Manifestation of quantum resonances and antiresonances in a finite-temperature dilute atomic gas

We investigate the effect of temperature on resonant and antiresonant dynamics in a dilute atomic gas kicked periodically by a standing-wave laser field. Our numerical calculations are based on a Monte Carlo method for an incoherent mixture of noninteracting plane waves, and show that the atomic dynamics are highly sensitive to the initial momentum width of the gas. We explain this sensitivity by examining the time evolution of individual atomic center-of-mass momentum eigenstates with varying quasimomentum, and we determine analytic expressions for the evolution of the second-order momentum moment to illustrate the range of behaviors.

Figure 1

(Color online) Momentum distributions [(a), (c), (e)] and corresponding second-order momentum moments [(b), (d), (f)] of a $\delta$-kicked particle. In each case the initial condition is a zero-momentum eigenstate. Parameters are $\mathcal{N}=1$, ${\varphi }_d=0.8\pi$, and $T=$ (a), (b) $T_T∕2$, (c), (d) $(1+\sqrt{5})T_T∕2$, and (e), (f) $T_T$. The solid lines in (b), (d), and (f) are analytic results from Eqs. (54, 16) (with $⟨{\widehat{p}}^2{⟩}_0=0$), and (50), respectively.

Figure 2

(Color online) Momentum distributions [(a), (c), (e)] and corresponding second-order momentum moments [(b), (d), (f)] of a $\delta$-kicked particle. In each case the initial atomic momentum distribution is given by Eq. (36). Parameters are $\mathcal{N}=10000$, ${\varphi }_d=0.8\pi$, $w=2.5$, and $T=\left(\mathrm{a}\right),\left(\mathrm{b}\right)$ $T_T∕2$, (c), (d) $(1+\sqrt{5})T_T∕2$, and (e), (f) $T_T$. The solid lines in (b), (d), and (f) correspond to the linear result (16).

Figure 3

(Color online) $⟨⟨{\widehat{p}}^2⟩{⟩}_n^{1∕2}$ of a $\delta$-kicked particle initially in the plane-wave state $\mid \beta ⟩$. Parameters are $\mathcal{N}=1$, ${\varphi }_d=0.8\pi$, and $T=$ (a) $T_T∕2$ and (b) $T_T$.

Figure 4

(Color online) $⟨⟨{\widehat{p}}^2⟩{⟩}_n^{1∕2}$ of a $\delta$-kicked particle initially in the plane-wave state $\mid p⟩$. Parameters are $\mathcal{N}=1$, ${\varphi }_d=0.8\pi$, and $T=T_T∕2$.

Figure 5

(Color online) $⟨⟨{\widehat{p}}^2⟩{⟩}_n^{1∕2}$ of a $\delta$-kicked particle initially in the plane-wave state $\mid p⟩$. Parameters are $\mathcal{N}=1$, ${\varphi }_d=0.8\pi$, and $T=T_T$.

Figure 6

(Color online) Second-order momentum moment of a $\delta$-kicked atom cloud. The initial state is a Gaussian momentum distribution with standard deviation $w=(\times )1∕128$, $(엯)$ $1∕32$, and $(+)$ $1∕8$. Parameters are $\mathcal{N}=10000$, ${\varphi }_d=0.8\pi$, and $T=T_T$. The solid lines are analytic results for square distributions [see Eq. (52)], chosen with an initial standard deviation in agreement with the corresponding Gaussian case. The upper dotted line corresponds to the quadratic growth (50), and the lower dotted line corresponds to the classical linear growth (16), taking $⟨p^2{⟩}_0=0$. The vertical dashed lines indicate $n=n_R$ [see Eq. (51)].

Figure 7

(Color online) Second-order momentum moment of a $\delta$-kicked atom cloud. The initial state is a Gaussian momentum distribution with standard deviation (a) $w=$ $(◻)$ $0$, $(\times )$ $1∕128$, and $(엯)$ $1∕32$, and (b) $w=(+)1∕8$, $(*)$ $1∕4$, $(▷)$ $1∕2$, and $(◇)$ $2.5$. Parameters are $\mathcal{N}=10000$, ${\varphi }_d=0.8\pi$, and $T=T_T∕2$. In (a) the solid lines are given by Eq. (56) and the vertical dashed lines indicate $n=n_A$ [see Eq. (55)]. The solid lines in (b) are given by Eq. (16).