Dynamic dipole polarizabilities for the low-lying triplet states of helium

The dynamic dipole polarizabilities for the four lowest triplet states ($2{}^{3}S, 3{}^{3}S, 2{}^{3}P$, and $3{}^{3}P$) of helium are calculated using the $B$-spline configuration interaction method. Present values of the static dipole polarizabilities in the length, velocity, and acceleration gauges are in good agreement with the best Hylleraas results. Also the tune-out wavelengths in the range 400 nm–4.2 $\mu \mathrm{m}$ for the four lowest triplet states are identified, and the magic wavelengths in the range 460 nm–3.5 $\mu \mathrm{m}$ for the $2{}^{3}S\to 3{}^{3}S, 2{}^{3}S\to 2{}^{3}P$, and $2{}^{3}S\to 3{}^{3}P$ transitions are determined. We show that the tune-out wavelength of $2{}^{3}S$ state is $413.03828\left(3\right)$ nm, which corroborates the value of Mitroy and Tang [Phys. Rev. A 88, 052515 (2013)], and the magic wavelength around 1066 nm for the $2{}^{3}S\to 3{}^{3}P$ transition can be expected for precision measurement to determine the ratio of transition matrix elements $(2{}^{3}S\to 2{}^{3}P)/(3{}^{3}P\to 6{}^{3}S)$.

Figure 1

Dynamic dipole polarizabilities (in a.u.) of helium for the photon energy $0.035\le \omega \le 0.06$ a.u. The solid black line denotes the dynamic polarizabilities for $2{}^{3}S$ state, and the dashed blue line represents the dynamic polarizabilities for $3{}^{3}S$ state. The crossing points denoted as solid magenta circle are the tune-out wavelengths, and the crossing points marked as blank red circle are the magic wavelengths. The vertical lines are the resonance transition positions, and the green line is a horizontal zero line.

Figure 2

Dynamic dipole polarizabilities (in a.u.) of helium for the photon energy $0.06\le \omega \le 0.10$ a.u. The solid black line denotes the dynamic polarizabilities for $2{}^{3}S$ state, and the dashed blue line represents the dynamic polarizabilities for $2{}^{3}P(M=0)$ state. The crossing points denoted as solid magenta circle are the tune-out wavelengths, and the crossing points marked as blank red circle are the magic wavelengths. The vertical lines are the resonance transition positions, and the green line is a horizontal zero line.

Figure 3

Dynamic dipole polarizabilities (in a.u.) of helium for the photon energy $0.06\le \omega \le 0.10$ a.u. The solid black line denotes the dynamic polarizabilities for $2{}^{3}S$ state, and the dashed blue line represents the dynamic polarizabilities for $2{}^{3}P\left(\right|M|=1)$ state. The crossing points denoted as solid magenta circle are the tune-out wavelengths, and the crossing points marked as blank red circle are the magic wavelengths. The vertical lines are the resonance transition positions, and the green line is a horizontal zero line.

Figure 4

Dynamic dipole polarizabilities (in a.u.) of helium for the photon energy $0.02\le \omega \le 0.04$ a.u. The solid black line denotes the dynamic polarizabilities for $2{}^{3}S$ state, and the dashed blue line represents the dynamic polarizabilities for $3{}^{3}P(M=0)$ state. The crossing points denoted as solid magenta circle are the tune-out wavelengths, and the crossing points marked as blank red circle are the magic wavelengths. The vertical lines are the resonance transition positions, and the green line is a horizontal zero line.

Figure 5

Dynamic dipole polarizabilities (in a.u.) of helium for the photon energy $0.04\le \omega \le 0.05$ a.u. The solid black line denotes the dynamic polarizabilities for $2{}^{3}S$ state, and the dashed blue line represents the dynamic polarizabilities for $3{}^{3}P(M=0)$ state. The crossing points denoted as solid magenta circle are the tune-out wavelengths, and the crossing points marked as blank red circle are the magic wavelengths. The vertical lines are the resonance transition positions, and the green line is a horizontal zero line.

Figure 6

Dynamic dipole polarizabilities (in a.u.) of helium for the photon energy $0.01\le \omega \le 0.05$ a.u. The solid black line denotes the dynamic polarizabilities for $2{}^{3}S$ state, and the dashed blue line represents the dynamic polarizabilities for $3{}^{3}P\left(\right|M|=1)$ state. The crossing points denoted as solid magenta circle are the tune-out wavelengths, and the crossing points marked as blank red circle are the magic wavelengths. The vertical lines are the resonance transition positions, and the green line is a horizontal zero line.