Quantum dynamical response of ultracold few-boson ensembles in finite optical lattices to multiple interaction quenches

The correlated nonequilibrium quantum dynamics following a multiple interaction quench protocol for few-bosonic ensembles confined in finite optical lattices is investigated. The quenches give rise to an interwell tunneling and excite the cradle and a breathing mode. Several tunneling pathways open during the time interval of increased interactions, while only a few occur when the system is quenched back to its original interaction strength. The cradle mode, however, persists during and in between the quenches, while the breathing mode possesses distinct frequencies. The occupation of excited bands is explored in detail revealing a monotonic behavior with increasing quench amplitude and a nonlinear dependence on the duration of the application of the quenched interaction strength. Finally, a periodic population transfer between momenta for quenches of increasing interaction is observed, with a power-law frequency dependence on the quench amplitude. Our results open the possibility to dynamically manipulate various excited modes of the bosonic system.

Figure 1

Sketch of a triple pulse MIQ protocol, $g\left(t\right)$, with pulse width $\tau$. $g_{\mathrm{in}}$ ($g_f$) refer to the pre-(post-) quenched interaction strength and $\delta g=g_f-g_{\mathrm{in}}$ is the pulse or quench amplitude.

Figure 2

As a function of the quench amplitude $\delta g$ are shown the following: (a),(b) fidelity evolution for a single quench and a double pulse ($n_p=2$) MIQ, respectively, and (c),(d) the corresponding fidelity spectra. Parameter values are $g_{\mathrm{in}}=0.1,\tau =50$, and $N=4$.

Figure 3

As a function of the quench amplitude $\delta g$ are shown the following: (a),(b) spectrum of the intrawell asymmetry $\mathrm{\Delta }{\rho }_L\left(\omega \right)$ following a single quench and a double pulse ($n_p=2$) MIQ, respectively. Spectrum of ${\sigma }_M^2\left(\omega \right)$ following (c) a single quench and (d) a double pulse MIQ protocol. Parameter values are $g_{\mathrm{in}}=0.1,\tau =50$, and $N=4$.

Figure 4

Time evolution of the probability $P_N^{\left(0\right)}(t;\tau =25)$ to find all four bosons within the ground band with respect to the quench amplitude $\delta g$ following a five pulse ($n_p=5$) MIQ protocol. (a),(b) $P_N^{\left(0\right)}(t;\tau =25)$ for varying $\delta g$ including correlations and for the MF approximation, respectively. The insets (${\mathrm{a}}_1$),(${\mathrm{b}}_1$) show $P_N^{\left(0\right)}(t;\tau =25)$ of (a),(b), respectively, only within the second pulse. (c) Profiles of $P_N^{\left(0\right)}(t;\tau =25)$ for different $\delta g$ (see legend). For better visibility of the oscillatory behavior during the positive half of the second pulse we show in the inset $P_N^{\left(0\right)}(45<t<80;\tau =25)$. The system consists of four initially weakly interacting, $g_{\mathrm{in}}=0.1$, bosons confined in a triple well.

Figure 5

(a) Time evolution of the probability to find all four bosons within the ground band $P_N^{\left(0\right)}(t;\tau )$ for varying pulse width $\tau$ following a five pulse $n_p=5$ MIQ protocol with $\delta g=1.0$. (b) The corresponding profiles of $P_N^{\left(0\right)}(t;\tau )$ for different values of $\tau$ (see legend). (c),(d) The same as above but for $\delta g=2.9$. The insets (${\mathrm{a}}_1$),(${\mathrm{c}}_1$) show $P_N^{\left(0\right)}(40<t<120;\tau =25)$ of (a),(c). The system consists of four initially weakly interacting $g_{\mathrm{in}}=0.1$ bosons in a triple well.

Figure 6

Time evolution of the probability to find one or two bosons in higher bands (see legend) following a five pulse MIQ protocol with fixed pulse width $\tau =25.0$ and varying amplitude (a) $\delta g=1.0$, (b) $\delta g=2.5$, and (c) $\delta g=4.0$. (d),(e),(f) The same as above but for fixed quench amplitude $\delta g=4.0$ and varying pulse width (d) $\tau =2$, (e) $\tau =8.5$, and (f) $\tau =10$. The system consists of four bosons initially prepared in the ground state with $g_{\mathrm{in}}=0.1$ of a triple well.

Figure 7

(a) Fidelity evolution with varying $\delta g$, employing a five pulse $n_p=5$ MIQ protocol with $\tau =50$. The inset (${\mathrm{a}}_1$) depicts $F(t;\tau =50)$ of (a) only within the duration of the second pulse. (b) The same as in (a) but with varying pulse width $\tau$ and $\delta g=2.9$. The inset (${\mathrm{b}}_1$) shows $F(80<t<250;\tau )$ of (b). The system consists of three bosons confined in an eight well potential.

Figure 8

Momentum distribution as a function of time for (a) $\delta g=1.0$ and (b) $\delta g=2.9$. (c) The same as (a) but within the MF approximation. The horizontal axis represents the lattice momenta in units of the inverse lattice vector $k_0=\pi /l$. The system consists of an eight well lattice potential with five bosons being subjected to a five pulse ($n_p=5$) MIQ characterized by $\tau =25$. (d) Dominant oscillation frequency ${\omega }_1$ that appears in the momentum distribution for varying quench amplitude $\delta g$. Different curves correspond to different initial conditions, approximations, and system size (see legend).

Figure 9

$F(t;\tau =25)$ for a varying number of SPFs (see legend) following a five pulse ($n_p=5$) MIQ with (a) $\delta g=1$ and (b) $\delta g=3.0$. For better visibility of the evolution within the positive halves of the MIQ protocol, we show in the insets $F(t;\tau =25)$ only during the third pulse.