Electric-field-induced helium-helium resonances

The tunability of the helium-helium interaction through an external electric field is investigated. For a static external field, electric-field-induced resonances and associated electric-field-induced bound states are calculated for the ${}^4\mathrm{He}\text{−}{}^4\mathrm{He},{}^3\mathrm{He}\text{−}{}^4\mathrm{He}$, and ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}$ systems. Qualitative agreement is found with the literature for the ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ and ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}$ systems [E. Nielsen, D. V. Fedorov, and A. S. Jensen, Phys. Rev. Lett. 82, 2844 (1999)]. The implications of the predicted electric-field-induced resonances for ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}$ on the wave packet dynamics, initiated by intense laser pulses, are investigated. Our results are expected to guide next generation experiments.

Figure 1

Polarizabilities as a function of the internuclear distance $r$ (note the logarithmic scale of the horizontal axis). The solid and dotted lines show ${\alpha }_{\perp }$ and ${\alpha }_{\parallel }$ using the ab initio data from Ref. [20]. The dash-dotted and dashed lines show ${\alpha }_{\perp }$ and ${\alpha }_{\parallel }$ using the analytical polarizabilities [see Eqs. (2) and (3)]. The constant contribution of $2{\alpha }_0$ is not included in the plots.

Figure 2

Binding energy $E_{\mathrm{bind}}$ for (a) ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}$, (b) ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$, and (c) ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}$ as a function of the field strength ${\epsilon }_{0,\text{S}}$. The solid lines show the binding energy of states that are even in $z$ while the dashed lines show the binding energy of states that are odd in $z$. Note that the binding energy is shown on a logarithmic scale that covers five orders of magnitude.

Figure 3

Scattering lengths for (a) ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}$, (b) and (c) ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$, and (d) and (e) ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}$ as a function of the field strength ${\epsilon }_{0,\text{S}}$. The solid lines in (a), (b), and (d) show the scattering length $a_{0,0}$ while the dashed lines in (c) and (e) show the scattering length $a_{1,1}$. The narrow resonance at ${\epsilon }_{0,\text{S}}\approx 0.11$ a.u. in (a) has notable $d$-wave admixture. The resonances in the $(l,l^{\prime })=(1,1)$ channel [see (c) and (e)] are extremely narrow. The solid circles in (c) and (e) show $a_{1,1}$ as predicted by the Born approximation; the Born approximation reproduces the “background value” very well but does not capture the resonances (the scattering lengths in the Born approximation are directly proportional to $-|{\epsilon }_{0,\text{S}}{|}^2)$.

Figure 4

Enlargement of the scattering length $a_{1,1}$ for ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ in the vicinity of a resonance. The data and symbol/line styles are the same as in Fig. 3.

Figure 5

Alignment signal for stretched Gaussian laser pulse with ${\epsilon }_{0,\text{G}}=0.0843949$ a.u. and $\tau =311$ fs. Results are shown for four different hold times: (a) and (e) $t_{\text{hold}}=0.5$ ps, (b) and (f) $t_{\text{hold}}=2$ ps, (c) and (g) $t_{\text{hold}}=4$ ps, and (d) and (h) $t_{\text{hold}}=8$ ps. (a)–(d) Contour plots of the alignment signal $C_2(r,t)$. A spherically symmetric wave packet would yield an alignment signal of $1/3$. The dashed, dotted, dash-dotted, and solid lines in (e)–(h) show cuts of $C_2(r,t)$ for $r=3$ Å = 5.669 a.u., $r=5$ Å = 9.449 a.u., $r=10$ Å = 18.90 a.u., and $r=20$ Å = 37.79 a.u., respectively. The curves are offset from each other for ease of readability.

Figure 6

Same as Fig. 5 but for a larger peak field strength, namely for ${\epsilon }_{0,\text{G}}=0.11$ a.u.