Recoil momentum effects in quantum processes induced by twisted photons

We consider physical processes caused by the twisted photons for a range of energy scales, including optical (eV) and nuclear (MeV). We demonstrate that in order to satisfy angular momentum conservation, absorption of a twisted photon leads to a transverse recoil of the final particle or a system of particles, leading to an increased threshold energy requirement for the reaction to proceed. Modification of the threshold energy is predicted for photoabsorption on cold trapped ions of ${}^{40}{\mathrm{Ca}}^{+}$, along with emerging new transverse-motion sidebands, and for photodisintegration of deuterium.

Figure 1

Twisted photon's helical wavefront (a plane of constant phase for a twisted photon) and an atomic target located at an impact parameter $b$ from the photon's vortex axis (or phase singularity), here chosen to be the $z$ axis. The momenta $p_T$ and $p_z$ show transverse recoil and longitudinal recoil, respectively.

Figure 2

Mean angular momentum transfer ${\langle {\ell }_z\rangle }_{\mathrm{c}.\mathrm{m}.}$, Eq. (1), along the beam direction passed by twisted light of total angular momentum $m_{\gamma }$ to an atom's c.m. motion for (a) $S\to P$ transitions, (b) $S\to D$ transitions, and (c) $S\to F$ transitions. For all cases, $\mathrm{\Lambda }=+1$ where $\mathrm{\Lambda }$ is (paraxially) the spin angular momentum of the twisted photon. The horizontal axis shows atom's position $b$ with respect to the vortex center measured in units of light's wavelength. The figures are for pitch angle [3, 18] 0.1 radian. See text for further comments.

Figure 3

Same as Fig. 2, but for $\mathrm{\Lambda }=-1$.

Figure 4

Ratio of transverse to longitudinal recoil momentum of a free atomic target after absorbing a twisted photon in $S\to P$ transition. (a) $S\to D$ transition (b) and $S\to F$ transition. For all cases, $\mathrm{\Lambda }=+1$, i.e., the spin of a twisted photon is aligned with its orbital AM. The horizontal axis shows atom's position $b$.

Figure 5

Same as Fig. 4, but for $\mathrm{\Lambda }=-1$.

Figure 6

Recoil energy as a function of impact parameter for longitudinal recoil and transverse recoil at different values of total AM of the absorbed photon, $\mathrm{\Lambda }=1$, for $\lambda$ = 397 nm $E1S\to P$ transition on ${}^{40}\mathrm{Ca}^{+}$ ion.

Figure 7

The black dotted curve shows the probability $P_D\left(t\right)$ for an $S_{1/2}\to D_{5/2}$ transition, specifically for $m_{\gamma }=-2, m_i=-1/2, m_f=-3/2$, and a measurement time of $26\mu \mathrm{s}$ (the same as for the data for the same transition in [6]). Also shown is the transition probability multiplied by the further probability that the atom is put into an excited state in its trapping potential by the linear transverse kick. The latter is shown for two cases: a red dashed line for an atom with an almost pointlike spatial distribution, and a blue solid line for a realistic case in which an atom is spread over some region in a harmonic oscillator potential, in this case, with a 10 nm RMS spread. In this plot, $b$ is the displacement of the target atom location leftward or rightward relative to the beam axis, along a horizontal direction.