with varying driving frequency. Several cases are shown for different values of $g_0$ and $\Delta g$.

Figure 3

Occupation of adiabatic eigenstates of Hamiltonian for $g_0=0$, $\Delta g=0.5$ close to the second and the first resonance (a) $\omega =1.98$ and (b) $\omega =0.998$.

Figure 4

Time evolution of the expectation value of the energy for $\Delta g=20.0$, $g_0=0$ and several frequencies close to resonance. Acceleration shown close to the resonant frequency.

Figure 5

Floquet eigenspectrum for (a) increasing driving frequency $\omega$ with $g_0=0.5$ $\Delta g=0.5$, (b) increasing initial interaction strength $g_0$ for the resonant frequency $\omega =1$ and $\Delta g=0.5$.

Figure 6

Lowest eigenenergies with increasing interaction $g$ for (a) three and (b) four bosons.

Figure 7

(a) Population of instantaneous eigenstates for three particles with $g_0=2.0$, $\Delta g=0.05$ and $\omega =0.9$. (b) Population of the instantaneous ground state for different numbers of particles $N=2,3,4$, $g_0=0.0$, $\Delta g=1.0$, and $\omega =0.6$.

Figure 8

One-body density for the case of three particles as in Fig. 7 for several time snapshots.